DFI JOURNAL - Deep Foundations Institute · DFI JOURNAL The Journal of the ... This paper studies the effect of voids ... load bearing capacity of drilled shafts with anomalies under

Vol. 6, No. 2 December 2012

DFI JOURNALThe Journal of the Deep Foundations Institute

PAPERS:

Behavior of Axially Loaded Drilled Shaft Foundations with Symmetric Voids Outside and Inside the Caging – Masood Hajali & Caesar Abishdid [3]

Uplift Performance of Multi-Helix Anchors in Desiccated Clay – Armin W. Stuedlein & Jesi Young [13]

Strain Distributions in Full-Scale Energy Foundations(DFI Young Professor Paper Competition 2012)– John S. McCartney & Kyle D. Murphy [26]

Performance-Based Reliability Design for Deep Foundations Using Monte Carlo Statistical Methods (DFI Student Paper Competition 2012)– Haijian Fan & Robert Liang [39]

Reliability-Based Optimization Design for Drilled Shafts/Slope System (DFI Student Paper Competition 2012)– Lin Li & Robert Liang [48]

Deep Foundations Institute is the Industry Association of Individuals and Organizations Dedicated to Quality and Economy in the Design and Construction of Deep Foundations.

DFI JOURNAL Vol. 6 No. 2 December 2012 [1]

From the Editors and Publisher 2012 DFI Board of TrusteesPresident:James A. MorrisonKiewit Engineering Co.Omaha, NE USA

Vice President:Patrick BerminghamBermingham Foundation SolutionsHamilton, ON Canada

Secretary:John R. WolosickHayward Baker Inc.Alpharetta, GA USA

Treasurer:Robert B. BittnerBittner-Shen Consulting Engineers, Inc.Portland, OR USA

Immediate Past President:Rudolph P. FrizziLangan Engineering & Environmental ServicesElmwood Park, NJ USA

Other Trustees:David BorgerSkyline Steel LLCParsippany, NJ USA

Maurice BottiauFranki Foundations Group BelgiumSaintes, Belgium

Dan BrownDan Brown and Associates, PLLCSequatchie, TN USA

Gianfranco Di CiccoGDConsulting LLCLake Worth, FL USA

Bernard H. HertleinAECOM Technical Services Inc.Vernon Hills, IL USA

Matthew JanesIsherwood AssociatesBurnaby, BC Canada

James O. JohnsonCondon-Johnson & Associates, Inc.Oakland, CA USA

Douglas KellerRichard Goettle, Inc.Cincinnati, OH USA

Samuel J. KosaMonotube Pile CorporationCanton, OH USA

Kirk A. McIntoshAMEC E&I, Inc.Jacksonville, FL USA

Raymond J. PolettoMueser Rutledge Consulting EngineersNew York, NY USA

Arturo L. Ressi di CerviaKiewit Infrastructure GroupWoodcliff Lake, NJ USA

Michael H. WysockeyThatcher Engineering Corp.Chicago, IL USA

Journal PublisherManuel A. Fine, B.A.Sc, P.Eng

Journal EditorsAli Porbaha, Ph.D., P.E. Central Valley Flood Protection Board Sacramento, CA, USADan A. Brown, Ph.D. Dan Brown and Associates, Sequatchie, TN, USAZia Zafir, Ph.D., P.E. Kleinfelder Sacramento, CA, USA

Associate EditorsLance A. Roberts, Ph.D., P.E.RESPEC Consulting & ServicesRapid City, SD USAThomas Weaver, Ph.D., P.E.Nuclear Regulatory CommissionRockville, MD USA

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Mission/Scope The Journal of the Deep Foundations Institute publishes practice-oriented, high quality papers related to the broad area of “Deep Foundations Engineering”. Papers are welcome on topics of interest to the geo-professional community related to, all systems designed and constructed for the support of heavy structures and excavations, but not limited to, different piling systems, drilled shafts, ground modification geosystems, soil nailing and anchors. Authors are also encouraged to submit papers on new and emerging topics related to innovative construction technologies, marine foundations, innovative retaining systems, cutoff wall systems, and seismic retrofit. Case histories, state of the practice reviews, and innovative applications are particularly welcomed and encouraged.

DFI JOURNAL

Three of the papers in the current edition are papers submitted in response to the 2012 DFI Young Professor or Student Paper Competitions. The winners and runners-up in each category are given the option of publication in the Proceedings of the Annual Conference or submittal for publication in the DFI Journal, where the papers are subjected to a more rigorous review process. The other two papers in this edition also came from academic sources. We are happy to see academics undertaking studies on subjects relating to application of geotechnical design and to construction issues. There was some difficulty on obtaining reviewers who felt comfortable in reviewing some of these papers, resulting in a delay in completing this edition. There is no doubt that the review process resulted in changes to the papers that improved the end product.

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Behavior of Axially Loaded Drilled Shaft Foundations with Symmetric Voids Outside and Inside the CagingMasood Hajali, Ph.D., Candidate, Department of Civil and Environmental Engineering, Florida

International University, Miami, FL, USA; mhaja002@fi u.edu

Caesar Abishdid, Director of External Programs, College of Engineering and Computing, Florida

International University, Miami, FL, USA; abishdid@fi u.edu

ABSTRACTDrilled shaft foundations usually carry very high design loads, and often serve as a single load-carrying unit. These conditions have created a need for a high-level of quality assurance during and after construction process. During the construction process, different types of anomalies such as necking, soft-bottom gap at the base, voids and soil intrusions can occur. Anomalies throughout the length can significantly reduce the axial load capacity of the drilled shaft. This paper studies the effect of voids inside and outside the reinforcement cage on the strength and structural capacity of drilled shafts. The objective of this research is to quantify the extent of loss in axial strength and stiffness of drilled shafts due to presence of three different types of symmetric voids throughout their lengths; also, to evaluate the potential for buckling of longitudinal bars within the various types of voids. To complete these objectives, fifteen large-scale drilled shaft samples were built and tested using a hydraulic actuator at the Florida International University’s (FIU) Titan America Structures and Construction Testing (TASCT) laboratory. During the static load test, load-displacement curves were recorded by the data acquisition system (MegaDAC). Results show that the presence of symmetric voids outside the rebar cage (void Type C) that occupy 40% of the cross sectional area of the drilled shafts cause 27% reduction in the axial capacity, while the symmetric voids that penetrate inside the core (void Type B) cause 47% reduction in the axial capacity. The findings indicate that the voids Type B decrease the capacity and stiffness of drilled shafts more than other types due to the resulting inadequate confinement of the concrete and reinforcement.

INTRODUCTIONDrilled shaft foundations are constructed by placing fluid concrete and a steel rebar cage in drilled holes in the ground. Advances in construction technology of drilled shaft foundations in the last ten years caused them to become an economic replacement to group piles and driven piles. A reason for this trend is the capability of using nondestructive testing (NDT) as an essential component of deep foundation construction for quality assurance. Several NDT techniques that can be used to detect anomalies are described in detail in Wightman et al (2004) and Haramy et al., (2007). Cross-hole sonic logging (CSL) (Barker et al., 1991 and O’Neill and Reese, 1999), sonic mobility (Olson 1998), cross-hole tomographic (Hollema and Olson 2002), Impulse echo testing, and gamma-gamma testing are all NDT techniques that are used in the field (Hertlein and Davis 2006). Iskander, et al. (2003) concluded that down hole methods such as CSL and cross hole tomography are generally able to identify defects exceeding

10% of the cross sectional area in size. NDT methods mentioned above can detect different types of anomalies such as necking, bulging, soft bottom, voids, lack of concrete cover over reinforcement or cavity created during concrete placement. Some previous works evaluated the effects of single voids in one side of the shaft on the shaft axial capacity. However, they neither consider the various percentages of voids as covered in this study, nor did they compare the results with intact specimen, both experimentally and analytically.

Iskander, et al. (2003) studied drilled shafts constructed with built-in defects located in various areas within the shaft. The purpose of the study was to assess the effect of anomalies on the axial capacity in varved clay. Six drilled shafts were tested, the void size varying from 5 to 11% of the cross-sectional area, and soil inclusions varying from 5-17% of the cross-sectional area. A soft bottom resulted in a 33% reduction in end bearing relative to a sound bottom. The capacity of the drilled

[4] DFI JOURNAL Vol. 6 No. 2 December 2012

shaft with no planned structural anomalies but with soft bottom were 5% to 10% higher than the shaft with a sound bottom and some structural anomalies. The increase of strength was insignificant, so the difference between the two drilled shafts was not recorded during construction.

O’Neill, et al. (2003) and Sami and O'Neill (2003) studied the effect of two different asymmetric voids of 15% on the axial load capacity. Eleven scaled drilled shaft samples were tested in the lab to study the behavior of drilled shafts with minor flaws under flexural and axial loading. The study concluded that minor anomalies in the form of small voids decrease the strength of a shaft in axial compression by less than 10 percent. Jung G., et al. (2006) evaluated the effect of artificial anomalies including soft bottom, concrete segregation and contractions of cross sections by 10-20% on drilled shaft capacity.

Haramy (2006) presented a comprehensive study on performance monitoring of concrete mix during its hydration process, CSL detection of anomaly locations, tomographic imaging of the anomaly, and the effects of anomalies on drilled shaft capacity. Haramy, et al. (2007), focused on the evaluation of load bearing capacity of drilled shafts with anomalies under various conditions using 3-D numerical analysis and modeling to evaluate the serviceability of a defected drilled shaft. The study results showed that friction angles of surrounding geo-materials, soil density, and percentage of consolidation influence the stress concentration around anomalies; and that such stress concentration can trigger crack propagation and worsen the corrosion process (Amiri (2011). When anomalies occur, the NDT methods can assist in detecting their locations and sizes. Anomalies near the top of a drilled shaft will significantly affect its structural capacity, Chang and Nghiem (2008).

Anomalies throughout the length can significantly reduce the axial load capacity of a drilled shaft. The shape and size of such voids can influence drilled shaft axial load carrying capacity in different manners as shown in Fig. 1. It is therefore important to evaluate the effect of various types of voids on the axial load capacity of the shaft as a function of different percentages of the cross-sectional area. Fifteen (15) scaled drilled shaft

samples were tested in the lab to study their structural behavior with respect to symmetric voids under uniaxial compression loadings. Tests were performed to determine the effects of shape, size and length of voids on the shafts’ axial load capacity; and to evaluate the crack pattern and stress concentration near the voids, or the fracture behavior (field observation) of the drilled shaft under axial loading.

[FIG. 1] Void Anomalies in a Drilled Shaft due to pulling the casing too fast [8]

TESTING PROGRAMFifteen drilled shaft samples were tested at FIU’s TASCT laboratory under axial compression using a hydraulic actuator with a maximum load capacity of 235 kips (1046 kN). Axial load and vertical displacement at top of the shaft sample was recorded during the tests. The length and diameter of the shafts, stirrup spacing, length of anomaly, and steel reinforcement amount were kept constant in all samples.

Void Shapes and Locations Considered

Different anomaly types were considered in the form of symmetric voids with different cross sectional areas ranging from 10 % to 40 % of the gross cross sectional area of the shaft model based on the common void percentages in real-life drilled shafts. Also, the void sizes were determined based on the maximum size of the voids in drilled shaft foundations which can be detected by NDT methods. Three different symmetric voids shape were considered: (a) void Type A, (b) void Type B, and (c) void Type C as shown in Fig. 2, with different arc length or arc angle, X°. X° is the same for void Type A and


void Type C. For void Types A and C, the arc lengths are 3.53, 7.07, 10.68, and 14.14 inches (90, 180, 270, and 360 mm) on each side thus occupying 10% to 40% of the cross sectional area of the drilled shafts. For void Type B, the arc lengths are 1.77, 3.53, 5.26, and 7.07 inches (45, 90, 135, and 18o mm) that occupy 10%, 20%, 30%, and 40% of the cross sectional area of the drilled shafts, respectively.

Void Type A penetrates through the concrete cover and the longitudinal bars. Void Type B penetrates inside the concrete core, and void Type C just penetrates the concrete cover. The concrete core inside the void Type B has a diameter of 4 inches (101.6 mm). The length of the voids, VL, is the same for all the samples which is 10 inches (254 mm) along the length of the shaft as shown in Fig. 3. All voids in the scaled shafts were located at the middle of the sample while being tested in axial compression.

(a) Void Type A (b) Void Type B (c) Void Type C

Void

[FIG. 2] Shape of the Voids considered in the experimental program

[FIG. 3] Drilled Shaft Profi le with Void at the middle

Test Specimens

Table 1 summarizes the characteristics of the test specimens used in this study. All of the considered shaft specimens were one-fourth scale of a full-size drilled shaft in Florida with a diameter of 3 feet (914 mm) and length of 16 feet (4.88 m). The samples were tested at the FIU’s TASCT Laboratory. The diameter and length of the shaft samples were kept constant at 9 inches (229 mm) and 4 feet (1220 mm), respectively. The shafts were longitudinally reinforced with 6 No. 4 (12.7 mm) steel bars that were equally spaced around the perimeter. This amount of steel corresponded to 2 percent

[TABLE 1] Characteristics of Tested Drilled Shaft Specimens

Specimen No.

Void Type

Concrete Strength (MPa)

Diameter(mm)

Longitudinal Steel

Void Percentage (%)

Arc AngleX°

1

A20.8 228.6 6 No. 4 (12.7 mm) 10 45

2 20.8 228.6 6 No. 4 (12.7 mm) 20 90

3 20.8 228.6 6 No. 4 (12.7 mm) 30 136

4 20.8 228.6 6 No. 4 (12.7 mm) 40 180

5

B20.8 228.6 6 No. 4 (12.7 mm) 10 22.5

6 20.8 228.6 6 No. 4 (12.7 mm) 20 45

7 20.8 228.6 6 No. 4 (12.7 mm) 30 67

8 20.8 228.6 6 No. 4 (12.7 mm) 40 90

9

C48.3 228.6 6 No. 4 (12.7 mm) 10 45

10 48.3 228.6 6 No. 4 (12.7 mm) 20 90

11 48.3 228.6 6 No. 4 (12.7 mm) 30 136

12 48.3 228.6 6 No. 4 (12.7 mm) 40 180

13 No Void 48.3 228.6 6 No. 4 (12.7 mm) 0 0

14 No Void 20.8 228.6 6 No. 4 (12.7 mm) 0 0

15 No Void 20.8 228.6 6 No. 3 (9.5 mm) 0 0


of the gross cross-sectional area of the shaft. The longitudinal bars were Grade 80 with the nominal yield strength of 80 ksi (552 MPa). The ties were No. 3 (9.5 mm) and were spaced along the axis of the shaft at 4 inches (102 mm) O.C. The clear cover used on all steel reinforcement was 1 inch (25.4 mm)

Specimens 1 to 4 had void Type A with void areas of 10, 20, 30, and 40 percent of the gross cross-sectional area of the shaft model (void area as shown in Fig. 2a). The arc lengths for specimens 1 to 4 were 5.53, 7.07, 10.68, and 14.14 inches (140, 180, 270, and 360 mm) respectively. Specimens 5 to 8 had void Type B and specimens 9 to 12 had void Type C with the same percentages. The arc length for specimens 5 to 8 were 1.77, 3.53, 5.26, and 7.07 inches (45, 90, 135, and 180 mm), respectively. Specimens 13, 14, and 15 were constructed without anomalies. Specimens 13 and 14 were the control specimens, and did not include any form of void with six equally spaced No. 4 (12.7 mm) longitudinal rebars around the perimeter. The last specimen, specimen 15, did not include any form of voids and was longitudinally reinforced with 6 No. 3 (9.5 mm) steel bars equally spaced around the perimeter.

The casting form for the drilled shaft specimens consisted of a cardboard Sonotube with an inside diameter of 9 inches (228.6 mm). Before the steel cage was positioned inside the Sonotube, eight plastic spacers with 1 inch (25.4 mm) length were installed throughout the length of the cage to keep the cage at the middle of form, and ensure the 1 inch (25.4 mm) concrete cover. Fig. 4a shows the steel cage of a shaft and the plastic spacers on it before concrete placement. A wood framework was built and placed at the bottom of the Sonotube to ensure that the steel cage was aligned properly, and to secure the fluid concrete during casting (Fig. 4b). To make the voids, the Sonotube was cut at the middle with a length of 10 inches (254 mm) and a width equal to that of the arc lengths which depends on the arc angle and the void percentage, as shown in Fig. 5. Plywood was used to fabricate the void shape between the Sonotube and the steel cage; it was secured at the center of the steel cage before casting. Silicone glue was used at the end to cover the holes between the plywood pieces and steel cage to avoid any concrete leakage (Fig. 5).

Concrete was pumped vertically inside the Sonotubes for all the specimens to ensure uniformity. Concrete was not vibrated after casting to simulate actual conditions where concrete in drilled shafts is not consolidated. All specimens were tested 30 days after casting.

[FIG. 4] (a) Steel Cage of Specimen, (b) Sonotube with Void Type B, 10%

[FIG. 5] Specimens formwork before concrete placement

Material Properties

The concrete used in this study was normal weight concrete with unit weight of 150 lbs/ft3 (2400 kg/m3). Standard concrete cylinder samples with 4-inch (102 mm) diameters and 8-inch (203 mm) lengths were tested using the Concrete Compression Machine in the laboratory at FIU. The average measured axial compressive capacity for three standard cylinders was 37,900 lbs (168600 N) at 28 days. Therefore, the cured concrete cylinders had a compressive strength at 28 days equal to 3,015 psi (20.8 MPa). The concrete slump was measured to be 4 inches (102 mm) at the time of casting, and the maximum coarse aggregate size (rounded river gravel) was 0.5


inch (12.7 mm). Fine aggregate was based on ASTM C33 natural sand with a fineness modulus of 3.0. The cement was type I Portland cement and comprised about 24 percent of the weight of the mix. The water to cement ratio varied between 0.4 and 0.42, depending on the moisture content of the aggregate. Specimens 9 to 13 were constructed with concrete with compressive strength of 7,000 psi (48.3 MPa), with the same slump and same maximum coarse aggregate size.

A No. 3 (9.5 mm) bar was tested using a Universal Tensile Testing Machine in the laboratory at FIU. The tensile test loading ratio was 100 lbs/sec (445 N/sec). The longitudinal steel and ties in all the tested specimens were Grade 80, with yield strength of 80 ksi (551.6 MPa). The actual yield strength was less than the nominal value (75 ksi, 517.1 MPa), and the modulus of elasticity was 29×106 psi (2×105 MPa). The stress-strain curve obtained for the No. 3 (9.5 mm) steel rebar is shown in Fig. 6.

0100200300400500600700800

0 0.1 0.2 0.3 0.4

Stre

ss (M

Pa)

Strain (mm/mm)

[FIG. 6] Stress-Strain Curves of Steel Rebar

Testing Procedures

Load tests were performed in general accordance with American Society for Testing and Materials (ASTM) D1143 test method for shafts under axial compressive load. All tests were performed in the same laboratory temperature to minimize thermal effects. All load tests were carried to structural failure. The test program was organized into two groups. Group I consisted of testing twelve specimens with voids (Specimens 1 to 12). The first four specimens were cast with void Type A with void percentage from 10 to 40 percent; second four specimens with void Type B and third four specimens with void Type C, all with the same voids percentage. Group II consisted of testing control specimens without any voids (Specimens 13, 14, and 15). Specimen 13 was

the control specimen for those shafts cast with concrete compressive strength of 7,000 psi (48.3 MPa) and Specimens 14 and 15 were the control specimens for shafts cast with concrete compressive strength of 3,015 psi (20.8 MPa). All fifteen specimens were tested in pure axial compression in the TASCT laboratory at the FIU. The eccentricity of the applied load was approximated to be ±1.0 inch (±25.4 mm).

The machine used for axial testing the drilled shaft specimens was a Shore Western hydraulic actuator with maximum capacity of 235 kips (1,046 kN) as shown in Fig. 7. The actuator moves from -10 inch (-243mm) to +10 inches (+254 mm) which is total 20 inches (508 mm) of displacement from top to bottom. A displacement control procedure was adopted for all the tests at a rate of 0.012 in./min (0.305 mm/min). The hydraulic actuator was equipped with a manually controlled electric pump, which allowed having a constant loading. All instruments were connected to a data acquisition system, which is a MegaDAC with a sampling frequency of 1 Hz. The actuator deflection and shaft head displacement were recorded with the Linear Displacement Transducer (LDT) and the loading was recorded with the actuator’s load cell.

[FIG. 7] Hydraulic Actuator machine used for the tests at FIU’s TASCT Laboratory

A solid steel plate with thickness of 1 inch (25.4 mm) was placed at the bottom of the specimens to provide a strong base. Two 2×2×6 ft (0.61×0.61×1.83 m) concrete blocks were constructed to use as lateral base support. These blocks were keeping the specimens immobile during the loading process. Angle iron bars of 1.5×1.5×0.25 in (38×38×6.3 mm) were cut and used to make the support for


the specimens. Two supports were considered at the bottom and middle of the specimen to prevent buckling of the samples in the first mode before failure, as shown in Fig. 8. Fig. 8 also shows the instrumentation scheme, geometry, and loading procedure for the specimen loaded axially.

[FIG. 8] Test Setup

Test Results and Discussion

The behavior of the drilled shafts subject to axial load was investigated in this study. The axial load versus vertical displacement for specimens in test Group I is shown in Figs. 9, 10 and 11. The axial load versus displacement in Specimens 1 to 4, 5 to 8, and 9 to 12 is shown respectively in Figs. 9, 10 and 11. The test results show that the presence of symmetric voids within the cross-section affected both the strength and the stiffness of the shaft. The effect on the stiffness was much more pronounced, especially when the void penetrated inside the core of the shaft (void Type B). This result is due to having inadequate confinement of the concrete and reinforcement and local buckling of the longitudinal steel bars in the shaft.

[FIG. 9] Axial Load versus Vertical Displacement for Specimens 1-4 (void Type A)

[FIG. 10] Axial Load versus Vertical Displacement for Specimens 5-8 (void Type B)

[FIG. 11] Axial Load versus Vertical Displacement for Specimens 9-12 (void Type C)

[TABLE 2] Maximum Axial Load Capacity for Shafts with Different Types of Voids

Void Type A Void Type B Void Type C

Void percentageAxial Load

(kN)%

reductionAxial Load

(kN)%

reductionAxial Load

(kN)%

reduction

0% 773.28 773.28 951.91

10% 693.54 10.31 632.18 18.25 878.33 7.73

20% 658.35 14.86 521.19 32.60 843.34 11.41

30% 604.87 21.78 420.72 45.59 789.38 17.07

40% 483.575 37.46 406.46 47.44 686.52 27.88


Table 2 shows that—compared to the intact specimen—the shafts with Type A void exhibited 10 to 37 percent lower axial compressive strength; shafts with Type B void exhibited 18 to 47 percent lower axial compressive strength, with concrete strength of 3,015 psi (20.8 MPa). The decrease in axial compressive strength for the shafts with Type C void was about 7 to 27 percent in comparison to the shaft without anomaly and with concrete strength of 7,000 psi (48.3 MPa). These results show that the presence of a void inside the cage (void Type B) will significantly decrease the axial strength of the shaft.

Specimens Failure

Fig. 12 shows the fractured specimens after the conclusion of the testing. For all specimens,the shape of the void, size of the void, and length of the void greatly affected the axial compressive strength and stiffness of the shaft specimens. It can be seen that cracks in most specimens started around and in the vecinity of the voids, and weakened the specimens during loading. In specimens with Type B void, it can be seen that the fractures was clearly due to lack of confinement of the concrete and its reinforcement, because of its proximity to the void location. Specimens with void Type B had less critical buckling load or buckling capacity because the arc length was smaller. Buckling was a main reason of fracture for specimens with Type A void since the arc length of the void was much more than that in specimens with Type B void. Also, in specimens with Type A void, most of the longitudinal bars were placed in the void area. For example, specimen 4 had two symmetric voids with 180 degree arc angles each, which meant that it covered the entire perimeter of the specimen. Most of the growth cracks in the shaft specimens were in the longitudinal direction of the shaft, and they show a shear failure in the specimens under axial loading. All specimens behaved similarly up to the shafts’ failure point. At that point, the shaft specimens with void Type A and B failed by crushing and shearing of the concrete, and by the outward buckling of the steel bars. The specimens with void Type C are stronger than those with voids Types A and B because of the concrete cover around the longitudinal bars.

Specimen 1 Specimen 2





Failures in Specimens 13, 14, and 15, the intact specimens are shown in Fig. 12. It can be seen that the failure cracks started from the top support location and grew in the longitudinal direction towards the top of the specimens. Also, the compressive axial load resulted in pure compression failure and material crushing in the region where the actuator was bearing on the specimens.

ANALYTICAL EVALUATIONThe results of the experimental test program were compared with the ACI 318, (1999) and the AASHTO LRFD Bridge Design Specifications (2010) formula for axially-loaded reinforced concrete members as shown in Eqn. [1]. The nominal theoretical axial load strength for the special case of zero eccentricity may be written as:

[1]

where f’c is the nominal 28-day concrete

compressive strength (psi), fy is nominal steel

yield strength of the longitudinal bars (psi), Ag

is the gross area of the shaft section (in2), and A

s is total area of the longitudinal reinforcement

(in2). Table 3 compares the experimental data with the analytical results for the compressive axial load capacity of the intact specimens. Table 3 shows that the analytical result of the axial load capacity based on Eqn. [1] is almost 20% larger than the experimental results.

[TABLE 3] Experimental vs. Analytical Axial Loads for the Drilled Shaft Specimens

Specimen No.

Pn(max)

Experimental (kN)

Pn(max)

Analytical (kN)

Difference (%)

13 951.91 1143.32 16.74

14 773.28 880.96 12.22

15 530.38 745.60 28.87

Fig. 13 shows a comparison of the axial load versus the vertical displacement for Specimens 14 and 15—the intact specimens without voids. Specimen 14 was longitudinally reinforced with 6 No. 4 (12.7 mm) steel bars that were equally spaced around the perimeter, and Specimen 15 with 6 No. 3 (9.5 mm) steel bars. It was determined that the strength of Specimen 14 at failure was 173.84 kips (773.28 kN) and that of Specimen 15 was 119.23 kips (530.38 kN), which is about 69% that of Specimen 14.




Specimen 15

[FIG. 12] Failure in Shaft Specimens after testing


[FIG. 13] Axial Load versus Vertical Displacement for Specimens 14 and 15 (intact specimens)

CONCLUSIONSThis paper presented the results on fifteen drilled shaft specimens under axial compressive load tested at the TASCT laboratory at FIU. The shaft specimens were constructed with three different types of built-in symmetric voids in an attempt to study the effect of voids outside and inside the caging on the axial load capacity of drilled shafts. Void Type A resulted in a 21% reduction in axial strength, void Type B resulted in a 36% reduction, and void Type C resulted in a 15% reduction in axial strength. The test results showed that the presence of symmetric voids within the cross section affected both the strength and the stiffness of the drilled shafts. The effect on the strength and the stiffness was much more noticeable especially when the void penetrated inside the caging of the shaft (void Type B). This was deduced to be due to the lack of concrete confinement for the longitudinal bars.

Stress concentrations near the void location were much larger than other locations, and they caused shear cracks to appear around the voids, and the consequent failure of the specimen. The presence of symmetric voids outside the rebar cage (void Type C), that take up 40% of the cross sectional area of the drilled shafts, reduced the axial resistance of the shaft by only 27%; those that penetrated inside the core (void Type B) reduced the axial resistance of the shaft by up to 47%. Drilled shafts with all types of voids behaved in a similar fashion up to the shafts’ failure point. At that point, drilled shafts with void Types A and B failed by crushing and shearing of the concrete and

by outward buckling of the steel bars. Drilled shafts with void Type C showed more strength than those with void Types A and B due to the concrete cover around the longitudinal bars that provided confinement effects.

Comparisons between the experimental and the analytical results of the compressive axial load capacity of the intact specimens showed that the analytical results are nearly 20% larger than the experimental results.

Drilled shaft capacity is affected by the size and location of the void. Location and size of the void will have a significant influence on the confinement of the longitudinal bars, causing structural capacity reduction. The study showed that voids extending into the concrete core were more critical to the structural performance of a shaft than those located within the concrete cover. Voids penetrating the reinforcement cage result in more drilled shaft capacity reduction. The presence of voids outside the rebar cage will cause less axial capacity reduction due to the better confinement. It is recommended that a reduction factor R be used in the structural design codes and specifications for drilled shafts. A reduction factor R = 0.90 is recommended for drilled shafts located in environments where corrosion is not expected. This reduction factor can be changed depending on the location of the voids after nondestructive testing on the shaft.

ACKNOWLEDGEMENTThe authors thank Supermix Co. for donating concrete for our experimental work. The first writer is also thankful to the University Graduate School for providing him with a Doctoral Year Fellowship to complete his doctoral work.

REFERENCES1. AASHTO, LRFD Bridge Design Specifications,

Customary U.S. Units, 5th Edition, American Association of State Highway and Transportation Officials, 2010.

2. ACI 318, Building Code Requirements for Reinforced Concrete, American Concrete Institute, Detroit, MI, 1999.

3. Amiri, S., N., 2011, “A comprehensive study on soil consolidation: The pore pressure development/dissipation during consolidation and effect of variable permeability and compressibility on the


consolidation behavior”, Publisher VDM Verlag Dr. Müller, pp. 124.

4. Barker, R. M., et al., 1991. “Manual for the Design of Bridge Foundations,” National cooperative Highway Research Program Report 343, Transportation Research Board, Washington, DC.

5. Chang N., Nghiem H., 2008, “Drilled Shaft Axial Capacity Due to Anomalies.” Report No. FHWA-CFL/TD-08-008. Federal Highway Administration Colorado.

6. Haramy K. Y., 2006, Structural Capacity Evaluation of Drilled Shaft Foundations with Defects, MS thesis, University of Colorado Denver.

7. Haramy K. Y., Rock A., Chang N. Y., 2007, Numerical Analysis of Load Bearing Capacity of Drilled Shafts with Defects, Proceedings, DFI 32nd Annual Conference on Deep Foundations, Colorado Springs, CO.

8. Hertlein, B., Davis, A., 2006, “Nondestructive Testing of Deep Foundation.” John Wiley & Sons Ltd, TA775. H395.

9. Hollema, D. A., Olson, L. D. (2002), “Crosshole Sonic Logging and Tomography Velocity Imaging of a New Drilled Shaft Bridge Foundation”, The American Society for Nondestructive Testing, Inc., Structural Materials Technology V Conference.

10. Iskander, M., Roy, D., Kelley, S., and Ealy, C., 2003, “Drilled Shaft Defects: Detection, and Effects on Capacity in Varved Clay”, 10.1061/ASCE,1090-0241, 129:12,1128

11. Jung G., Kwon, Jung S.J., and Kim, 2006, Evaluation of Full-Sized Cast-in-Place Pile Capacity with Artificial Defects. Journal of the Transportation Research Board, No. 1975, TRB, Washington D.C.

12. O’Neill, M., and Reese, L., 1999. ‘‘Drilled shafts: construction procedures and design methods.’’ Report No. FHWA-IF-99-025, Washington, D.C.

13. O’Neill M., Tabsh S.W., Sarhan, H., 2003, “Response of drilled shafts with minor flaws to axial and lateral loads.” Engineering Structures, Vol 25, Issue 1, pp 47-56.

14. Sami W Tabsh and Michael W. O’Neill, 2003, “Effects of Minor Anomalies on Axial Capacity of Drilled Shafts.” Transportation Research Record, Paper No. 01-0176, pp 65-72.

15. Wightman, W.E., Jalinoos, F., Hanna, K. (2003), Application of Geophysical Methods to Highway Related Problems, Publication No. FHWA-IF-04-021.


Uplift Performance of Multi-Helix Anchors in Desiccated ClayArmin W. Stuedlein, Ph.D., P.E., Assistant Professor and Loosley Faculty Fellow, Oregon State

University, Corvallis, Oregon, USA; 541.737.3111, [email protected]

Jesi Young, Civil Engineer, Bonneville Power Administration, Portland, Oregon, USA; 360.619.6533,

[email protected] (MS Graduate, June 2012)

ABSTRACTHelical anchors provide an accepted means for the support of compressive and tensile foundation loading. Despite their prevalence, the load-displacement and capacity of multi-helix anchors has not been adequately documented. Full-scale uplift loading tests on square shaft multi-helix anchors installed in desiccated Beaumont clay were performed at a well characterized test site. The stiffness and strength of the anchors is characterized, and compared against the variability in undrained shear strength determined in consideration of inherent variability, measurement error, and transformation error. The large-displacement softening behavior exhibited by the test anchors was shown to reflect the in-situ stress-strain behavior of the high plasticity clay, and the amount of softening with post-peak displacement was characterized. The prediction accuracy of design models was assessed using the bias and its statistical characterization, and indicated that the variability in model accuracy lies within the uncertainty in undrained shear strength.

INTRODUCTIONThe use of helical anchor foundations dates to their invention in the 1830s, designed to support lighthouses and other over-water structures (Lutenegger, 2011). Since then, single and multi-helix anchors have been used to support transmission tower structures, provide uplift resistance for buried structures and reaction frames, used for seismic retrofit of existing structures, and a host of other applications. Although a variety of other anchorage alternatives exist, helical anchors provide the advantage of spoil-free installation: anchors are screwed into the ground with relatively lightweight construction equipment capable of providing the torque necessary to advance the anchor to required depth. On the contrary, drilled and grouted anchors require the excavation and disposal of soil spoils, and can suffer from caving or squeezing ground conditions (Perko, 2009). Lutenegger (2008) presented the results of nine uplift load tests of single helix anchors in varved clay. The helical anchors were embedded 7.5 to 23 plate diameters, D, below the ground surface, and had diameters ranging from 203 to 406 mm. The results indicated that when displacements were normalized by plate diameter, and when setting anchor capacity to the resistance at a displacement equal to 10 percent of D, the

load-displacement performance of the anchors collapsed to a common curve exhibiting approximately 25 percent variability. Mooney et al. (1985) presented the results of eight multi-helix anchor loading tests in marine clay. The helical anchors were embedded 4 to 12D, and were characterized by an average plate spacing of 3.76D. The results indicated variability in capacities of approximately 20 percent, and did not appear to correlate with depth. However, Young (2012) showed that the load-displacement behavior of the Mooney et al. (1985) load test results did depend on depth when the load was normalized by the ultimate resistance and the displacement normalized by D. The load-displacement model for helical anchors in clay developed by Young (2012), while proving somewhat accurate for service loads, indicated significant variability. Therefore, despite their prevalence for the support of light to medium loads, the full-scale behavior of multi-helix anchors in cohesive soils warrants additional study.

This paper presents the results of uplift loading tests of seven square shaft multi-helix anchors installed in desiccated clay to provide reaction for footing loading tests. The geology and subsurface characterization of the test site is described, with special emphasis on the stress-strain behavior and variability of the


undrained shear strength, estimated through the consideration of inherent variability, measurement error, and the transformation error associated with correlations. A simple technique is used to correct the observed load-displacement curves for slack in the anchor connections. The load-displacement behavior of each load test is examined with respect to its stiffness and strength, and the loss of resistance with post-peak displacement is analyzed. Comparison of anchor capacity to various prediction models is made using the bias and its statistical characterization, with emphasis on prediction accuracy and variability. This study shows that models based on theoretical failure mechanisms and correlations can predict the anchor capacity within the uncertainty of the estimate in undrained shear strength.

TEST SITE DESCRIPTION

Geographic and Geologic Setting

The test site was located adjacent to Interstate 10 in Baytown, Texas, situated about 50 km east of Houston. Baytown lies due north of the Upper San Jacinto Bay, which is part of the San Jacinto River that drains Lake Houston to the north and empties into the broader and more southerly Galveston Bay. The test site is situated within the Quaternary Coastal Plain of Texas. This plain forms a belt approximately 110 to 150 km (68 to 93 mi) wide, and is parallel to the coastline of the Gulf of Mexico (Bernard et al., 1962; Al-Layla, 1970; O’Neill and Yoon, 2003). The governing stratigraphy at the test site is known as the Beaumont clay formation, and comprises tan and brownish-red clay with intermittent lenses of silt and fine sand. The Beaumont clay formation was deposited at the beginning of the Wisconsin Glacial stage, during the period approximately 100,000 to 50,000 years BP, on a floodplain during periods of overflow. The terrace was subjected to stages of prolonged lowering of the nearby Gulf of Mexico (by approximately 120 m or 400 ft) during glacial stages following its deposition (O’Neill, 2000), resulting in global overconsolidation.

Stratigraphy and Geotechnical Characterization

The subsurface conditions at the test site, detailed by Stuedlein et al. (2012a, 2012b),

were evaluated with several in-situ and laboratory tests. The exploration plan included nine piezocone tests and five mud rotary borings distributed throughout the 420 m2 (4,520 sq ft) rectangular test site. Fig. 1 presents the site and exploration plan, indicating the distribution of in-situ tests (and their depth), footing tests, and instrumented uplift anchor tests.

Fig. 2 presents the subsurface profile estimated along Section A-A’ of Fig. 1. Commonly encountered in the Beaumont clay formation, a thin layer of heavily overconsolidated, desiccated clay crust extended from the ground surface to a depth of 0.66 m (2.2 ft) [Fig. 2]. Below the crust, a 3.4 m (11.2 ft) thick layer of moist, slightly sandy, very silty lean clay (CL) was separated from a deep deposit of moist, slightly silty fat clay (CH) by a thin, 0.45 m (1.5 ft) thick layer of moist to wet, silty sand and sandy silt (SM/ML). Intermittent, thin layers of lean clay were encountered in split-spoon samples within the deep layer of fat clay. Groundwater was encountered at 2.4 m (7.9 ft) at the time of drilling; a piezometric surface of approximately 1.6 to 1.8 m (5.25 to 5.90 ft) was identified from piezocone tests.

[FIG. 1] Site and exploration plan indicating location of test anchors (adapted from Stuedlein and Holtz, 2012)


Consolidated isotropic undrained (CIU) triaxial strength tests were performed on a number of undisturbed samples retrieved from Borings B-3, B-4, and B-5. Two suites of triaxial testing were undertaken, including recompression tests (Berre and Bjerrum, 1973) and SHANSEP tests (Ladd and Foott, 1974; Ladd, 1991). Fig. 3a presents the comparison of stress-strain behavior for recompression triaxial tests; the specimens prepared from samples of lean clay indicated general hyperbolic-type hardening behavior, whereas specimens prepared from the more prevalent fat clay exhibited distinct softening after achieving peak strength, which occurred at axial strains ranging from 3 to 5 percent. Specimens were inspected following shearing, and indicated that shearing largely occurred on slickensided planes typical of desiccated clay. Mahar and O’Neill (1983) showed that Beaumont clay exhibited normalized strength behavior. A SHANSEP test program was performed to accommodate the potential for sample disturbance and to generate an estimate of the variation of undrained shear strength, s

u, with

overconsolidation, OCR. Fig. 3b presents the SHANSEP curve modified using the liquid limit to account for variability in the mineralogical content following Mahar and O’Neill (1983). The SHANSEP curve is characterized with a coefficient of determination, standard error, and COV (defined as the ratio of standard

deviation to the mean) of 0.97, 3.45, and 8.2 percent, respectively, indicating that s

u may be estimated with

confidence through the use of normalized strength and a profile of preconsolidation stress. The effective stress failure envelope determined for the test site soils was characterized with an apparent cohesion and friction angle of 22 kPa (3.2 psi) and 22 degrees, respectively. Stuedlein et al. (2012a) present additional geotechnical information for the test site.

ESTIMATION OF UNDRAINED SHEAR STRENGTH

Piezocone test data were transformed to geotechnical design parameters, such as undrained shear strength, s

u, and

overconsolidation ratio, OCR, using correlations and successfully compared to laboratory strength and oedometer test results within the framework of the geostatistical test site characterization (Stuedlein et al. 2012b). The undrained shear strength at each anchor location was estimated using the SHANSEP procedure by first computing the preconsolidation stress σ'

p:

σ'p = 0.305

(q

t - σ

vo) [1]

using the corrected cone tip resistance, qt,

and total stress, σvo

after Chen and Mayne (1996). Piezocone-based OCR’s were then used in conjunction with the SHANSEP procedure and the site-specific SHANSEP curve (Fig. 3) to develop the profiles of undrained shear strength. Stuedlein et al. (2012b) presents the derivation of the second moment probabilistic approach (e.g., Phoon and Kulhawy 1999) for Eqn. 1 and the site-specific SHANSEP model used to incorporate the error arising from inherent variability, measurement error (of cone tip resistance), and transformation error. Fig. 4 shows the mean and bounds of one standard deviation in s

u modeled at the locations of Borings

B-3, B-4, and B-5 along with estimates of su

and corresponding error bars (representing

ATD

CPT

0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25

Desiccated CrustR

elat

ive

Elev

atio

n (m

)

Distance (m) South North

Upper Clay Layer (CL)

Sandy SILT/Silty SAND

Lower Clay Layer (CH)with interrmittantlayers of lean clay (CL)

Cone Tip Resistance (MPa) and SPT N-Values

??? ?

CPT-1, B-1 CPT-2, B-2 CPT-3

(SM/ML)

-

-

-

-

-

-

-

-

-

Approximatedepth of anchors

[FIG. 2] Cross-section A-A indicating general site stratigraphy and results of in-situ testing (adapted from Stuedlein and Holtz, 2012)


the COV in su, or COVs

u) developed from the

oedometer test results, pocket penetrometer results, and Skempton’s regression (Skempton 1957; Chandler 1988) for specimens retrieved from the corresponding borings. Despite the relatively large uncertainty in s

u (COVs

u = ~53

percent) predicted by the geostatistical model, Fig. 4 indicates that the model satisfactorily estimates the undrained shear strength for samples retrieved from the test site. The geostatistical cone tip resistance model was then used to estimate the profile in undrained

[FIG. 4] Validation of Geostatical Undrained Shear Strength estimation at test site (modifi ed from Stuedlein et al [2012b]): Boring B-3, (b) Boring B-4, and (c) Boring B-5. Error bars correspond to the total coeffi cient of variation in su accounting for inherent variability and transformation uncertainty

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

0 100 200 300 400

Dep

th (m

)

su (kPa)

Skempton's Regression Kriged Su Profile (SHANSEP)Oedometer Tests Kriged Su Profile (SHANSEP) +/- Standard DeviationPocket Penetrometer Tests

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

0 100 200 300 400

su (kPa)

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

0 100 200 300 40

su (kPa)

(a) (b) (c)

and SHANSEP curvesu

su

0

20

40

60

80

100

120

0 3 6 9 12 15

Shea

r Sre

ss (k

Pa)

Axial Strain (%)

Test R3 (CL); OCR = 8.7 Test R5 (CH); OCR = 3.6

Test R6 (CL); OCR = 17.2 Test R7 (CH); OCR = 4.8

σ'3 = 62 kPa

σ'3 = 83 kPa

σ'3 = 46 kPa

σ'3 = 174 kPa(a)

[FIG. 3] Stress-Strain-Strength behavior of desiccated clay at test site (a) comparison of stress-strain behavior of lean and fat clay at test site, and (b) modifi ed SHANSEP curve presenting variation in undrained shear strength with overconsolidation ratio (OCR)

0

10

20

30

40

50

60

70

80

90

1 10

(su

* LL)

/ σ’

vc

Overconsolidation Ratio

Beaumont Clay(Mahar and O'Neill, 1983)Montgomery Clay(Mahar and O'Neill, 1983)Test Site

Fitted Line

Fitted Line +/- Std. Error

= 14.95 OCR 0.72

R2 = 0.97

(su *LL)

σ’vc

(b)


shear strength at each anchor location (Fig. 5) using the correlation to preconsolidation stress and the site-specific SHANSEP curve. Because several CPTs did not extend to the elevation of the tips of the helical anchors, and since the lower clay layer was relatively uniform (Fig. 3; see also Stuedlein et al. 2012a), the kriged q

t profile at each anchor location was spliced

with qt corresponding to the nearest deep CPT

to estimate the full su profile. In practice, the

undrained shear strength may be averaged over some interval of interest for use in a design model, in which the application of a variance reduction function (e.g., Vanmarcke 1977) to reduce the modeled variability is often justified.

HELICAL ANCHOR UPLIFT LOADING

Anchor Installation and Test Program

The square shaft helical anchors were installed to provide uplift resistance to a small and large reaction frame assembled for the purpose of evaluating the compression behavior of spread footings supported on the unimproved and aggregate pier-improved clay subgrade. The details of the footing load test program are found in Stuedlein and Holtz (2010) and Stuedlein and Holtz (2012). The anchors were supplied by Atlas Systems, Inc., produced with a helix spacing ratio, defined as the vertical

spacing between plates divided by the average plate diameter, S/D, equal to 3, plate thickness of 13 mm (0.5 in) , and square shafts 57 mm (2.25 in) in width. The anchors were installed with a Texoma 600, equipped with a 75 mm (3 in) kelly bar and rated to 53 kN-m (39,000 ft lb) torque. Anchors were installed to practical refusal, typically occurring when the torque motor stalled twice at a given elevation; unfortunately, the installation torque was not measured. Perko (2009) indicated that torque motors can exhibit inefficiencies of 30 to 40 percent. Therefore, although the Texoma 600 was rated to 53 kN-m (39,000 ft lb) of torque, it is likely that the actual torque applied to the anchor stem was on the order of 30 to 50

percent of the rated value, given that the allowable torque on the 57 mm (2.25 in) shaft was approximately 31 kN-m (23,000 ft lb), and no torsion failure was observed. Loading tests occurred one to two days following installation. Fig. 1 identifies the location for each of the instrumented helical anchors; Table 1 provides the geometrical characteristics and comments for each of the anchor loading tests.

Each large test footing required eight helical anchors for reaction (Fig. 6), whereas three anchors were used to provide reaction for the small footing load tests. The displacements of the

anchors were monitored during loading of the footings using optical level surveying with an accuracy and resolution of 0.8 mm (0.03 in). The uplift load carried by one anchor was monitored continuously during the footing load test using a Geokon 3000 load cell rated to 890 kN (100 tons) with an accuracy and resolution of 0.25 percent of full scale and 0.45 kN (100 lb), respectively. During the first large footing loading test, corresponding to the southeastern-most footing, it was noted that the reaction anchors were displacing continuously to maintain a total reaction of approximately 2,900 kN (325 tons) . The

[FIG. 5] Variation in Undrained Shear Strength with depth for each anchor location (a) Anchors S1, S3, and S6; (b) Anchors S2, S4, S5, and S7

0

2

4

6

8

10

12

14

16

0 50 100 150 200 250 300Undrained Shear Strength, su (kPa)

ANCHOR S2

ANCHOR S4

ANCHOR S5

ANCHOR S7

0

2

4

6

8

10

12

14

16

0 50 100 150 200 250 300

Dep

th (m

)

Undrained Shear Strength, su (kPa)

ANCHOR S1

ANCHOR S3

ANCHOR S6

(b)(a)


instrumented anchor corresponds to Anchor S7 in Table 1 and Fig. 1. The large center-west footing was loaded next, and also resulted in uplift failure of the reaction anchor system; the corresponding instrumented anchor was Anchor S3. Thereafter, anchors were installed with an additional 406 mm (16 in) diameter plate to provide sufficient uplift resistance for the footing load tests. Following several subsequent footing loading tests, it was decided to evaluate the uplift resistance deliberately, with a view to improve the understanding of the uplift behavior of helical anchors in desiccated clay.

Steel plateLoad cell

[FIG. 6] Typical footing load test using square shaft Multi-Helix Anchors

Correction for Slack in Shaft Couplings

The anchor stem lengths evaluated at the test site were 1.52 m (5.0 ft) long and required the use of numerous couplings, each requiring two shear bolts to provide load transfer to vertically adjacent stems. Because of design bolt clearance requirements, long anchors may require noticeable vertical upward displacement to engage vertically adjacent anchor stems and eliminate system slack. Fig. 7 presents an example of the observed load-displacement behavior exhibiting noticeable system slack and the procedure used to estimate and eliminate the slack from the load-displacement curves for the purposes of presentation and analysis. For the first load increment, Anchor S1 (Fig. 7a) provided 30 kN (6,744 lb) of uplift resistance over a vertical displacement of approximately 11 mm (0.43 in), indicating fairly low stiffness (2.7 MN/m or 92.5 ton/ft). With increasing load, Anchor S1 stiffened only slightly, requiring an additional 11 mm (0.43 in) to achieve 74 kN (8.3 tons) of uplift resistance. The load-displacement curve indicated a considerable increase in stiffness (equal to 9.3 MN/m or 318.6 ton/ft) over the following two load increments, and even further increases thereafter (up to 21.9 MN/m or 750 ton/ft). During loading, the helical plates nearest to the point of load application engage first, requiring additional displacement

[TABLE 1] Summary of Test Helical Anchor Geometry and Loading Test Information

Dameter of Helical Piles (mm)

Test

Anchor

Depth toTop

HelicalPlate,

(H) (m)

NormalizedDepthH/D

Plate1

Plate2

Plate3

Plate4

Plate5

Plate6

Duration of

Load Test(min)

Remarks

S1 7.00 19 406 406 356 305 254 254 486 No failure

S2 7.00 19 406 406 356 305 254 254 516 No failure

S3 6.27 19 406 356 305 254 N/A N/A 444Unanticipated failure,

monotonic loading

S4 7.00 19 406 406 356 305 254 254 472 No failure

S5 7.00 19 406 406 356 305 254 254 46Deliberate failure, 2nd load cycle observed

S6 7.00 19 406 406 356 305 254 254 474/30Deliberate failure, load/unload/reload observed

S7 6.27 19 406 356 305 254 N/A N/A 488Unanticipated failure,

monotonic loading


to eliminate slack in deeper couplings and mobilize the correspondingly deeper plates. Because anchors designed for tensile loads are typically pre-stressed to remove slack, load-displacement curves presented herein were corrected to eliminate the initial system slack and provide representative in-service behavior. Linear regression models were fit to those portions of the load-displacement curves where the helical anchor plates begin to result in significant and consistent uplift resistance, representative the condition where a majority of anchor plates are fully engaged with the subsurface. The fitted line is back-extrapolated to the zero load condition, and the entire load displacement curve uniformly shifted such that the point of intersection with the zero load condition coincides with the new or corrected origin (Fig. 7b). Although this correction will not provide the “true” load-displacement curve, this procedure was deemed satisfactory in the absence of fully instrumented helical anchor stems, and applied to the load-displacement curves for Anchors S1 through S7.

0

100

200

300

400

Aplli

ed L

oad

(kN

)

Fitted line extended to zero tensile load

Estimated slack equal to 14.24 mm

0

100

200

300

400

0 10 20 30 40 50

Aplli

ed L

oad

(kN

)

Displacement (mm)

(b)

(a)

[FIG. 7] Illustration of Load-Displacement Curves correction for slack in stem couplings (a) raw load-displacement data for Anchor S1; (b) slack-corrected load-displacement curve for Anchor S1

Uplift Load-Displacement Performance

The uplift load-displacement behavior for the seven test anchors are plotted in Fig. 8. For comparison, anchors displaced less than that required to mobilize ultimate resistance are plotted in Fig. 8a, whereas those anchors exhibiting a true capacity are plotted in Fig. 8b. In general, the test anchors indicate a wide degree of variability in stiffness and ultimate resistance (where mobilized). The mean secant stiffness, defined herein as the average secant stiffness over the initial 25 mm (1 in) of displacement, is a useful parameter for the assessment of serviceability in instances where the foundation response stiffens with increasing displacement, as in the case of several of the multi-helix anchors.

0

100

200

300

400

500

600

Load

(kN

)

S1

S2

S4

(a)

0

100

200

300

400

500

600

0 20 40 60 80 100 120 140

Load

(kN

)

Displacement (mm)

S3S5S6S7

(b)

[FIG. 8] Uplift Load-Displacement Curves for Helical Anchors (a) S1, S2, and S4; and (b) S3, S5, S6, and S7

Table 2 indicates that the mean secant stiffness ranges from 7.7 to 20.7 MN/m (264 ton/ft to 709 ton/ft), and appears to exhibit no


dependence on geometrical and temporal conditions, such as the anchor length and embedment, duration following installation, loading rate, or load cycle (i.e. load vs. reload). The coefficient of variation (COV), defined as the ratio of standard deviation, estimated using the short-cut method for small sample sizes (e.g., Lacasse and Nadim 1996) and the mean secant stiffness is 36.3 percent, a significant degree of variability in the secant stiffness. The ultimate resistance (i.e., capacity), defined as the maximum observed anchor resistance, of anchors S3, S5, S6, and S7 ranged from 310 to 516 kN (35 to 58 tons), with a COV of 25.3 percent, somewhat less variable than the secant stiffness. The displacement required to mobilize peak resistance ranged from approximately 25 to 50 mm (1 to 2 in). Similar to the mean secant stiffness, the capacity of these anchors does not appear to be sensitive to geometrical characteristics or temporal conditions. The lack of sensitivity of stiffness and capacity to anchor length and embedment can be partially attributed to the anchor cross-section; square shafts create a void between the shaft and the surrounding soil and results in the loss of shaft resistance. All of the anchors loaded to uplift failure exhibited softening following mobilization of peak resistance, in agreement with the stress-strain behavior expected from triaxial test specimens retrieved from the moderately to highly plastic lower clay layer (Fig. 3). The reduction in anchor uplift resistance, presented as a function of the displacement continuing after mobilization of ultimate resistance as shown in Fig. 9, generally behaves in a similar manner. However, the post-peak behavior exhibited by Anchor S3 departs markedly from the other anchors; given

the subsurface information available, similarity in anchor geometry, and insensitivity to temporal variables, no physical explanation can be offered for the deviation in anchor behavior. Excluding Anchor S3, the anchors generally lose 5 and 10 percent of their ultimate resistance at post-peak displacements of approximately 18 and 26 mm (0.6 to 1.0 in), respectively, following a trend well-characterized by a power law model. Further uplift loading tests in Beaumont clay are required to confirm the behavior modeled in Fig. 9.

0

20

40

60

80

0 3 6 9 12 15

Post

-Pea

k D

ispl

acm

ent (

mm

)

Reduction in Resistance, ΔRult (% of Ultimate)

S3

S5

S6

S7

0.5696 ultRδ = ⋅ ΔR2 = 0.87

[FIG. 9] Post-peak softening of Anchor Capacity as a function of Anchor Displacement

PERFORMANCE OF PULLOUT CAPACITY MODELS

Factors Affecting Pullout Capacity

The failure mechanisms exhibited by helical anchors loaded in uplift have been studied by many researchers, resulting in the development of several models for the prediction of ultimate uplift resistance. Factors affecting the helical anchor capacity in clayey soils include

[TABLE 2] Summary of Helical Anchor Performance Observations

AnchorDesignation

Mean SecantStiffness to 25 mm

Displacement, δ

(MN/m)

UpliftResistance at δ

=1/10 HelixDiameter

(kN)

Displacement, δat Observed

AnchorCapacity

(mm)

ObservedAnchor

Capacity

(kN)

S1 10.5 -- -- --

S2 12.5 -- -- --

S3 14.3 336 53 364

S4 11.6 -- -- --

S5 20.7 393 25 395

S6 7.7/9.4 275 49 310

S7 19.1 504 37 516


geometrical characteristics of the anchor (e.g., embedment depth, anchor spacing), location of the anchorage below the ground surface (e.g., shallow versus deep), and soil characteristics (e.g., undrained shear strength, sensitivity). Meyerhof and Adams (1968), Mitsch and Clemence (1985), Mooney et al. (1985), Rao et al. (1993), and Lutenegger (2008, 2009) investigated the effect of anchor depth using the embedment ratio (H/D, defined as the depth of the top plate from the ground surface, H, to the average anchor diameter) and the spacing ratio (previously defined) on the governing failure mechanism. Although findings varied somewhat from study to study, likely due to the sensitivity of the clay soil investigated, the consensus appears to indicate that anchors will generally behave in a “deep” failure mode, characterized by local shearing in proximity to the anchor plate and where the failure surface extending from the anchors does not intersect the ground surface, for H/D greater than four to five. The helical anchors investigated in this study were characterized with H/D equal to 19 such that the deep failure mode governs.

Helical anchors are known to exhibit two possible deep failure mechanisms, including the individual plate breakout mechanism, where each anchor helix acts independently, and the cylindrical shear mechanism, in which a cylindrical shearing surface develops between the top and bottom anchor. Rao et al. (1991), Rao and Prasad (1993), and Lutenegger (2009) investigated the effect of relative anchor plate spacing, S/D, on the resulting failure mechanism and uplift capacity. Small scale studies by Rao et al. (1991), Rao and Prasad (1993) suggested that a relative plate spacing of 1.5 serves as the transition point from cylindrical shearing to individual plate breakout. Work by Lutenneger (2009) pointed to a relative plate spacing of 2.25 as the analytically-based transition point, but full scale testing of helical anchors characterized with S/D ranging from 0.75 to 3.0 did not indicate a sharp transition in capacity as predicted analytically. Nonetheless, the field tests by Lutenegger (2009) suggested that individual plate breakout governs the working stress resistance of helical anchors loaded in uplift in clayey soil. In practice, and in the absence of experience with anchor performance in a particular geologic unit, the capacity associated with each failure mechanism should be computed and the design capacity taken as the smaller of the two resulting values.

Available Methods for Estimation of Pullout Capacity

The methods available for estimating pullout capacity of helical anchors ranges from those based on theoretical failure mechanisms, empirical estimates based on in-situ, and tests empirical correlations to installation torque, each characterized with their own model bias and uncertainty. Although a complete review of the development and basis for each available method is beyond the scope of this paper, the following presents a brief overview of several methods selected for comparison to the observed loading test results. As discussed above, the individual plate breakout mechanism assumes that each helical plate acts independently, such that a localized upward bearing-type failure surface develops above the plate. Neglecting shaft resistance, as appropriate for square shaft anchor stems (Pack 2006), the uplift resistance at failure, or the uplift capacity, is equal to the sum of the individual plate capacities, and is given by:

, ,1

n

ult cu u i p ii

R N s A=

= ⋅ ⋅∑

[2]

where Ncu

= uplift breakout factor, and Ap is the

area of the ith helical plate. Mooney et al. (1985) summarize the values of N

cu back-calculated

from loading tests, which vary as a function of H/D. For the present case, the value of 9.4 is adopted based on the embedment depth of the anchors and the findings presented in Mooney et al. (1985). The undrained shear strength at each anchor plate location, s

u,i,

was taken from the corresponding su profile

in Fig. 5 and averaged over plus and minus one plate diameter. The cylindrical shearing method assumes that the uppermost plate acts individually, and that a cylindrical shearing surface develops within the surrounding soil between the bottom and topmost anchors. The uplift capacity (neglecting shaft resistance) estimated by the cylindrical shear method is computed using:

Rult

= Ncu • S

u,i • A

p,top + π • D

avg • S

u,avg • (H

bottom- H

top) [3]

where Hbottom

and Htop

equal the depth to the bottom- and uppermost anchor, D

avg = average

plate diameter, su,avg

= the average undrained shear strength over the length of the assumed cylinder (Fig. 5). Hoyt and Clemence (1989) report the mean bias, defined as the ratio of


square shaft in units of inches. Eqn. 5 was developed for the uplift resistance observed at a displacement equal to a tenth of the average helix plate diameter. Because the torque was not measured for the anchors described herein, the observed capacity of the test anchors cannot be compared to the capacity produced by Eqn 5.

Comparison of Observed and Predicted Capacities

In an effort to determine appropriate methods for estimating the uplift resistance of helical anchors in desiccated Beaumont clay, a comparison of the selected design methods outlined above to the full scale load test data is presented. The undrained shear strength profiles presented in Fig. 5 were used to estimate anchor capacity for use with the individual breakout and cylindrical shear methods; SPT blow counts were averaged over the plate elevations for use with the Eqn 4. Table 3 presents the comparison of prediction model bias and COV in bias for each test anchor. Overall, capacity methods based on theoretical failure mechanisms appear to best predict the observed capacity (indicated by an average bias of near unity). However, the average bias is skewed by the apparently spurious capacity exhibited by Anchor S7. If Anchor S7 is excluded from the mean, the individual plate breakout method remains relatively accurate, but the cylindrical shear

measured and predicted capacity, and the COV in bias for the individual bearing and cylindrical shear methods as 1.56 and 82 percent, and 1.50 and 79 percent, respectively, based on 91 pullout tests of anchors in sands, silts, and clays.

Despite the large measurement errors associated with the Standard Penetration Test (SPT), the SPT blow count, N

SPT, has been

shown to correlate with the undrained shear strength (e.g., Terzaghi and Peck 1967, Hara et al. 1974), albeit with large transformation error. Therefore, the uplift capacity of individual plates in cohesive soils should be somewhat correlated to N

SPT. Perko (2009) presents a

correlation of the ultimate bearing pressure, qult

, of an individual anchor plate in clay to the SPT blow count corrected to 70 percent efficiency:

qult

= 11 • λ

SPT • N

SPT [4]

where λSPT

is a conversion factor (equal to 6.2 kPa/blow/0.3 m or 0.9 psi/blow/ft). The ultimate bearing pressure, equal to the product of uplift breakout factor and undrained shear strength shown in Eqn 2, is estimated for each anchor plate, multiplied by the area of the plate, and summed to produce the total uplift resistance of the anchor. Perko (2009) indicated that the prediction bias and COV in Eqn. 4 equaled 1.03 and 46 percent based on an evaluation of 47 full-scale load tests. Limited bearing pressure data for pullout testing suggested that no significant difference existed between the compression and uplift bearing pressure predictions, indicating that Eqn 4 could be used for uplift estimates (Perko 2009).

The well-recognized correlation of helical anchor capacity to installation torque presented by Hoyt and Clemence (1989) has been accepted by the industry because the capacity can be inferred directly during construction. Perko (2009) presented an updated capacity-to-torque correlation for 98 helical anchors loaded in uplift as a function of the effective shaft diameter, d

eff, defined as the diameter of the

anchor shaft or hypotenuse of a square shaft:

1.0123.1t effK d −= ⋅ [5]

where Kt = the ratio of capacity to installation

torque in units of ft-1 and deff

is the effective shaft diameter, defined as the diameter of a circular shaft or the hypotenuse of a

[TABLE 3] Comparison of Prediction Bias and Uncertainty in selected Uplift Capacity Models for Test Anchors

Anchor Designation

Individual Plate

Breakout

Eqn. 2

CylindricalShear

Eqn. 3

SPTCorrelation

Eqn. 4

S3 1.13 0.92 1.27

S5 0.85 0.70 1.01

S6 0.79 0.65 0.79

S7 1.83 1.50 1.81

Mean Bias 1.15 0.94 1.22

COV in Bias (%)

44 43 40


method over-predicts pullout capacity by 32 percent. Interestingly, the SPT correlation to pullout capacity is also relatively accurate (mean bias = 1.03) once Anchor S7 is excluded. Equations 2, 3, and 4 also appear to exhibit similar prediction uncertainty, ranging from 40 to 44 percent. Although high, this uncertainty should not be surprising given the total uncertainty in undrained shear strength (53 percent); thus, it appears that these three methods may be used confidently within the range of uncertainty in s

u for Beaumont clay.

SUMMARY AND CONCLUSIONSHelical anchors were selected to provide uplift reaction forces for footing load tests in Beaumont clay. Due to the goals of this research-related full-scale test program, the test site subsurface was well characterized, offering a level of geotechnical detail that is seldom available in practice. Because the uncertainty in undrained shear strength was characterized with a high degree of sophistication, this case history offers a clear comparison to the uncertainty in capacity model predictions as presented herein.

The results of seven instrumented uplift loading tests on square shaft helical anchors were presented over a range in loading duration and displacements. Due to the number of anchor stem couplings, load tests results were corrected for the apparent slack introduced in the coupling bolt connections. The slack correction technique used herein may offer practitioners a ready alternative for evaluation of uplift loading tests on helical anchors. The corrected test results indicate that when taken to large displacements, the load-displacement behavior of the anchors exhibited a significant degree of softening, and followed the stress-strain behavior exhibited by recompression-consolidated triaxial test specimens. When normalized against the ultimate resistance, the resistance reduced up to 12 percent at 30 mm (1.18 in) of post-peak displacement. Capacity prediction models based on theoretical failure mechanisms provided the best overall prediction accuracy, however, the SPT-based capacity model appeared relatively accurate as well. The cylindrical shear, individual plate breakout, and SPT-based capacity models provided variability in prediction accuracy of 40 to 44 percent, less than the uncertainty in undrained shear

strength at the test site. The findings presented herein indicate that these models may be used confidently within the uncertainty in undrained shear strength of Beaumont clay. These results point to the well-known importance of adequate test site characterization for design of foundation elements.

ACKNOWLEDGEMENTSThe authors would like to acknowledge Hayward Baker, Inc., for funding of the test site characterization and load test program. The writers thank Fugro Southwest for the donation of X-ray photographs of undisturbed samples, and Hart Crowser, Inc., for the use of their laboratories for testing the site soils. The second author gratefully acknowledges the support of the School of Civil and Construction Engineering, Oregon State University, for funding of her graduate studies.

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7. Hoyt, R.M. and Clemence, S.P. (1989) “Uplift Capacity of Helical Anchors in


Soil,” Proceedings of 12th International Conference on Soil Mechanics and Foundation Engineering, Rio de Janeiro, Brazil. Pp. 1019-1022.

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12. Lutenegger, A.J. (2009) “Cylindrical Shear or Plate Bearing? – Uplift Behavior of Multi-Helix Screw Anchors in Clay,” Contemporary Issues in Deep Foundations, GSP 185, ASCE, pp. 456-463.

13. Lutenegger, A.J. (2011) “Historical Development of Iron Screw-Pile Foundations: 1836–1900,” Int. J. for the History of Eng. & Tech., Vol. 81 No. 1, pp. 108–28.

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15. Meyerhof, G.G. and Adams, J.I. (1968) “The Ultimate Uplift Capacity of Foundations,” Canadian Geotechnical Journal, 5(4), pp. 224-244.

16. Mitsch, M.P. and S.P. Clemence. (1985) “The Uplift Capacity of Helix Anchors and Sand.” Uplift Behavior of Anchor Foundations in Soil, ASCE, pp. 26–47.

17. Mooney, J.S., Adamczak, S., and Clemence, S.P. (1985) “Uplift Capacity of Helix Anchors in Clay and Silt,” Uplift Behavior of Anchor Foundations in Soil, ASCE pp. 48–72.

18. O’Neill, M.H. (2000) “National Geotechnical Experimentation Site - University of Houston,” National Geotechnical Experimentation Sites, GSP No. 93, ASCE, Reston, Virginia. 72-101

19. O’Neill, M.H. and Yoon, G.L. (2003) “Spatial Variability of CPT Parameters at

University of Houston NGES,” Probabilistic Site Characterization at the National Geotechnical Experimentation Sites, GSP 121, ASCE, Eds Fenton & Vanmarcke, Reston, VA. pp. 1-12.

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21. Perko, H.A. (2009) Helical Piles: A Practical Guide to Design and Installation, John Wiley & Sons, Inc., Hoboken, NJ., 512 p.

22. Phoon, K.K. and Kulhawy, F.H. (1999) “Evaluation of Geotechnical Property Variability,” Canadian Geotechnical Journal., Vol. 36, No. 4, 625-639.

23. Rao, S.N. and Prasad, Y.V.S.N. (1993) “Estimation of Uplift Capacity of Helical Anchors in Clays.” Journal of Geotechnical Engineering, Vol. 119, No. 2, pp. 352–357.

24. Rao, S., Prasad, Y.V.S.N. and Veeresh, C. (1993) “Behavior of Embedded Model Screw Anchors in Soft Clays,” Geotechnique, 43, 605-614.

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27. Stuedlein, A.W. and Holtz, R.D. (2010) “Undrained Displacement Behavior of Spread Footings in Clay,” The Art of Foundation Engineering Practice, Honoring Clyde N. Baker, Jr., GSP No. 198, ASCE, 653-669.

28. Stuedlein, A.W., and Holtz, R.D. (2012) “Analysis of Footing Load Tests on Aggregate Pier Reinforced Clay,” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 138, No. 9. pp. 1091-1103.

29. Stuedlein, A.W., Kramer, S.L., Arduino, P., and Holtz, R.D. (2012a) “Geotechnical Characterization and Random Field Modeling of Desiccated Clay,” Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 138, No. 11. pp. 1301-1313.


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Strain Distributions in Full-Scale Energy Foundations(DFI Young Professor Paper Competition 2012)John S. McCartney, Ph.D., P.E,.Assistant Professor, University of Colorado Boulder. Department of

Civil, Environmental, and Architectural Engineering. Boulder, CO, USA; [email protected]

Kyle D. Murphy, M.S., E.I.T., Graduate Research Assistant, University of Colorado Boulder.

Department of Civil, Environmental, and Architectural Engineering. Boulder, CO, USA;

[email protected]

ABSTRACTThis paper focuses on the thermo-mechanical response of two full-scale energy foundations installed at the new Denver Housing Authority Senior Living Facility in Denver, Colorado. The energy foundations were formed by attaching heat exchanger tubes to the inside of the reinforcement cages of drilled shafts. The heat exchange tubes were connected to a ground-source heat pump system, which circulates a methanol-water mixture through the tubing to absorb or shed heat into the foundation and surrounding soil or rock. Instrumentation was incorporated to assess the heat exchange response of the foundations as well as the thermo-mechanical strains during construction and typical building operation. The temperature changes within the foundations are stable during heating and cooling operations and the corresponding thermal axial strains are within acceptable limits. The thermal axial strain profiles measured for both foundations follow trends expected for end-bearing boundary conditions with greater strains near the top of the foundations (upward expansion). The mobilized thermal expansion coefficients inferred from the instrumentation confirm that side shear stresses provide resistance to thermally induced movements. The results from this study indicate that energy foundations can be implemented in new buildings to gain improved heat exchange capabilities without major impacts on the foundation performance, for little added installation cost.

INTRODUCTIONEnergy foundations are drilled shafts that incorporate ground-source heat exchange elements, which can be used to transfer heat to or from the ground to the building (Brandl 2006; Laloui et al. 2006; McCartney 2011). Ground-source heat exchange systems exploit the relatively constant temperature of the ground to improve the efficiency of heat pump systems for heating and cooling of buildings. Traditional geothermal systems typically require a series of small-diameter, deep boreholes, which are installed outside of the building footprint. The additional drilling costs of these boreholes can be prohibitive (Hughes 2008). To counter this problem heat exchange elements can be incorporated into deep foundation elements, which are already being installed, to avoid this additional installation cost. Although energy foundations may not provide the full amount of energy required to heat and cool residential and commercial buildings, they may provide sufficient heat exchange to cover the base heating and cooling

load for the building, which is typically 10 to 20 percent of the peak heating or cooling load. In this case, a conventional heating or cooling system would not be required except during peak heating or cooling events.

To better understand the behavior of energy foundations during building operation, this study presents data from strain gauges and thermistors installed within a pair of full-scale energy foundations in a newly constructed building in Denver, Colorado. The instrumentation results are used in this paper to evaluate typical temperature variations within the foundations during heating and cooling operations, along with the corresponding changes in axial strain distributions.

BACKGROUNDAs a structural element is heated and cooled, thermal axial strains will be superimposed onto mechanical strains already present in the element. Limited knowledge has been collected regarding thermo-mechanical strains in energy foundations under thermal loading conditions.


Several experimental studies have been performed in the laboratory using centrifuge-scale models of energy foundations in order to identify mechanisms of soil-structure interaction in energy foundations (McCartney et al. 2010; McCartney and Rosenberg 2011; Stewart and McCartney 2012). Several full-scale energy foundations have been installed throughout Europe and Asia, although there have only been two well-documented thermo-mechanical tests on full-scale foundations to date; in Switzerland (Laloui et al. 2006), and in the UK (Bourne-Webb et al. 2009; Amatya et al. 2012). In these studies, proof load tests along with heating/cooling tests were used to evaluate the thermo-mechanical stress-strain response in the foundations. Data from these tests were used to develop soil-structure interaction design tools (Knellwolf et al. 2011). Other studies on full-scale foundations included evaluations of the efficiency of energy extraction (Ooka et al. 2007; Wood et al. 2009; Adam and Markiewicz 2009) and system thermal conductivity tests (Ozudogru et al. 2012). However, these studies did not evaluate the performance of energy foundations under typical building operation conditions.

INSTRUMENTED ENERGY FOUNDATIONS

Building and Conventional Ground-Source Heat Pump System Descriptions

Two of the sixty drilled shaft foundations installed as part of the construction of the new Denver Housing Authority senior residential facility, in Denver Colorado, were converted into energy foundations as part of a demonstration project for this new technology. The two energy foundations were coupled into a conventional ground-source heat pump (GSHP) system which was already being incorporated into the building. The conventional GSHP system consists of forty 101.6 mm diameter boreholes, each extending to depths of 143 m (469 ft) below grade, drilled in a parking lot outside of the building footprint. A heat exchanger loop, composed of 44 mm (1.75 in) diameter polyethylene tubing formed in a U-shape, was installed into each of the boreholes. The boreholes were backfilled with sand-bentonite after installation of the heat exchanger tubing. A heat pump is used to absorb or reject heat into fluid circulating through the heat exchanger tubing.

The network of borehole heat exchangers in the conventional GSHP system is capable of providing approximately 75 thermal tons (263.5 kW-hr) to the heat pump, which is sufficient to provide the peak heating and cooling load for the building. To absorb this thermal load, the heat pump was designed to circulate a supply line fluid temperature through the borehole network of 32.2 °C (90°F) during cooling operations or 1.7 °C (35°F) during heating operations. The fluid within the heat exchange system consists of a 10% methanol-water mixture to prevent freezing during building heating operations. The supply and return lines from the borehole field are connected through a set of two manifolds that run to the inlet and outlet lines of the heat pump. In order to avoid preferential flow through the heat exchangers in the energy foundations (which are much shorter than the deep boreholes), the flow of heat exchanger fluid to the energy foundations was restricted to approximately 50% using ball valves.

Subsurface Conditions

A series of 10 exploratory borings extending to depths ranging from 8.8 m to 11 m (29 ft to 36 ft) below finished grade was performed throughout the site. The conditions encountered in each of the borings were similar, with a typical profile shown in Fig.1. Urban fill extends from grade to a depth of approximately 3 m (10 ft) and consists of slightly moist, medium dense, clayey sand with gravel. Beneath the fill, a layer of non-expansive, medium dense, sand and gravel with silt seams extended to a depth of approximately 7.6 m (25 ft) below grade. Below this layer, to the maximum depth explored of 11 m (36 ft), the subsurface conditions consisted of hard sandy claystone bedrock from the Denver formation. The characteristics of the soil layers measured during the site investigation are listed in Table 1. These results indicate that the urban fill layer is relatively soft, while the sand and gravel layer. Swell potential tests on the fines fraction indicates that they are non-expansive. Perched groundwater was encountered in three of the ten boreholes at depths ranging from 6.4 m to 8.2 m (13 ft to 27 ft) below grade level. Because of the potential for caving during drilling through the overburden and possible perched ground water conditions, a cased-hole method was chosen for installation of the drilled shaft foundations at the site.


(b)

[FIG. 1] (a) Soil Stratigraphy and Foundation Instrumentation layout; (b) Plan view of Foundation layout for the building

Energy Foundations

Profiles of the two energy foundations evaluated in this study along with the different soil and rock strata are shown in Fig. 1(a), while a plan view of the foundation layout showing the location of the two energy foundations is shown in Fig, 1(b). Foundation A is located below an interior column while Foundation B is located directly under an exterior wall. Foundations A and B are both 910 mm (36 in) in diameter and extend to depths of 14.8 m, and 13.4 m (48.5 and 44 ft) respectively, and are bearing in the Denver formation (claystone). The foundations at the site function as rock-socketed, end-bearing elements in the bedrock. Foundation A is expected to carry a load of 3.84 MN (432 ton) and Foundation B is expected to carry a load of 3.65MN (410ton). Although the rock socket for Foundation B is shorter than that of

(a)


Foundation A because of difficulty in drilling in the wet claystone, both are within their design depth tolerance set by the structural engineer. Each shaft contains a full-length reinforcing cage 760 mm (30 in) in diameter with nine #7 (22 mm) vertical reinforcing bars tied to #3 (9.5 mm) lateral reinforcing hoops spaced 0.36 m (14 in) on center. A reinforced slab on grade with a thickness of 150 mm (6 in) was cast at grade level.

The energy foundations were coupled with a traditional deep borehole geothermal system that was already being installed to provide heating and cooling for the building, in order to demonstrate the feasibility of energy foundations. The heat exchanger system in each energy foundation consists of 44 mm (1.75 in) diameter polyethylene tubing attached to the inside of the reinforcing cages. Foundation A contains a total of 82.3 linear meters (270 ft) of tubing configured into three loops running the length of the reinforcing cage, as shown in Fig. 2(a). Similarly, Foundation B contains of a total of 109.7 linear meters (360 ft) of polyethylene tubing arranged in four loops running the length of the reinforcing cage, shown in Fig. 2(b).

The heat exchanger tubing was attached to the interior of the reinforcing cage using wire ties connected at every other hoop along the length of the reinforcing cage. The heat exchanger tubing was routed along the inside perimeter of the reinforcing cage to avoid crossing the diameter of the cage, which could block concrete flow or cause segregation of concrete. Equal angular spacing of the tubing was maintained to ensure relatively uniform temperature along the circumference of the shafts. The tubing was installed away from the vertical reinforcement to

ensure an adequate bond between the concrete and reinforcement and to ensure good contact between the concrete and the tubing itself. The supply and return lines for each loop were arranged on opposite sides of the reinforcing cage to reduce thermal short-circuiting, which occurs when heat flows directly from the inlet

TABLE 1. Soil Layer Characteristics Measured during Field Investigation

Soil LayerDepth below grade level

(m)

SPT N-Value (blows per 300 mm)

Gravimetric water content

(%)

Dry density (kN/m3)

Fines content (Smaller than

75 μm)

Average plasticity

index of fines

Urban Fill (Clayey and Silty Sands with Gravel)

0.0 – 3.0 7 to 8 10 to 14 14.4 to 16.5 20 24

Sand and Gravel with Silt Lenses

3.0 – 7.6 19 to 28 1 to 8 18.1 to 19.2 2 to 16 Not measured

Claystone 7.6 +50 blows/200 mm

Not measured Not measured Not applicable Not applicable

(a)

(b)

[FIG. 2] Heat Exchanger tubing attached to reinforcement cages: (a) Foundation A, (b) Foundation B


of the loop to the outlet of the loop before the fluid has circulated through the entire energy foundation.

Instrumentation

An instrumentation system was incorporated into the two foundations to monitor the distributions of temperature and axial strain with depth, as well as the supply and return temperatures of the heat exchanger fluid. Six vibrating wire concrete-embedment strain gauges were installed in each energy foundation at the locations shown in Fig. 1(a). The concrete embedment vibrating wire strain gauges (VWSG) (Model 52640299 from Slope Indicator of Mukilteo, WA) were oriented longitudinally and attached to the lateral reinforcing hoops then cast in concrete during construction. The VWSGs were positioned at depths within the shaft so that the cumulative strain distribution throughout the entire shaft length could be characterized. Each VWSG contained a thermistor to monitor temperature in the concrete at each sensor location. Cables from each sensor were routed from the energy foundations to the mechanical room prior to casting of the floor slab. A Geokon, Inc datalogger (Model 8002-16 LC-2×16) was used to record data hourly from December 29, 2011 to April 18, 2012. During installation, a VWSG located at 3.2 m (10.5 ft) below grade in Foundation A was damaged. Although the VWSG at this depth did not function, the corresponding thermistor remained operational. In addition to the instrumentation in the foundations, four pipe-plug thermocouples were installed in the plumbing manifold to record inlet and outlet fluid temperatures for each of the two energy foundations. Fluid temperature measurements were recorded every five minutes using Lascar EL-USB-TC data loggers to capture the intermittent and long-term operations of the heat pump and the energy foundations.

RESULTS

Thermal Behavior

Seasonal variations in ground temperature beneath the building were characterized using measurements from the thermistors prior to operation of the GSHP system, as the foundations were installed in October 2010 but the heat pump was not operational until

March 2012. Typical temperature profiles at different times throughout the year shown in Fig. 3 indicate a decrease in seasonal variability of temperature with increasing depth and a relatively constant ground temperature below a depth of 6 m (20 ft), which is consistent with observations of Moel et al. (2010). Foundation A exhibited less seasonal variability due to the location within the building footprint and was relatively insulated by the concrete floor slab. Foundation B was located at the outer edge of the building and consequently the temperature in the upper portion of the foundation was more susceptible to fluctuations in outside ambient air temperature. These observations demonstrate that ground temperatures in the winter months will be warmer than surface air temperatures and can be used as a source of heat. Conversely, the subsurface ground can be used as a heat sink in warm months when ground temperatures are lower than surface air temperatures.

(a)

(b)

[FIG. 3] Seasonal Ground Temperature fl uctuations measured after installation of the foundations but before operation: (a) Foundation A, (b) Foundation B


The temperatures of the heat exchange fluid entering and exiting the foundations during heat pump operation were monitored using pipe-plug thermocouples installed in the inlet and outlet ports of the manifold for each of the two energy foundations. The temperature of the heat exchange fluid entering the foundations is controlled by the heat pump. Because the temperature of the ground is beneath about 6 m (20 ft) is at a constant temperature, the fluid will cool off if the temperature of the heat exchange fluid is above the average ground temperature, while the fluid will heat up if the temperature of the heat exchange fluid is below the average ground temperature. In this manner, the fluid flowing through the tubing in the energy foundations is able to extract or dump heat into the ground. The heat exchanger fluid temperatures as a function of time are shown in Figs. 4(a) and 4(b) for Foundations A and B, respectively. The difference in the inlet and outlet temperatures, ΔT

out-in, also shown in

Fig. 4, reflects the magnitude of heat exchange. Further, the sign of ΔT

out-in reflects whether the

GSHP system is in heating or cooling mode. Although Foundation A appears to be in cooling mode during the winter months, the building was not occupied until March 2012. Further, the pipe-plug thermocouples in the manifold were not properly insulated until February 23, 2012, before which the temperatures of the heat exchange fluid measured were affected by the ambient temperature of the mechanical room. After March 2012, the two foundations show similar behavior consistent with normal operation of conventional heat

pump systems. The reason that the inlet and outlet temperature show spikes is that the heat pump only pumps heat exchange fluid through the GSHP system when it is trying to change the temperature of the building. Typical of spring weather conditions in Denver, the system transitioned frequently from heating to cooling.

The heat exchange capacity of the energy foundations can be assessed by evaluating the values of ΔT

out-in observed in Fig. 4 and the

temperatures within the foundation. Thermal energy is withdrawn from the ground to heat the building by introducing a cold fluid to the heat exchange loops within the energy foundation, which absorbs heat from the ground and returns to the heat pump at a warmer temperature. Larger values of ΔT

out-in

reflect a greater amount of heat gained or lost from the ground. Brandl (2006) indicates that a temperature difference of ΔT

out-in > 2°C

(3.6°F) between supply and return lines of the heat exchanger fluid is sufficient for normal operation of a heat pump, as long as the temperature of the ground does not start to change significantly. The data in Fig. 4 indicates that the maximum difference in inlet and outlet temperatures observed in this project was approximately 10°C (18°F), indicating potential for good heat exchange. The inlet and outlet temperatures of the two foundations are similar after March even though Foundation B had one more heat exchange loop. This indicates that the number of loops may lead to a more uniform temperature distribution in the foundation, but may not improve heat exchange. Further

(a)

[FIG. 4] Inlet and Outlet Temperatures of the fl uid circulating within the Heat Exchange loops in the Energy foundations: (a) Foundation A, (b) Foundation B

(b)


assessment of the long-term thermal response of the foundations is required to confirm the impact of the number of heat exchangers in energy foundation.

The thermistors at different depths within each of the foundations were used to monitor temperatures within the foundation on an hourly basis, as shown in Figs. 5(a) and 5(b) for Foundations A and B, respectively. Once the heat pump operation started in March 2012, the temperature distributions throughout the length of both energy foundations were relatively uniform. The only exception is the top of Foundation B, which showed slightly greater changes in temperature than the rest of the foundation. This is because Foundation B is located under the corner of the building and the top of the foundation is sensitive to variations in ambient air temperature. However, the effect of the ambient outside air temperature

on the temperature of the foundation is much less significant after heat pump operations started than before (see changes in temperature observed in Fig. 3).

Thermo-Mechanical Behavior

An important aspect of this study was to evaluate thermally induced axial strains and stresses in the energy foundations caused by temperature changes. The first step to define the thermal axial strain is to isolate the impact of the mechanical loading due to the self-weight of the building. The structure was completed in October 2011 (i.e., the dead load was fully applied), and no further significant changes in mechanical strain occurred after this time (i.e., the live load is a small fraction of the dead load). The value of mechanical strain after this point is constant, assuming that there is negligible drift in the mechanical strain over

(a)

(c)

[FIG. 5] Data from Instrumentation embedded in the foundations during heat pump operation: (a) Temperature fl uctuations in Foundation A; (b) Temperature fl uctuations in Foundation B; (c) Thermal Axial Strain in Foundation A; (d) Thermal Axial Strain in Foundation B

(b)

(d)


time. Accordingly, the measured strain values ε

m were zeroed by subtracting the mechanical

axial strain εmechanical

. Next, the zeroed strain values were corrected to account for thermal effects on the gauge. During heating of the gauge, the vibrating wire within the VWSG will expand, causing the VWSG to appear to go into compression instead of correctly showing expansion. The thermal axial strains were defined from the measured strains as follows:

εΤ = (εm- ε

mechanical) +α

s ∆T [1]

where αs is the coefficient of linear thermal

expansion of the steel wire in the gauges (-12 με/°C) and ∆T is the change in temperature of the foundation.

A global thermal correction factor was also applied to all of the gauges to account for the impact of the differential expansion of the reinforced concrete and the steel body of the VWSG (i.e., the tubing that separates the vibrating wire from the surrounding concrete). Although heating tests on the vibrating wire strain gauges before installation indicate that they all have similar thermal expansion behavior, it was not possible to measure the global thermal correction factor experimentally after installation and concrete curing because of scheduling and access restrictions to the site during construction. The ideal methodology to measure the global thermal correction factor would have involved measuring the axial heave of the foundation during heating of the foundation before construction of the building and comparing this with the measured thermal axial strains using a soil-structure interaction analysis such as that of Knellwolf et al. (2011). In the absence of this type of test, the global thermal correction factor for the gauges was estimated in this study by evaluating the thermal axial strains during heating to check if they were less than the free expansion strain of reinforced concrete, given by:

εΤ,free= α

c ∆T [2]

where αc is the coefficient of linear thermal

expansion of reinforced concrete, which was assumed to be 10 με/°C, a reasonable value for concrete with quartz aggregate (Choi and Chen 2005; Stewart 2012). Although it is impossible for the reinforced concrete foundation to expand or contract more than given by Eqn. [2], it is possible for the thermal axial strains in the foundation to be less than this limit because of

soil-structure interaction (Amatya et al. 2012). The same global thermal correction factor of 0.5 was applied to all of the gauges. This value was defined so that the maximum thermal axial strain observed in both foundations was less than the strain given by Eqn. [2]. Although a smaller value of the global thermal correction value could also have been applied using this same argument, the magnitude of thermal axial strains near the toe of Foundations A and B are consistent with those measured in a centrifuge model test performed by Stewart (2012) on an end-bearing energy foundation having similar prototype dimensions. Nonetheless, the choice of the global thermal correction factor can have a major impact on the magnitudes of thermal axial strains and stresses, so it should be better characterized in future studies. Regardless of the magnitude of the global thermal correction factor, the trends in thermal axial strain with depth are unaffected by this correction, as the same factor was applied to all of the gauges. The corrected thermal axial strains ε

T,c are

shown in Figs. 5(c) and 5(d) for Foundations A and B, respectively. In these figures, positive strains indicate compression while negative strains indicate expansion.

In order to define profiles of thermal axial strain representative of the energy foundation performance, instances in time at which the energy foundations had experienced average changes in temperature of 1°C (1.8 °F) increments were identified. The temperature profiles for these average temperature increments are shown in Figs. 6(a) and 6(b) for Foundations A and B, respectively. For the period of data collected for this study, the maximum extents of temperature change corresponded to ∆T = -5°C (-9°F) during building heating and ∆T = 3°C (5.4°F) during building cooling, with respect to the initial temperature of the foundation at startup of the heat pump. The slight differences in temperature at the top of Foundation B compared to the rest of the foundation are due to the influence of the outside air temperature. The profiles of thermal axial strain corresponding to the average changes in temperature are shown in Figs. 6(c) and 6(d) for Foundations A and B, respectively. During cooling of the energy foundations (i.e., heating of the building), axial contraction occurs as reflected in the positive sign of the strain measurements. Conversely, during heating


(a)

(c)

(e)

(b)

(d)

(f)

[FIG. 6] Profiles of Temperature, Thermal Axial Strain, and Thermal Axial Stress on the Energy Foundations during heat pump operation: (a) Temperature profiles for different average changes in foundation temperature in Foundation A; (b) Temperature profiles for different average changes in foundation temperature in Foundation B; (c) Thermal Axial Strain in Foundation A; (d) Thermal Axial Strain in Foundation B; (e) Thermal Axial Stress in Foundation A; (f) Thermal Axial Stress in Foundation B


of the energy foundations (i.e., cooling of the building), axial expansion occurs as reflected in the negative sign of the strain measurements. The maximum thermal axial tensile axial strain was 26.2 µε in Foundation B during a temperature change of ∆T = 5°C (9°F), while the maximum thermal axial compressive is -27.4 µε in Foundation A under a temperature change of ∆T = 3°C (5.4°F). These thermal axial strain magnitudes are much less than limits for reinforced concrete set by the ACI 318-08 code (4000 µε for beams). The shapes of the thermal axial strain profiles in both energy foundations during cooling of the building are similar to those observed by Stewart (2012) for end-bearing foundations characterized in a geotechnical centrifuge. Specifically, the smallest strain is observed at the bottom of the foundation, indicating that the foundations are expanding upwards from the relatively rigid bedrock. For the maximum change in temperature of 3°C (5.4 °F) observed in the data collected to date during cooling of the building (heating of the foundation), a maximum upward axial displacement of 0.003 mm (.00012 in) is expected, which is unlikely to cause damage to the building.

The thermal axial stresses induced in the foundation by temperature changes can be calculated from the measured thermal axial strains at the location of each gauge as follows:

σT= E (εT - α

c ∆T) [3]

where εT is the thermal axial strain after

application of the global thermal correction factor and E is the Young’s modulus of reinforced concrete, which is assumed to be 30 GPa (4,350 ksi) based on local experience with this type of concrete mix design. The calculated thermal axial stress profiles are shown in Figs. 6(e) and 6(f) for Foundations A and B, respectively. The locations of the smallest strain in the energy foundation correspond to the locations of the maximum thermal axial stress. Compressive (positive) thermal axial stresses occur during cooling of the building (heating of the foundation) when the axial expansion of the foundation is restrained by the overlying building, underlying bedrock, or the side shear resistance of the soil surrounding the foundation. With the exception of the high thermal axial stresses noted at the top of Foundation B during heating, which are likely

due to the higher ambient temperature at this time, the stress profiles indicate that the highest stresses are at the bottoms of both foundations. The decrease in compressive stress with height is due to resistance to thermal axial expansion from the mobilization of side shear stresses. It is possible that the smaller stresses noted in Foundation B between depths of 2 and 6 meters (6.5 and 19.5 ft) may have occurred due to residual stresses encountered during cooling of the foundation, which deserves further study.

The maximum compressive and tensile profiles of thermal axial strain observed during heating and cooling of the building (cooling and heating of the energy foundation) were superimposed upon the strains due to mechanical loading to define the total thermo-mechanical axial strains, as shown in Figs. 7(a) and 7(b) for Foundations A and B, respectively. The mechanical strain profiles are difficult to interpret; it was expected

(a)

(b)

[FIG. 7] Axial Strains induced by mechanical loading along with those induced by thermo-mechanical loading during heating and cooling operations: (a) Foundation A, (b) Foundation B


that the greatest axial strain would be observed near the top of the foundation, and would either decrease with depth if there was side shear resistance or remain uniform with depth if there was negligible side shear resistance. However, both foundations show an inconsistent mechanical strain profile with depth. This is attributed partially to the impact of curing on the calculation of the mechanical strains in the foundations from the raw VWSG readings. Nonetheless, the magnitudes of the average mechanical strains are consistent with the design axial loads for the foundations, assuming a Young’s modulus of 30 GPa (4,350 ksi). Regardless of the shapes of the mechanical strain profiles, it is clear that heating and cooling operations lead to a shift in the thermo-mechanical strain profiles to the left or right. However, the thermal axial strains are not as significant as those generated due to the self-weight of the building, and the magnitudes of the thermal axial stresses are well below those that may cause structural damage. Further monitoring is needed to see if thermal axial strains during cooling lead to development of tensile strains near the bottom of the foundations.

The thermal axial strains are shown as a function of temperature for Foundations A and B in Figs. 8(a) and 8(b), respectively. Hysteresis is noted in the strain measurements during heating and cooling, which is likely due to the presence of different materials in and around the gauges. Nonetheless, the strain measurements follow a linear trend with temperature. The slopes of the thermal axial strain versus temperature plots can be used to define the mobilized coefficient of thermal expansion for the reinforced concrete at the depth of each of the gauges, as summarized

in Fig. 8(c).

If the soil surrounding the foundation did not provide any resistance to movement, and if the building did not provide any constraint, then the mobilized coefficient of thermal expansion would be equal that for free expansion (-10 µε/°C). However, the results in this figure clearly show that all of the gauges have an average mobilized coefficient of thermal expansion less than this value. The mobilized coefficients of thermal expansion are closest to that representing free expansion near the top of the foundation, indicating that the overlying building provides less constraint for thermal expansion than the underlying bedrock.

CONCLUSIONSThe results from a thermo-mechanical evaluation of two full-scale energy foundations during typical operation of a building in Denver, Colorado indicate potential for

(a)

(b)

(c)

[FIG. 8] (a) Temperature vs. Strains for Foundation A; (b) Temperature vs. Strains for Foundation B; (c) Mobilized Thermal Expansion Coefficients


incorporation of energy foundation technology in drilled shaft construction. During typical heating and cooling operation, the magnitudes of thermal axial strains measured are within acceptable limits. Further, the total strain magnitudes during mechanical and thermal loading are well within industry accepted limits. Analysis of data collected from strain gauges embedded in the energy foundations indicates that the magnitudes and trends of thermal axial strains and stresses are consistent with end-bearing foundations and are not expected to lead to structural issues. Overall, the results from this study indicate that energy foundations can be implemented in new buildings to gain improved heat exchange capabilities for little added installation cost.

ACKNOWLEDGEMENTSThe authors acknowledge the support of Milender-White Construction Company, KL&A Structural Engineers, AMI Mechanical, Rocky Mountain Geothermal, and the Denver Housing Authority for agreeing to incorporate the energy foundations into the building. Financial support from the National Science Foundation grant CMMI 0928159 is appreciated.

REFERENCES1. Adam, D. and Markiewicz, R. (2009). “Energy

from Earth-Coupled Structures, Foundations, Tunnels and Sewers.” Géotechnique. 59(3), 229–236.

2. Amatya, B.L., Soga, K., Bourne-Webb, P.J., Amis, T. and Laloui, L. (2012). “Thermo-mechanical Behaviour of Energy Piles.” Géotechnique. 62(6), 503–519.

3. Bourne-Webb, P., Amatya, B., Soga, K., Amis, T., Davidson, C. and Payne, P. (2009). “Energy Pile Test at Lambeth College, London: Geotechnical and Thermodynamic Aspects of Pile Response to Heat Cycles.” Géotechnique 59(3), 237–248.

4. Brandl, H. (2006). “Energy Foundations and other Energy Ground Structures.” Géotechnique. 56(2), 81-122.

5. Choi, J.H., and Chen, R.H.L. (2005). Design of Continuously Reinforced Concrete Pavements using Glass Fiber Reinforced Polymer Rebars. Publication No. FHWA-HRT-05-081. Washington, D.C.

6. Hughes, P.J. (2008). Geothermal (Ground-Source) Heat Pumps: Market Status, Barriers to Adoption, and Actions to Overcome Barriers. Oak Ridge Nat. Lab. Report ORNL-2008/232.

7. Knellwolf, C. Peron, H., and Laloui, L. (2011). “Geotechnical Analysis of Heat Exchanger Piles.” ASCE Journal of Geotechnical and Geoenvironmental Engineering. 137(10). 890-902.

8. Laloui, L., Nuth, M., and Vulliet, L. (2006). “Experimental and Numerical Investigations of the Behaviour of a Heat Exchanger Pile.” International Journal of Numerical and Analytical Methods in Geomechanics. 30, 763–781.

9. McCartney, J.S., Rosenberg, J.E., and Sultanova, A. (2010). “Engineering Performance of Thermo-Active Foundation Systems. GeoTrends: The Progress of Geological and Geotechnical Engineering in Colorado at the Cusp of a New Decade. ASCE Geotechnical Practice Publication 6. Goss, C.M., Kerrigan, J.B., Malamo, J.C., McCarron, M.O., and Wiltshire, R.L. pg. 27-42.

10. McCartney, J.S. and Rosenberg, J.E. (2011). “Impact of Heat Exchange on the Axial Capacity of Thermo-Active Foundations.” GeoFrontiers 2011. Dallas, TX. 10 pg.

11. McCartney, J.S. (2011). “Engineering Performance of Energy Foundations.” 2011 PanAm CGS Geotechnical Conference. Toronto, Canada. October 2-6, 2011. 14 pg.

12. Moel, M., Bach, P.M., Bouazza, A., Singh, R.M., and Sun, J.O. (2010). “Technological Advances and Applications of Geothermal Energy Pile Foundations and their Feasibility in Australia.” Renewable and Sustainable Energy Reviews. 14(9), 26832696.

13. Ooka, R., Sekine, K., Mutsumi, Y., Yoshiro, S. SuckHo, H. (2007). “Development of a Ground Source Heat Pump System with Ground Heat Exchanger Utilizing the Cast-in Place Concrete Pile Foundations of a Building.” EcoStock 2007. 8 pp.

14. Ozudogru, T., Brettmann, T., Olgun, G., Martin, J., and Senol, A. (2012). “Thermal Conductivity Testing of Energy Piles: Field Testing and Numerical Modeling.” ASCE GeoCongress 2012. Oakland, CA. March 25-29th, 2012. 10 pg. CD ROM.


15. Stewart, M.A. and McCartney, J.S. (2012). “Strain Distributions in Centrifuge Model Energy Foundations.” ASCE GeoCongress 2012. Oakland, CA. March 25-29th, 2012. 10 pg.

16. Stewart, M.A. (2012). Centrifuge Modeling of Strain Distributions in Energy Foundations. MS Thesis, University of Colorado Boulder.

17. Wood, C.J., Liu, H. and Riffat, S.B. (2009). “Use of Energy Piles in a Residential Building, and Effects on Ground Temperature and Heat Pump Efficiency.” Géotechnique 59(3), 287–290.


Performance-Based Reliability Design for Deep Foundations Using Monte Carlo Statistical Methods(DFI Student Paper Competition 2012)Haijian Fan, Research Assistant, Department of Civil Engineering, The University of Akron.

Akron, OH, USA. [email protected]

Robert Liang, Distinguished Professor, Department of Civil Engineering, The University of Akron.

Akron, OH, USA, [email protected]

ABSTRACTDeep foundation designs for service limit state are still deterministic in the current AASHTO LRFD Specifications. To address this deficiency, a performance-based reliability design methodology is developed using the Monte Carlo statistical techniques. In the proposed methodology, the design criteria are defined in terms of the allowable displacement. The spatial variability of soil parameters is considered in the proposed methodology by modeling soil parameters as random fields. Failure is defined as the event that the induced displacement exceeds the limiting displacement. The probability of failure by Monte Carlo approach is the ratio of the number of unsatisfactory performance events to the sample size. Three numerical examples are given to illustrate the application of the proposed methodology for laterally loaded and axially loaded drilled shafts, respectively. The spatial variability and correlation of soil properties were shown to exert significant influences on the foundation design.

INTRODUCTIONWith load and resistance factor design (LRFD) implemented by the Federal Highway Administration (AASHTO 2010), foundation designs have migrated from Level I codes (e.g., allowable stress design) to the current Level II codes (e.g., LRFD). In LRFD, the resistance factors for strength limit states are provided by the AASHTO (2010) Specifications. However, the current AASHTO Specifications still uses a deterministic approach for the service limit check. Unfactored loads are applied to evaluate the deformation response of deep foundations. If the displacement induced by the load effects is within the allowable limit, the service limit check is considered satisfactory. Clearly, in the current service limit check, uncertainties arising from various sources, such as soil properties, cannot be systematically taken into account. Current foundation designs in the AASHTO Specifications for the service limit state could be improved by adopting a level III approach in which the site specific soil properties and their uncertainties and spatial correlations could be systematically accounted for.

The objective of this paper is to present a performance-based reliability design (PBRD) methodology and the associated computational

algorithms for both laterally loaded and axially loaded drilled shafts using sampling-based methods. In the proposed PBRD framework, input to the computational models for the nonlinear soil structure interaction problem, such as p-y, t-z, and q-w curves, is treated as random variables. Soil properties, such as strength parameters, soil modulus, and unit weight, are modeled as random fields to account for soil spatial variability. The response in terms of deformation of drilled shafts to random input of soil properties is evaluated by the load transfer computational models. In each simulation, if the deformation exceeds the specified performance criteria, then failure is said to occur. Consequently, the probability of failure (i.e., unsatisfactory performance) p

f,

is simply the ratio of the number of failures to the total number of simulations. In PBRD, the design parameters of a deep foundation, such as shaft diameter D and shaft length L, are determined such that the desired target reliability level is met. To implement the PBRD methodology for the design of drilled shafts, two computer programs (i.e., P-LPILE for lateral loading and P-TZPILE for axial loading) were developed by the authors. In the developed computer programs, the commonly-used p-y method (Reese 1977) is applied for lateral


loading and the load transfer model (Coyle & Reese 1966) is applied for axial loading. Monte Carlo methods are employed to evaluate the probability of failure. Three design examples are given to demonstrate the application of the proposed PBRD methodology.

LOAD TRANSFER CONCEP TSThe p-y method has been widely used to evaluate the lateral deflection of a pile. In the p-y method, it is assumed that the pile is an elastic beam and that the soil-pile interaction could be modeled as discrete nonlinear springs. The governing differential equation is given as

[1]

where EI is the flexural rigidity of the shaft, y is the lateral deflection of the shaft at point z along the shaft length, Q is the axial load acting on the pile, and p is the lateral soil reaction per unit shaft length. In this study, the p-y method is adopted for its accuracy and simplicity.

The load-transfer model has been widely used to predict load-settlement curves for axially loaded drilled shafts. In this method, the drilled shaft is divided into a finite number of segments, for which the interaction between the soil and the drilled shaft for each segment is modeled by discrete springs using the t-z curves for side friction and the q-w curves for end bearing, where t and q represent side shear on the shaft and the tip resistance at the toe, respectively, and z and w represent the vertical displacements of the shaft segment and the toe of the drilled shaft, respectively. The capacity R for an axially loaded pile is evaluated by the following equation:

[2]

where D is the pile diameter, ti and h

i are the

side friction and the thickness for the i-th soil layer, respectively. The load transfer model is adopted here for the following reasons: 1) the load-transfer curves could be nonlinear and 2) multiple layers of soils could be considered.

PROBABILISTIC SOIL PROFILE DESCRIPTION

Coefficient of Variation

Natural occurring soils are indeed a non-homogeneous material so that spatial variations

of soil properties need to be considered in any reliability-based design of deep foundations. At the point level, a mean μ and a standard deviation σ are required to statistically characterize a soil parameter. The standard deviation σ is a measure of dispersion from the mean μ. A dimensionless measure of variability is the coefficient of variation (COV) defined as:

[3]

The COV of a soil parameter delivers a relative sense of variation. As the variation of soil properties exists, it should be quantified and accounted for in the design of foundations.

Correlation Length

The mere modeling of uncertainties of soil properties at the spatial point level is inadequate due to the fact that spatial dependence of soil properties does exist. To statistically characterize a stationary random field (i.e., mean, variance and higher moments are constant), the field mean, field variance, and the correlation structure are needed (Fenton and Griffiths 2008). To model the spatial correlation between two points, a third parameter called correlation length is required (Vanmarcke 1977). Take the Markovian correlation structure as an example, the one-dimensional correlation function is expressed as follows:

[4]

where τ is the separation distance between two points and θ is the correlation length. As can be seen from Equation [4], the correlation between two points decays exponentially with increasing separation distance. Adopting the same correlation structure as in Griffiths et al. (2009), Equation (4) is employed to statistically characterize how rapidly a random field varies along depth. To illustrate the implications of incorporating the correlation length in generating random fields, Fig. 1 shows two sample realizations of a 1D random field with different correlation lengths for the same mean and variance. In this figure, X(z) denotes the value of a soil property at location z. Inspection of Fig. 1 indicates that a random field with a short correlation length exhibits more roughness compared with that with a relatively long correlation length. To estimate the correlation length, a number of techniques are available (Fenton and Griffiths 2008),


such as evaluating the area under the sample correlation function, fitting to a correlation function or semivariogram, and the method of maximum likelihood. The adopted method for generating random field samples herein is the local averaging subdivision (LAS), which is proven a fast and accurate method of producing random fields. More details of LAS could be referred to Fenton and Griffiths (2008).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-2

0

2

4

X(z

)

= 0.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4

-2

0

2

4

z

X(z

)

= 2.0

[FIG. 1] Examples of 1-D random fi elds with different correlation lengths

PROBABILISTIC LOAD DESCRIPTIONSThe design loads are uncertain to some degree. According to Nowak and Collins (2000), COVs for dead load could range from 0.08 to 0.10 for buildings and bridges while those for live load including sustained live load and transient live load could range from 0.18 to 0.89. Previous investigations (e.g., Ellingwood & Tekie 1999; Ellingwood et al. 1980) have found that normal, lognormal, gamma, Type-I and Type-II Gumbel distributions are possible choices to statistically characterize load models. For example, the maximum live load can be statistically characterized by Type-I Gumbel distributions while sustained live load can be modeled as a gamma distributed random variable.

Loads in the proposed PBRD framework are treated as random variables. The uncertain loads in the computational model are simulated according to their probability distributions. The simulated loads are used as input along with the simulated soil properties to evaluate the structural response of the foundations.

INFLUENCE OF EPISTEMIC UNCERTAINTYEpistemic uncertainty is always present, as any computational model is an idealization or

simplification of the real world. The method for accounting for epistemic uncertainty is described below. Suppose G(X) denotes a prediction based on an input vector X for a model, and N is a bias factor that describes the epistemic uncertainty of the model, then the actual response denoted as Y

m can be related to

the prediction and the bias factor as follows:

Ym=N∙G(X) [5]

It is noted that the error term N is a random variable, which can be statistically characterized as a normal or lognormal variable (e.g., Kung et al. 2007; Phoon and Kulhawy 2005).

PERFORMANCE-BASED DESIGNIn the current LRFD practices, strength limit state and service limit state are considered for various combinations of load effects. Appropriate load and resistance factors are applied to check whether the design satisfies both limit states. The final design would be governed by either strength limit state or service limit state. However, as mentioned earlier, currently, in service limit check, the load factors are taken as unity and deterministic methods are utilized for calculating the deflection or settlement of foundations. In the proposed PBRD framework, performance-based criteria can be established as the objectives for deep foundation design. The performance criteria are expressed in terms of allowable or tolerable deformation of the foundation structures at the pre-determined limit states. For example, the strength limit state for laterally loaded drilled shaft could be defined as the lateral deflection of the drilled shaft head to be 5% of the shaft diameter (Brown et al. 2010), while the service limit state could be defined as 2 inch, etc. The advantage of using performance-based design (PBD) is that the ambiguity of the so-called “capacity” or “nominal resistance” can be removed. In the PBD methodology, a foundation design would be safe and serve its intended functions satisfactorily provided the specified performance criteria are satisfied for the prescribed load effects.

PERFORMANCE-BASED RELIABILITY DESIGNMonte Carlo simulation (MCS) is a standard statistical method in which the response of a system is calculated repeatedly using a sequence of random samples as input. The MCS-based approach for evaluating the probability


of failure for deep foundations is expressed as follows:

[6]

where n is the sample size, yt is the shaft-head

displacement, ya is the allowable displacement

specified by the performance criteria, I[∙] is the indicator function. The indicator function is equal to 1.0 if y

t is equal to or greater than

ya, and zero, otherwise. There are several

advantages of using Monte Carlo statistical method: 1) the Monte Carlo method gives the unbiased estimate of the failure probability; 2) the accuracy of the estimator increases with increasing n; and 3) the method is mathematically simple.

In this paper, the target probability of failure of 1/1000 is deemed appropriate. The sample size should be large in order to capture the probability of failure. The selection of n depends on the probability level and the COV of the estimate. The COV of the estimate measures how accurate it is. If the desired COV for the probability of failure is approximately 30%, a rule of thumb (Robert and Casella 2004) for selecting a proper sampling size is as follows:

[7]

where ps represents a small

probability and δps

is its COV. Equation (7) says the sample size is approximately ten times the reciprocal of the underlying probability. From Equation (7), the smaller p

s is, the larger n is; the

smaller δps

is, the larger n is. Since the failure probability is targeted at 1/1000, the sampling size is approximately 10,000 if COV of 30% for pf is desired. However, a larger sample size is warranted in order to improve the accuracy of the estimate. Fig. 2 shows the convergence of Equation [6] for p

f =1/1000. It is believed that

sample size of 50,000 should be adequate for the probability level of 1/1000.

The flow chart for the PBRD methodology of deep foundations is shown in Fig. 3. The objective of the methodology is to find

out feasible foundation dimensions (i.e., D and L) that achieve the target reliability for the prescribed performance criteria. In the proposed framework, a deterministic computational method is selected first and the uncertainties of input variables are quantified accordingly. Then a combination of foundation dimensions and a sample size for MCS are assumed. In MCS, a different set of random fields and other random variables are generated

0 2 4 6 8 10

x 104

0

0.5

1

1.5

2

2.5

3x 10-3

n

Prob

abili

ty o

f fai

lure

[FIG. 2] Convergence of Equation [6]

[FIG. 3] Flow Chart of PBRD


in each realization. Then the response of the drilled shaft to random input is calculated repeatedly. The failure probability is evaluated with Equation (6) using the resulting output from the repetitive numerical calculations. The process is executed iteratively by adjusting the combination of foundation dimensions until the desired reliability is achieved.

DESIGN EXAMPLES

Example 1 — Lateral Loading

Consider an example extracted from a FHWA report (Brown et al. 2010). A drilled shaft shown in Fig. 4 is to be designed in a very stiff clay site with the design loads of 111 kN (25 kips) in shear and 678 kN∙m (500 kip-ft) in moment applied at the top of the drilled shaft on the ground level. The p-y curve for stiff clay without free water (Reese et al. 2004) is used to represent the lateral soil-pile interaction. The undrained shear strength of 103 kPa (15 psi), a unit weight γ’ of 19 kN/m3 (121 pcf), and the strain ε

50 of 0.005 corresponding to 50% of the

maximum principle stress difference are used for generating p-y curves. The limiting deflection of 12.7 mm (0.5 inch) at the shaft head is the same as the design example in the FHWA report. The compressive strength of concrete is 31 MPa (4,500 psi), while the reinforcement yield strength is 414 MPa (60 ksi). The elastic modulus of steel is taken as 200 GPa (29,010 ksi). These material properties are used to calculate the values of EI of the drilled shaft as a function of the bending moment (Reese 1997). In the FHWA report, a resistance factor of 0.67 was used in the strength limit check, while the computer program LPILE was used to calculate the lateral deflection of the drilled shaft head under the unfactored loads. It was found by Brown et al. (2010) that a drilled shaft with 1.22 m (4 ft) in diameter and 6.10 m (20 ft) in length would be satisfactory and its structural section would be

reinforced by 12 No. 11 (35 mm) bars with cover of 76 mm (3 inches).

This design is re-examined herein using the developed computer program and the proposed PBRD approach. Three soil parameters, namely, S

u,

ε50

and γ’, are required to construct the p-y curve. Their correlation lengths are denoted as θ

ln(Su),

θln(ε50)

and θln(γ’), respectively. For simplicity, it is

assumed that they follow lognormal distribution. Their mean values are 103 kPa, 0.005 and 19 kN/m3 (15 psi, 0.005, 121 pcf), respectively. The COVs and correlation lengths of soil parameters are varied in a typical range to investigate their influences. More specifically, the COVs for S

u and

ε50

are varied from 10% to 100%, while the COV of unit weight is varied from 1% to 10%. This is because the variation of unit weight is relatively small. The correlation lengths of soil parameters are varied from zero to infinity. The shaft dimension is deemed deterministic in this study.

Influence of Spatial Variability

To investigate the influence of spatial variability of S

u, with both θ

ln(ε50) and θ

ln(γ’) set to 1.0 m (3.3 ft), both θ

ln(Su) and the COV of S

u are varied

as noted before. To the knowledge of the authors, the COV of ε

50 was seldom discussed

in literatures and therefore taken as 20% herein. The COV of γ’ typically small and is taken as 4%. Fig. 5 shows the relationship between p

f and

the spatial variability of Su. It is evident that p

f

increases with increasing COV of Su. In addition,

pf varies significantly for different θ

ln(Su).

[FIG. 5] Relationship between pf and uncertainty of Su

To investigate the influence of spatial variability of ε

50, with θ

ln(Su) set to 8.0 m (26.3 ft) and θ

ln(γ’) set to 1.0 m (3.3 ft), both θ

ln(ε50) and the COV of

ε50

are varied as noted before. The COV of Su

is taken as 40% while that of γ’ is taken as 4%. [FIG. 4] Drilled Shaft in stiff clay


Fig. 6 shows the relationship between pf and

the spatial variability of ε50

. The calculated pf

exhibits some variations caused by the spatial variability of ε

50. However, the scale of variation

is smaller than that caused by the spatial variability of S

u.

[FIG. 6] Relationship between pf and uncertainty of γ’

To investigate the influence of spatial variability of γ’, with θ

ln(Su) set to 8.0 m (26.3 ft) and θ

ln(ε50)

set to 1.0 m (3.3 ft), both θln(γ’) and the COV of

γ’ are varied as noted before. The COV of ε50

is presumably taken as 20% while that of S

u

is taken as 40%. Fig. 7 shows the relationship between p

f and the spatial variability of γ’. It is

seen that pf is almost invariant with respect to

the spatial variability of γ’.

COV of '

Prob

abili

ty o

f Fai

lure

[FIG. 7] Relationship between pf and uncertainty of γ’

Influence of Uncertain Loads

In the previous discussions, the applied loads are assumed to be certain. This section is devoted for discussing the influence of the uncertainty related to the applied loads. To

investigate the difference caused by the load uncertainty, a baseline scenario is established in which the correlation lengths of the soil parameters are all set to 1.0 m (3.3 ft). The COVs of S

u, ε

50 and γ’ are taken as 40%, 20% and

4%, respectively. In addition, No. 11 (35 mm) bars of approximately 1% of the sectional area is used and the cover thickness is set to 7.6 cm (3 inches) for evaluating EI in the analysis. Suppose that the shear force applied at top of the drilled shaft is a gamma distributed variable with a mean of 111 kN (25,000 lb) and COV of 30%. Furthermore, it was assumed that the resulting bending moment at the top will vary proportionally with the shear force. Fig. 8 shows the probabilities of failure with consideration of the uncertainty of loads in solid line. The failure probabilities for the baseline soil properties are also presented in companion in dash line. If the uncertainty of loads is considered, it can be seen that a feasible design would be L=6 m (19.7 ft) and D≥2.1 m (6.9 ft), L=7 m (23 ft) and D≥1.6 m (5.3 ft), or L≥8 m (26.3 ft) and D≥1.4 m (4.6 ft). However, a drilled shaft of L=6 m (19.7 ft) and D≥1.2 m (3.9 ft), or L≥7 m (23 ft) and D≥1.1 m (3.6 ft) would be adequate if the load uncertainty is not accounted for. From Fig. 8, it can be seen that the feasible designs with consideration of uncertainties of loads are larger in dimension than those for the baseline case.

Prob

abili

ty o

f Fai

lure

[FIG. 8] Infl uence of uncertainty of loads

Example 2 — Uplift

Consider a drilled shaft subjected to uplift of 400 kN (90,000 lb) in cohesive soils as shown in Fig. 9. The limiting displacement at the top of the drilled shaft is specified as 25 mm (1 inch). The structural section of the reinforced


concrete shaft has a steel ratio of 1%. The elastic modulus of concrete is taken as 26.6 GPa (3,858 ksi) and that of steel is 200 GPa (29,010 ksi). A typical value of 24 kN/m3 (153 pcf) is used for the unit weight of reinforced concrete. With these material properties, EA, the stiffness of the structural section of the drilled shaft is 3.204E007 kPa∙m2 (7.198E009 psf-ft2). Furthermore, they are treated as deterministic since the focus of this example is on uncertainties of soil properties. The undrained shear strength S

u of the soil is a lognormal

variable with mean of 30 kPa (4.35 psi), COV of 50%, correlation length of 1.0 m (3.3 ft). The alpha method and the load-transfer curve for cohesive soils (AASHTO 2010) are employed to calculate the load-displacement curve.

As the drilled shaft is in uplift, the toe resistance in Equation (2) is ignored and only the side resistance is considered. Fig. 10 shows that the computed probability of failure decreases with increasing shaft length and diameter. For the target probability of

failure of 0.001, a feasible design could be a drilled shaft with D=1.40 m (4.6 ft) and L≥5.80 m (19 ft), D=1.30 m (4.3 ft) and L≥6.60 m (21.7 ft), or D=1.20 m (3.9 ft) and L≥7.20 m (23.6 ft). Likewise, the feasible designs for other prescribed reliability levels can be found conveniently from this figure. Among the feasible designs, one can find the optimal design with a proper consideration of the economic constraint (e.g., Wang et al. 2011).

Example 3 — Compression

A drilled shaft of 1.2 m (3.9 ft) in diameter and 8.8 m (28.9 ft) in length is subjected to compression of 500 kN (112 kips) in cohesive soils as shown in Fig. 11. The compression is deemed deterministic for simplicity and the limiting displacement at the top of the drilled shaft is also specified as 25 mm (1 inch). The stiffness of the structural section of the drilled shaft EA is specified as 3.204E007 kPa∙m2 (7.198E009 psf-ft2). The undrained shear strength S

u of the soil is a lognormal variable

with mean of 55 kPa (8.0 psi), COV of 50%, correlation length of 1.0 m (3.3 ft). The alpha method and the load-transfer curve for cohesive soils (AASHTO 2010) are employed to calculate the load-displacement curve of the drilled shaft. In order to investigate the influence of epistemic uncertainty of the load transfer method, the statistical parameters of the bias factor N are assumed as: mean = 1.0 while COV of N (denoted as δ

N) is taken as 5%,

10% and 15%, respectively. The larger δN is,

the more uncertain the load transfer method is. Additionally, it is assumed that N follows lognormal distribution. With these statistical parameters, a random variable is generated for N in each realization and then applied to the

[FIG. 11] Drilled Shaft in Compression[FIG. 9] Drilled Shaft in Uplift

Prob

abili

ty o

f Fai

lure

L, m

[FIG. 10] Probabilities of failure by MCS


capacity using Equation [5]. Fig. 12 shows the convergence of the p

f estimates for different

levels of epistemic uncertainty. As can be seen, the failure probability increases with increasing δ

N. This indicates that the probability of failure

is sensitive to the epistemic uncertainty of the load transfer method. If the epistemic uncertainty of a design method becomes larger, then the design becomes less reliable.

[FIG. 12] Infl uence of Epistemic Uncertainty

SUMMARY AND CONCLUSIONSThis paper has presented a robust methodology that is able to perform reliability analysis for drilled shafts subjected to lateral or axial loads. The proposed methodology is MCS-based. In MCS, soil properties are modeled as random fields in order to account for the influence of soil spatial variability. To statistically characterize the random field for a soil property, the field mean, field variance and the correlation structure are required. In addition, loads in the proposed methodology are treated as random variable and their uncertainties are simulated by MCS. A performance-based approach was adopted; that is, if the induced displacement by applied loads is greater than the maximum allowable one, failure is said to occur. The probability of failure is evaluated by MCS. Two computer programs were developed to handle the computation of the failure probability. The following conclusions can be made:

1. The MCS based PBRD is practical. As the deformation of foundations could be evaluated probabilistically, the proposed PBRD can be applied to the service limit check to ensure that the induced deformation would be very unlikely to

exceed the limiting threshold values. As in the current LRFD practices the service limit check is still deterministic, the developed PBRD could bridge the gap towards the Level III RBD codes.

2. The spatial variability of soil properties could exert significant influences on the probability of exceeding the limiting lateral displacement. In particular, the probability of failure is very sensitive to the variation of the COV and correlation structure of undrained shear strength S

u. The larger the

COV is, the more uncertain the variable is. The longer the correlation length is, the more uniform the variable is. As shown in the numerical example, the difference caused by the correlation length of S

u could

be as much as several orders of magnitude. Compared with the correlation length of the undrained shear strength, those of ε

50

and γ' are relatively less significant. The probability of failure is almost invariant with respect to the COV and correlation structure of unit weight.

3. Consideration of the spatial variability of soil parameters is essential. If soil spatial variability is not properly accounted for, the calculated probability of failure could easily become biased. Since the probability of failure is significantly sensitive to the correlation structure of soil properties such as undrained shear strength, it is necessary to quantify the correlation structure as accurately as possible. As a result, simplifications on the correlation structure are not recommended. Practicing engineers cannot proceed with the assumption of infinite correlation length or zero correlation length, because the probability of failure calculated based on this assumption may be biased, which would consequently result in overdesign or unsafe design. Only when the suitable correlation structure of soil properties is used as input, a safe yet economical design can be achieved.

4. The epistemic uncertainty of a design method is critical in reliability analysis. The failure probability increases with increasing epistemic uncertainty of a design method. If the epistemic uncertainty is not taken into account, it can lead to unsafe design.

5. The proposed methodology is useful to


handle the soil variability and the epistemic uncertainty. However, the construction-related uncertainty is as important as the soil variability and the epistemic uncertainty. Poor construction may result in unsatisfactory performance, even if the design is safe. Therefore, caution should be exercised against construction-related uncertainty when applying the proposed approach.

REFERENCES1. American Association of State Highway and

Transportation Officials (AASHTO). (2010). AASHTO LRFD Bridge Design Specifications, 5th Edition, Washington, DC.

2. Brown, D. A., Turner, J. P. and Casetelli, R. J. (2010). “Drilled shaft: construction procedures and LRFD design methods.” No. FHWA-NHI-10-016, Federal Highway Administration.

3. Coyle, H. M. and Reese, L. C. (1966). Load transfer for axially loaded piles in clay. Journal of Soil Mechanics. & Foundation Division., 92(2):1-26.

4. Ellingwood, B. , Galambos, T. V., MacGregor, J. G. , and Cornell, C. A. (1980). Development of a Probability Based Load Criterion for American National Standard A58. NBS Special Publication 577. Washington, DC: National Bureau of Standards.

5. Ellingwood, B. and Tekie, P. B. (1999). “Wind load statistics for probability-based structural design”. Journal of Structural. Engineering. 125 (4):453-463.

6. Fenton, G. A. and Griffiths. D. V. (2008). Risk assessment in geotechnical engineering, Wiley, New Jersey.

7. Griffiths, D. V., Huang, J. and Fenton, G. (2009). “Influence of spatially variability on slope reliability using 2-D random fields”. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 135 (10):1367-1378.

8. Kung, Gordon T. C., Juang, C. Hsein, Hsiao, Evan C. L., and Hashash, Youssef M. A.. (2007). “Simplified model for wall deflection and ground-surface settlement caused by braced excavation in clays.” Journal of Geotechnical and Geoenvironmental. Engineering, ASCE, 133(6): 731-747.

9. Nowak, A. S. and Collins, K. R. (2000). Reliability of structures, McGraw-Hill, New York.

10. Phoon, K. K and Kulhawy, F. H. (2005). “Characterization of model uncertainties for laterally loaded rigid drilled shafts.” Geotechnique, Vol. 55(1), 45-54.

11. Reese, L. C. (1997). “Analysis of Laterally Loaded Piles in Weak Rock”. Journal of. Geotechnical and Geoenvironmental Engineering., 127(11):1010-1017.

12. Reese, L. C., Wang, S. T, and Isenhower, W. M. and Arrellaga, J. A. (2004). Computer program Lpile plus version 5.0 technical manual, Ensoft. Inc, Austin, Texas.

13. Vanmarke, E. (1977). Probabilistic modeling of soil profiles. Journal of the Geotechnical Engineering Division., ASCE, Vol. 103(GT11):1227-1246

14. Wang, Y., Au, S. K. and Kulhawy, F. H. (2011). “Expanded reliability-based design approach for drilled shafts”. Journal of Geotechnical and Geoenvironmental Engineering., 137(2):140-149.


Reliability-Based Optimization Design for Drilled Shafts/Slope System (DFI Student Paper Competition 2012) Lin Li, Research Assistant, Department of Civil Engineering, University of Akron, Akron, OH, USA;

[email protected]

Robert Liang, Distinguished Professor, Department of Civil Engineering, University of Akron,

Akron, OH, USA; [email protected]

ABSTRACTIn this paper, a reliability-based optimization design method is presented for design of a row of drilled shafts to stabilize an unstable slope while achieving the required target reliability index with minimum cost. In the previous developed deterministic analyses, the drilled shaft stabilization mechanisms for the reinforced slope were taken into account through the concept of soil arching, which was quantified by the load transfer factor in the limiting equilibrium analysis. However, due to the inherent uncertainties of the soil properties and the model error of the semi-empirical load transfer equation, a single value of factor of safety chosen in the deterministic approach may not yield the desired level of reliability. A modification of the deterministic method into a probabilistic method is developed in this paper. The monte carlo simulation (mcs) for the soil properties described by the log-normal distributions was employed to calculate the probability of failure (reliability index β) for the drilled shafts reinforced slope system. The developed theories are coded into a computer program (p-uaslope) for analyzing complex slope profile conditions. Finally, a case study (ohio ath-124 slope) is presented to illustrate the step by step design procedure using the developed probability approach..

INTRODUCTIONLandslides and slope failures occur frequently every year and affect the operational safety of roadways thereby adding financial burden to the highway agencies responsible for slope repairs and maintenance. A vast variety of slope stabilization methods have been presented by numerous researchers in the past. Among these methods, a concept of using a row of drilled shafts to reinforce unstable slopes has been used successfully by Ohio DOT (Liang, 2010). Analysis and design of drilled shafts to stabilize slope has been a research topic since the 1980’s. In general, the analysis methodologies for treating the effects of drilled shafts on slope, could be categorized into two approaches: a) an increase in the resistance due to the added shear strength of the reinforced concrete drilled shafts (e.g., Ito, et al. 1981; Hassiotis, et al. 1997; Reese, et al. 1992; Poulos, 1995), and b) a decrease in the driving force due to the soil arching as a result of the inclusion of rigid structural elements. The later approach associated with load transfer factor theory was pioneered by Liang and his associates (Liang and Zeng 2002, Yamin 2007, Al Bodour 2010 and Joorabchi 2011), to interpret the interaction between drilled shaft and the moving slope.

The most common deterministic methodologies for slope stability analysis include the limit equilibrium method (LEM) and strength reduction technique (SRT) based on finite element method (FEM). Frequently, the uncertainties in connection with the soil properties and slope failure mechanisms are addressed collectively by imposing a required factor of safety, such as choosing an arbitrary factor of safety between 1.2 and 1.5. Nevertheless, there is still not a universal constant (e.g. 1.2 or 1.5), which can suit any circumstance of slope stability in LRFD. Meanwhile, bigger factor of safety does not mean it can provide more reliability, since the prescribed factors of safety do not change regardless of the degree of variability and/or uncertainties in the slope problem. It could be stated that a slope with a nominal safety factor of more than one does not necessarily mean it is safe, because of the underlying geotechnical variability and inherent uncertainties in the computational methods.

Probability based approach for slope stability analysis has been a subject of research since 1970s. For example, Tang et al. (1976) presented a probability-based method for evaluating short term stability of a slope. Oka and Wu (1990) elucidated that the upper bound of the system


failure probability could be twice bigger than the failure probability of a critical slip surface. Liang et al (1999) developed the reliability and probability theory for assessing the reliability index and the corresponding probability of failure of multi-layered embankment dams and slopes. Malkawi et al. (2000) compared the FOSM and Monte-Carlo Simulation (MCS) for analyzing the reliability of a slope. Cheung and Tang (2005) proposed a procedure to model the slope deteriorating effect on the probability of failure with time. Griffiths, and Fenton (2004) analyzed the slope spatial variability using a 2-D random field. Babu and Srivastava (2010) employed first-order reliability method and response surface methodology to analyze the pipe-soil system. Low et al. (2011) efficiently calculated the bounds of system failure probability on a retaining wall and a soil slope. Despite of abundance of probability based theory for slope stability analysis, there is currently less reliability based design method for a slope reinforced with a row of drilled shafts. The purpose of this paper is to present a reliability-based analysis and design method to optimize the design of a slope stabilization using drilled shafts while considering the uncertainties in the soil properties and the soil arching.

DETERMINISTIC ANALYSIS FOR DRILLED SHAFT/SLOPE SYSTEM

Global Factor of Safety

Slopes reinforced by a row of piles or drilled shafts have been a subject of research by numerous researchers since the 1960’s. During the past years, the deterministic analytical methodologies for the drilled shafts/slope system have been dealt with using the concept of “increased resistance” (Eqn. [1]) or the concept of “decreased driving force” (Eqn. [2]).

D

shaftRR

F

FFFS

)(Δ+=

[1]

archingDD

R

FF

FFS

)(Δ−=

[2]

where, FS is global factor of safety of a slope/shaft system, F

R is the resistance Force, (∆F

R)shaft

is additional resistance due to drilled shafts, F

D

is driving force, and (∆FD)arching

is the drilled shaft induced arching effect on the driving force.

Soil Arching Theory and Load Transfer Factor

The concept of soil arching in a drilled shaft/slope system is that the presence of rigid inclusions (drilled shafts) in a slope would reduce the driving forces in the moving part of the soils on the down-slope side of drilled shafts due to the earth thrust being re-distributed to the drilled shafts. As a result, the driving forces for the portion of the soils on the down-slope side of the drilled shafts reduce, resulting in an increase in FS of the system. The concept of soil arching is depicted in Fig. 1a and 1b for top view and section view, respectively. The effect of drilled shafts is observed in the changes occurred in the horizontal stresses in the soil mass on the up-slope and down-slope sides of the shaft.

To apply arching theory in the drilled shafts/slope system, a load transfer factor, η, is introduced and defined as the ratio between the horizontal force on the down-slope side of the vertical plane at the interface between the drilled shaft and soil (i.e., P

down-slope) to

the horizontal force on the up-slope side of the vertical plane at the interface between the drilled shaft and soil (i.e., P

up-slope).

Mathematically, the load transfer factor is expressed as:

η=Pdown-slope

/Pup-slope

[3]

From 3-D finite element simulation results, the resultant forces in the soil up-slope and down-slope sides of the shaft are obtained by integrating the horizontal soil stresses of the vertical plane from the top of the shaft down to the failure surface as shown in Fig. 1b.

0

0 0

fL s

up xxP dsdzσ= ∫ ∫

[4]

0

0 0

fL s

Down xxP dsdzσ ′= ∫ ∫ [5]

where S0 is the model thickness (distance

between center to center of two adjacent drilled shafts), L

f is the distance from the top of the

shaft down to the failure surface, σxx

is S11

which denotes the horizontal soil stresses on the up-slope side of the shaft, and σ′

xx is S′

11

which denotes the horizontal soil stresses on the down-slope side of the shaft.


[FIG.1a] Defi nition of the Soil Arching

[FIG. 1b] Soil Stress Distribution

Joorabchi (2011) has proposed a semi-empirical equation, given in Eqn. [6], to compute η using regression analyses on 41 3-D finite element simulation results. The influencing factors consist of six parameters: soil cohesion c, friction angle φ, drilled shaft diameter D, center to center shaft spacing S

0, shaft location on

slope ξx, and slope angle β.

[6]

where, ξx = x

i/X, x

i is the horizontal distance

between slope toe and drilled shaft, and X is the horizontal distance between slope crest and slope toe.

Deterministic Limit Equilibrium Method of Slices Incorporating Arching Algorithm

The limiting equilibrium method developed by Liang and Zeng (2002) is modified herein by incorporating the newly developed η. Fig. 2a shows a typical slice with all force components

acting on the slice (Al Bodour, 2010). The load in the drilled shafts/slope system will be generated by gravity and friction and then be transferred slice by slice through the interslice force P

i. Without drilled shafts on the slope,

the interslice force Pi can be expressed as

an equilibrium equation shown in Eqn. [7]. However, with the insertion of drilled shafts on the slope, the force on the down-slope side of the drilled shaft will experience a reduction of P

i due to arching, i.e., multiply η by the previous

interslice force Pi-1

, shown in Eqns. [8] and [9]:

[7]

[8]

[9]

The net force applied to the drilled shaft due to the difference in the interslice forces can be calculated as follows:

Fshaft

= ( 1 - η) Pi - 1S

A [10]

where, Pi is the interslice force acting on the

downslope side of slice, Wi is weight of slice i, α

i

is inclination of slice i base, ci is soil cohesion

at the base of slice i, ϕi is soil friction angle at

the base of slice i, ui is the pore water pressure at slice i, and P

i-1 is the interslice force acting

on the upslope side of slice (Fig. 2b). Fshaft

is the force on the drilled shaft, and S

A is the center-to-

center area above the slip surface between two adjacent drilled shafts. Based on Eqn.s (7) to (9), factor of safety for a drilled shafts/slope system can be calculated in an iterative computational process by satisfying boundary load conditions and equilibrium requirements, along with Mohr-Coulomb strength criterion. A PC based computer program, UASLOPE, was developed by Liang (2002) based on the above algorithm to calculate the factor of safety and the shaft force for a drilled shaft reinforced slope system.

UNCERTAINTIES IN THE DRILLED SHAFTS/SLOPE SYSTEM

Uncertain Parameters in Shafts/Slope System

The influencing parameters in the drilled shafts/slope system can be divided into two


major categories: soil properties (cohesion c, friction angle ϕ, and unit weight γ) and drilled shaft related parameters (shaft diameter D, clear spacing S between the adjacent drilled shafts, the location of the shaft on the slope ξx). In this paper, the drilled shaft related parameters are considered to be certain, while the soil properties are considered to be uncertain for the development of this reliability analysis method. A lognormal distribution is assumed for these uncertain variables. In addition, the Ziggurat algorithm, an algorithm for pseudo-random number sampling based on the Accept-Reject algorithm, is used in the probability computational program as a pseudo-random number generator.

Bias of Load Transfer Factor

The semi-empirical load transfer factor (η) function given in Eqn. (6) contains bias as compared to the real value from the results of 41 finite element model simulations. The load transfer factor bias ( ) is considered as a random variable with the mean and variance statistically analyzed by comparing the finite element simulation results and the predictions

of the semi-empirical equation. The mean and c.o.v. of is 1.01 and 0.15, respectively. As indicated in the following expression, the load transfer factor can be randomly generated through the randomly generated bias:

[11]

where, is the randomly generated load transfer factor; is the randomly generated bias of load transfer factor; and are the randomly generated soil cohesion and friction angle, respectively; β, D, ξ

x and S

0 are considered as

deterministic parameters.

RELIABILITY-BASED OPTIMIZATION DESIGN

Monte-Carlo Simulation (MCS)

The probability of failure for the drilled shafts/slope system is computed by means of the Monte Carlo simulation method, as expressed by Eqns. [12] to [14]. A probabilistic version of the UASLOPE computer program (P-UASLOPE) based on the described algorithm was successfully coded for reliability analysis of a drilled shafts stabilized slope.

[12]

[13]

[14]

where, Pf is the probability of failure for

the drilled shafts/slope system, is the coefficient of variance (c.o.v.) of P

f, σ

Pf is the

standard deviation of Pf, μ

Pf is the mean of P

f,

I[FS<1] is the indicator function, N is the sample numbers, is the computed probability of failure, and β is the reliability index.

The design process can be separated into the following steps:

• Step 1: Specify the slope and drilled shafts geometry;

• Step 2: Specify the probability

[FIG. 2a] A typical slice showing all force components (Al Bodour, 2010)

[FIG. 2b] Slice force change due to arching


distribution for soil properties, (i.e. cohesion C, friction angle φ and unit weight γ); currently, it is assumed that these variables follow a log-normal function with the specified mean value and variance value;

• Step 3: Statistical analysis of the bias of the load transfer factor, expressed in the previous part;

• Step 4: Perform Monte-Carlo simulation based on the limit equilibrium method for the drilled shafts/slope system ;

• Step 5: Obtain the reliability index for a shafts/slope system.

• Step 6: Optimize the design parameters.

The flow chart of the probabilistic Monte-Carlo Simulation (MCS) method for the drilled shaft/slope system is shown in Fig. 3.

Step by Step Design example

The slope failure at the ATH-124 project site in Ohio was previously analyzed by Liang (2010) using the deterministic computer program UASLOPE. The failed slope at State Route ATH-124, from station 107 + 40 to 108 + 60, was part of a test site sponsored by Ohio DOT. The laboratory tests of soil samples retrieved from the field-included specific gravity, natural water content, direct shear test, CIU test, and UC test. For rock cores, RQD and unconfined compression strength of rock core were obtained. Based on the two site investigation reports, the simplified soil profile of the failed slope and the soil properties are presented in Fig. 4. The slip surface of the failed slope was determined from the inclinometer readings during the two years of monitoring after the occurrence of the first slippage in 2004, and is shown in Fig. 4 as well. The pertinent soil and rock properties including strength parameters, i.e., C, φ and γ, are summarized as mean values in Table 1, while the coefficient of variation (c.o.v.) of these soil parameters are taken from Phoon and Kulhawy (1999).

Step by Step Design Procedure for ATH-124 Slope

The probabilistic version of the UASLOPE program was developed based on the theories described in the previous sections. The design process utilizes the following steps.

Step 1: Data collection (i.e. the geometry of the slope, soil paremeters, underground water

table, critical slip surface, etc.) and generating random variables. All the parameters are shown in Fig. 4 and Table 1.

[FIG. 3] Flow Chart of MCS Method for the Drilled Shafts/Slope System

[FIG. 4] Slope Geometry for ATH-124 slope (shaft location: 26m)

[TABLE 1] Soil Properties at the Slope of ATM-124 Project

Meanc.o.v.

Layer No. 1 2 3 4 5

C (kN/M2) 3.35 3.35 0 3.35 7.42 0.2

φ (degree) 24 24 11.5 24 35 0.1

γ (kN/M3) 23.56 21.21 20.42 21.21 24.35 0.01

Based on Ching (2009), the relationship between unbiased Monte Carlo Simulation (MCS) samples number (N) and the coefficient of variation (c.o.v.) of probability of failure (P

f) can be

expressed as follows:

[15]

where, N is the number of samples, and Pf is

the probability of failure. In the current study, 30,000 samples for each cohesion C, friction angle φ and unit weight γ were generated by log-normal distribution based on the mean and c.o.v. of bias shown in Table 1.

Step 2: Set up the target reliability index. As recommended by Abramson (2001), the target reliability index β

Target is seleced as 3.0.


Step 3: Select different drilled shafts locations. Usually, the drilled shaft location ξ

x

can be chosen from 0.2 to 0.8. Considering the constructability and site accessibility issue, the allowable location for drilled shafts is between 23m - 30.5m (75 ft – 100 ft) horizontally from the top of the slope (shown in Fig. 4). The slope/shaft system will be analyzed for different shaft locations starting from X=23m (75 ft) to X=30.5m (100 ft) with an increment equal to 1.5m (5 ft).

Step 4: Select different pairs of clear spacing S and shaft diameter D combinations within the permissible range. Usually, this may depend on the site situations, or local availability of drilled shaft construciton equipment. In this example, the range for D is selected to be between 0.6m to 2.4m (2 ft – 8 ft), and the range of S/D is selected to be between 1.0 - 3.0. The following combinations for (S, D) were selected: (0.6, 0.6), (1.2, 0.6), (1.8, 0.6), (1.2, 1.2), (2.4, 1.2), (1.8, 1.8), (2.4, 2.4). All units in the parenthesis are in meters.

Step 5: For each (S, D) combination, plot the relationship between the computed reliability index and shaft location, as shown in Fig. 5.

[FIG. 5] Reliability Index of the Shaft/Slope System versus shaft location for different (S, D) combinations

[FIG. 6] Shaft Force versus shaft location for different (S, D) combinations

Step 6: For each (S, D) combination, plot the relationship between the computed net forces on the drilled shaft and shaft location, as shown in Fig. 6.

Step 7: Optimize the design parameters. As can be seen in Fig. 5, the reliability index β tends to increase with distance from the top of slope and then decrease slightly. The location of 27.5m (90 ft) provides the highest reliability index for the given shaft diameter and spacing. In addition, it can be seen that the following foundation dimensions would satisfy the chosen target reliability: (a) D=0.6m, S/D=1.0, (b) D=0.6m, S/D=2.0, and (c) D=1.2, S/D=1.0. However, as shown in Fig. 6, the shafts at the location equal to 27.5m (90 ft) are also subjected to the largest net forces, which would have resulted in higher bending moment and shear in the shaft requiring a higher reinforcement ratio as well. It appears that the force on the shafts would decrease after the location 27.5m (90 ft), and the computed reliability index β would still satisfy the target reliability index. Furthermore, the required length of drilled shafts could be reduced if the location of the drilled shafts is moved further downslope. From these considerations, three combinations are selected: (a) location X=30.5m, D=0.6m, S/D=1.0; (b) X=30.5m, D=0.6, S/D=2.0; (c) X=30.5m, D=1.2m, S/D=1.0m.

Step 8: The software LPILE is used for the structural analysis of the shaft. The three combinations obtained from step 7 (i.e., (a) D=0.6m, S/D=1.0, F=470kN; (b) D=0.6m, S/D=2.0, F=440kN; (c) D=1.2m, S/D=1.0, F=620kN) can be taken into LPILE to calculate the lateral deflection and the internal forces and moments on the shaft. The rock properties are taken from the results of the field borings and lab testing results; these properties were used as input in the computer code LPILE. In such a case, usually the p-y curves are internally generated in the computer code based on the input soil and rock properties. The appropriate load factor from the AASHTO LRFD Bridge Design Specifications should be used to determine the factored loads in the LPILE analysis. Assuming 20% total length of drilled shaft is inserted into rock layer, therefore, the total length of drilled shafts can be calculated as 11m for each of the three combinations. After calculation with LPILE, the lateral deflection on the top of the shaft is 8mm, 7.5mm, 15mm (0.31 in, 0.30 in and


0.60 in) respectively for the combinations of (a), (b) and (c). Meanwhile, if we set up the allowable deflection as half inch (12.7mm), therefore, option (c) needs to be excluded. As considering (a) and (b), the unit volume of drilled shafts is 2.591m3, 1.727m3, (3.389 cu. yd, 2.259 cu. yd) respectively. Finally, combination (b) can be chosen as the optimized design considering both construction cost and performance requirement.

To demonstrate the difference between the deterministic version and the probabilistic version of UASLPOE, one case (D=0.6m) has been analyzed and presented in Table 2. The results show that at the shaft location equals to 23.0m (75.5 ft), all the computed reliability index does not satisfy the target reliability index (β

Target=3.0), even though the calculated

FS is greater than one. By comparing the results with the S/D=1 at location 26.0m, 27.5m, 29m and 30.5m, (85.3 ft, 90.2 ft, 95.1 ft and 100.0 ft) all the four combinations have reaching the same reliability index, i.e., 4.75, but different global FS value, which implies different FS could achieve the same reliability. In other words, more global FS which may be produced by more construction cost does not guarantee that the slope has more reliability. The same results can also be shown in the combinations of S/D=2 at location 27.5m (85.3 ft) and 29m (90.2 ft). Meanwhile, the same global FS does not necessarily deliver the same reliability for the slope. As shown in Table 2, although all the global FS are reaching the same value, i.e., FS=1.31 in the combinations of S/D=1 at location 23m, S/D=2 at location 24.5m (80.4 ft) and S/D=3 at location 29m (95.1 ft), the reliability index

are 2.23, 2.19, 2.26, respectively. The case presented in Table 2 helps provide insight to the importance of using reliability based design/analysis approach for the slope stability problem, as a single value of FS cannot be properly chosen to accurately reflect the uncertainties associated with soil properties and the computational methods.

To evaluate the sensitivity of Pf due to

uncertainty of C, φ and γ, different COVs have been chosen from Table 3 to calculate the corresponding probability of failure. In the baseline model, shaft diameter D=0.9m (36 in), clear spacing S=1.8m (26.2 ft) and shaft location is 26m (85.3 ft) as shown in Fig. 4. All the mean of soil parameters are chosen from Table 1. Based on the guideline of inherent soil variability (Phoon and Kulhawy, 1999), the COV range of C, φ and γ are chosen as 0.2-0.45, 0.1-0.2 and 0.01-0.11, respectively. Fig. 7 shows that even though the COV of friction angle φ are smaller than the COV of C, the friction angle delivers the most sensitivity to the probability of failure. Comparing with friction angle, cohesion and unit weight have relatively less sensitivity. Apparently, the COV of friction angle should be chosen very carefully in the future slope stability design and analysis using drilled shaft.

[TABLE 3] Variability of COV for Different Soil Properties

COV Rate 0.0 0.2 0.4 0.6 0.8 1.0

C 0.2 0.25 0.3 0.35 0.4 0.45

φ 0.1 0.12 0.14 0.16 0.18 0.2

γ 0.01 0.03 0.05 0.07 0.09 0.11

[TABLE 2] Comparison between Reliability Index and Factor of Safety (D=0.6m)

Shafts Location (m) 23.0 24.5 26.0 27.5 29.0 30.5

S/D=1Reliability Index (β) 2.23 3.98 4.75 4.75 4.75 4.75

Global FS 1.31 1.64 2.24 3.62 3.28 3.16


Global FS 1.16 1.31 1.53 1.81 1.69 1.64


Global FS 1.06 1.14 1.25 1.36 1.31 1.29


[FIG. 7] Sensitivity Analysis for Uncertainty of Soil Properties

SUMMAry And ConClUSIonSIn this paper, a new probabilistic computational algorithm based on the Monte Carlo Simulation (MCS) technique, limit equilibrium based method of slices, and soil arching theory, was developed for analyzing a slope reinforced by a row of drilled shafts. A PC based computer program, P-UASLOPE, was also developed to implement the developed computational algorithms for analyzing complex slope geometry, soil profile, and general slip surface. A case study of a failed slope in Ohio was presented to demonstrate the step-by-step design procedure using the P-UASLOPE program. Specific conclusions based on the design example and comparisons between global FS and reliability index can be made as follows.

1. This paper presented reliability based methodologies for computing reliability index of a drilled shafts/slope system as well as the loads on the drilled shaft for determining internal forces and moments for structural design of a drilled shaft.

2. The location, spacing, diameter, and length of the drilled shafts are the fundamental design variables, which can be varied in different combinations to achieve the target reliability index. The final selection of the design combination should be based on economic analysis and consideration of constructability of the drilled shafts.

3. A single value of FS may not be adequate for slope stability analysis due to its lack of ability to take into account of uncertainties of soil properties and computational model errors. Meanwhile, bigger FS does not mean the slope has more reliability. The developed probabilistic computational

algorithm can provide an efficient design tool for considering these uncertainties.

reFerenCeS1. Al-Bodour, W. (2010). “Development of

design method for slope stabilization using drilled shaft”. Ph.D. Dissertation, The University of Akron, 2010.

2. Abramson, L. W. (2001). Slope Stability and Methods, 2nd Ed., Wiley, New York, N.Y.

3. Babu, G. L. S. and Srivastava, A. (2010). “Reliability analysis of buried flexible pipe-soil systems”. Journal of pipeline systems engineering and practice. ASCE, 1(1), 33-41.

4. Cheung, R. W. M. and Tang, W. H. (2005). Reliability of deteriorating slopes. J. Geotech. Geoenviron. Eng.; 131 (5): 589-597.

5. Ching, J.Y., Phoon, K. K. and Hu, Y.G. (2009). “Efficient evaluation of reliability for slopes with circular slip surfaces using importance sampling.” Journal of Geotechnical and.Geoenvironmental Engineering, 135 (6), 768-777.

6. Griffiths, D. V., and Fenton, G. A. (2004).“Probabilistic slope stability analysis by finite elements.” Journal of Geotechnical and.Geoenvironmental Engineering, 130 (5), 507-518.

7. Hassiotis, S., Chameau, J. L. and Gunaratne, M. (1997). “Design method for stabilization of slopes with piles”. Journal of Geotechnical and.Geoenvironmental Engineering. 3(4): 314-323.

8. Ito, T., Matsui, T. and Hong, P. W. (1981).“Design method for stabilizing piles against landslide—one row of piles.” Soils and Foundations, Vol. 21, No. 1, pp. 21-37.

9. Joorabchi, A. E. (2011). “Landslide stabilization using drilled shaft in static and dynamic condition.” Ph.D. Dissertation. The University of Akron.

10. Liang, R. Y. (2010). “Field Instrumentation, Monitoring of Drilled Shafts for Landslide Stabilization andDevelopment of Pertinent Design Method”. 2010 Report for Ohio Department of Transportation. StateJob Number: 134238.

11. Liang, R. Y., Al Bodour, W., Yamin, M. and Joorabchi, A. E. (2010).“Analysis method for drilled shaft-stabilized slopes using arching concept.” Transportation Research Record:


Journal of the Transportation Research Board, 38-46.

12. Liang, R. Y., Nusier b, O.K.and. Malkawi, A.H. (1999). A reliability based approach for evaluating the slope stability of embankment dams. Engineering Geology; 54: 271–285.

13. Liang, R. Y., Zeng, S. (2002). “Numerical study of soil arching mechanism in drilled shafts for slope stabilization.” Soil and Foundations, Japan. Geotechechnical Society., 42 (2), 83-92.

14. Low, B. K., Zhang, J., and Tang, W. H. (2011). “Efficient system reliability analysis illustrated for a retaining wall and a soil slope”. Computers and Geotechnics. 38, 196-204.

15. Malkawi, A. I., Hassan, W. F., Abdulla, F. A. (2000). “Uncertainty and reliability analysis applied to slope stability”. Structural Safety; 22: 161-187.

16. Oka, Y. and Wu, T. H. (1990). “System reliability of slope stability”. Journal of Geotechnical Engineering; 116(8):1185-1189.

17. Phoon, K. K., and Kulhawy, F. H. (1999).“Characterization of geotechnical variability.” Journal of Canadian Geotechnical Society, 36: 612-624.

18. Poulos, H. G. (1995). “Design of reinforcing piles to increase slope stability”. Canadian Geotechnical Journal, 32: 08-818.

19. Reese, L. C., Wang, S. T. and Fouse, J. L. (1992). “Use of drilled shafts in stabilizing a slope”. Proceedings Specialty Conference on Stability and Performance of Slopes and Embankment, Berkeley.

20. Tang, W. H., Yucemen, M. S. and Ang, A. H. S. (1976). “Probability-based short term design of soil slopes.” Canadian Geotechnical Journal, 13(3), 201-215.


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DFI JOURNAL - Deep Foundations Institute · DFI JOURNAL The Journal of the ... This paper studies the effect of voids ... load bearing capacity of drilled shafts with anomalies under