Pywall v3 Validation Notes

PYWALL VALIDATION NOTES Page 1 of 17

VERIFICATION OF COMPUTER PROGRAM PYWALL AS A VALID TOOL FOR DESIGN OF

FLEXIBLE RETAINING WALLS Shin-Tower Wang and Jose A. Arrellaga

July 6, 2007

1. Introduction

Flexible retaining structures have received much attention since 1940 because of

the widespread use in engineering construction. Flexible retaining walls, in contrast to

more-or-less rigid, gravity walls, usually mean a single row of piles that may be of

timber, reinforced concrete, or sheet steel that are mostly driven by hammers and have

their lower ends embedded in soil. Tschebotarioff presented the results of his famous

large-scale model tests for retaining structures in 1948 (Tschebotarioff, 1948). One of

the most important conclusions was that the distribution of earth pressure on sheet piles is

highly influenced by the deformations of walls.

The conventional method of design is based on a limit-equilibrium theory that has

a theoretical weakness for soil-structure-interaction problems. The behavior of retaining

structures is largely a matter of soil conditions and the details of the structural system.

Therefore, a rational method of design must include the nonlinear soil-resistance-

displacement relationships, shaft spacing, penetration depth, and structural properties.

As mentioned above, the interactions between the structure and the soil on

retaining walls will be governed by the retained soil at the back, supporting soil in the

front, as well as the structure itself. The response of the soil is a function of the soil-

structure system and of the permissible deflections of this system. It is recognized that

the limit-equilibrium analysis does not take into account the nonlinear mobilization of

soil reaction with wall deflection in the analysis and should not be recommended as

appropriate design procedure. The finite-element method shows promise to handle the

complicated stress-strain relationship for the retaining system. However, the constitutive

law of soil has not been understood well enough for this method to be used in engineering


practice with confidence. The behavior of a retaining wall, in results from the finite-

element method, is very difficult to interpret if the soil is not modeled correctly. In

addition, the level of efforts necessary to create and to evaluation a proper finite-element

model is very demanding.

2. Methods of Solution

The method of analysis for beams on nonlinear foundations, that employs the soil

response curves derived from full-scale experiments, has been accepted as a rational

design method by many engineers. The method commonly is referred to as p-y method

and has been very successful for the design of laterally-loaded piles. A flexible earth-

retaining structure is similar to piles loaded by lateral forces. The p-y method for

analyzing a beam on nonlinear foundation is basically a modified form of the subgrade

reaction method. Usage of the p-y curves for retaining systems has been introduced in

Geotechnical Engineering Circular No. 4 – Ground Anchors and Anchored System from

the Federal Highway Administration (Federal Highway Administration FHWA-IF-99-

015, 1999).

The program PYWALL considers the effects of soil-structure-interaction by using

a generalized beam-column model and analyzes the behavior of a flexible retaining wall

or soldier-pile wall with or without tiebacks or bracing systems. Displacements or

rotational restrains may be specified at any depth of the wall to simulate bracings or

tiebacks. The user may also specify active earth pressure as the distributed load, or ask

the program to generate the earth pressures internally. Passive soil resistance can be

represented either by linear springs or nonlinear soil-resistance curves. The program will

calculate the earth pressure above the dredge line, wall deflection, shear force, bending

moment, and force on the struts.

Soil behavior is modeled with p-y curves that are internally generated by the

computer program following published recommendations for various types of soils;

alternatively, the user can manually introduce external p-y curves. Special procedures are

programmed for developing p-y curves for layered soils and for rock.


Input parameters consist of the geometry of the retaining wall, structural

properties of the wall element, restrained conditions applied on the wall by the tiebacks

or other bracing systems, soil-resistance curves, unit weight of soils, strength parameters

of soils, and location of the water table.

The p-y method is being used extensively in the United States and elsewhere. To

illustrate its use, references are cited from Italy (Jamiolkowski, 1977), France (Baguelin

et al., 1978), Britain (George and Wood, 1976), and Australia (Poulos and Davis, 1980).

The p-y method is also included in publications from the following agencies:

• Federal Highway Administration, U.S. Department of Transportation (Reese,

1984), and adopted by most of the State Highway Departments in the United

States;

• Det Norske Veritas and Riso National Laboratory on Wind Turbines (DNV,

2001);

• Det Norske Veritas, on Offshore Structures, (DNV, 1977); and the

• American Petroleum Institute (1993). The publications of the API have guided

the design of onshore and offshore pile foundations in the United States and

elsewhere.

3. Basic Equations for the p-y Method

The laterally loaded beam column is modeled as shown in Fig. 1. The

mechanisms shown to represent the soil depict the soil as a nonlinear material. The

deformation of an elastic member under axial and lateral loading can be found by solving

Eq. 1, the standard beam-column equation.

02

2

2

2

2

2

=−−⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛Wp

dxydP

dxydIE

dxd

xpp ............................................ (1)

where

Px = axial load on the beam column, F,

y = lateral deflection of the beam column at point x along


the length of the beam column, L,

p = soil resistance per unit length, F/L,

W = distributed load along the length of the beam column, F/L,

EpIp = flexural stiffness, FL2.

Figure 1 Model of laterally loaded beam column

A physical definition of the soil resistance p is given in Fig. 2. Figure 2a shows a

profile of a beam column, and shows a thin slice of soil at some depth xi below the

ground surface. The assumption is made that the beam column has been installed without

bending so that the initial soil stresses at the depth xi are uniformly distributed, as shown

in Fig. 2b. If the beam column is loaded laterally so that a beam deflection yi occurs at

the depth xi the soil stresses will become unbalanced, as shown in Fig. 2c. Integration of

the soil stresses will yield the soil resistance pi with units of F/L:

pi = Esyi.................................................................................................. (2)

where


Es = a parameter with the units F/L2, relating beam

deflection y and soil reaction p.

It is evident that the soil reaction p will reach a limiting value (and perhaps decrease)

with increasing deflection. Furthermore, the soil strength in the general case will vary

with depth. Therefore, only in rare cases will Es, sometimes called the soil modulus, be

constant with depth.

Figure 2 Definition of p and y as related to the response

of a beam column to lateral loading

The bending stiffness EpIp of a metal beam column will probably be constant for

the range of loading of principal interest. However, the EpIp of a reinforced-concrete

section will change with the bending moment. In view of the nonlinearities of Eq. 1,

numerical methods must be utilized to obtain a solution. The difference-equation method

can be employed with good results. Eq. 3 is the differential equation in difference form,

where the beam column is subdivided as shown in Fig. 3.


ym – 2Rm-1 + ym-1(-2Rm-1 – 2Rm + Qh2) + ym(Rm-1 + 4Rm +Rm+1 – 2Qh2 + kmh4) +

ym+1(-2Rm – 2Rm+1 + Qh2) + ym + 2Rm+1 – Wmh4 = 0 ........................... (3)

where

Rm = EmIm, ........................................................................................ (4)

km = Esm ............................................................................................ (5)

The beam column is subdivided into n increments and n+1 equations can be

written of the form of Eq. 3, yielding n+5 unknown deflections. Two boundary

conditions at the bottom of the beam column and two at the top of the beam column

allow for a solution of the n+5 equations with selected values of R and k. The value of n

and the number of significant figures in y are selected to yield results with appropriate

accuracy. The solution of the equations proceeds readily by Gaussian elimination. The

value of n ranges from perhaps 50 to 200; on most computers double-precision arithmetic

is necessary with about 15 significant figures.

Figure 3 Representation of deflected beam column

The solution proceeds as illustrated in Fig. 4. Figure 4a shows a beam column

subjected to a lateral load. Figure 4b shows a family of p-y curves where the curves are


in the 2nd and 4th quadrants because soil resistance is opposite in direction to beam-

column deflection. Also in Fig. 4b is a dashed line showing the deflection of the beam

column, either assumed or computed on the basis of an estimated soil response. Figure

4c shows the upper p-y curve enlarged with the beam-column deflection at that depth

represented by the vertical, dashed line. A line is drawn to the soil resistance p

corresponding to the deflection y with the slope of the line indicated by the symbol Es.

Figure 4d shows the values of Es plotted as a function of x. In performing a computation,

the computer utilizes the computed values of Es and iterates until the differences in the

deflections for the last two computations are less than a specified tolerance. If desired,

bending moment along the beam column can be computed during iterations, using the

appropriate difference equation, and the value of EI can be computed and varied along

the beam column with each iteration.

Figure 4 Procedure for solving for response of a laterally loaded beam column

After deflections have been computed, difference equations can be employed to

compute rotation, bending moment, shear, and soil reaction as a function of x. The

number of iterations for a tolerance of 0.00025 mm is usually less than 20. A high-speed

computer can converge to a solution in less than one second of central-processor time.

Thus, if p-y curves are available, a solution to a given problem can be obtained with little

difficulty.


4. Soil Response Curves

Soil-response curves have been obtained from several full-scale experiments. The

piles were instrumented for the measurement of bending moment as a function of depth.

Loads were applied in increments and a bending-moment curve was obtained for each

load. Two integrations of each curve yielded pile deflection and two differentiations

yielded soil reaction (Matlock and Ripperger, 1958). The cross-plotting of deflection and

soil resistance yielded experimental p-y curves.

Methods for predicting p-y curves have been worked out for soft clay (Matlock,

1970), for stiff clay below the water surface (Reese et al., 1975), for stiff clay above the

water table (Welch and Reese, 1972), and for rock (Nyman, 1980). Several authors have

made use of reports in the technical literature on instrumented tests and on

uninstrumented tests to make other recommendations (Parker and Reese, 1971; Sullivan,

1977; Bhushan et al., 1981, O'Neill and Murchison, 1984; O'Neill and Gazioglu, 1984).

Some modifications of standard p-y curves obtained for piles are necessary for

applications to flexural retaining walls. The following considerations should be included:

(1) the active-pressure condition will exist in the soil behind the wall above the dredge

line; (2) the p-y curves for a continuous wall are the same as those for closely-spaced

piles except that the p-values are reduced by a group-reduction factor based on the

spacing; and (3) the p-y curves for the wall below the dredge line may be constructed

initially by using the recommended values on the passive-pressure side (inside the wall)

and subtracting from the ultimate p-values the portion of the value of the active pressure

(outside the wall) due to the overburden pressure. The p-y curves should include the

effect of active pressure from the backfill side.

5. Validation Examples

5.1 EXAMPLE 1. ACTIVE EARTH PRESSURE ON SHEET PILE

Sheet pile wall sections are to be used to shore up the sides of a trench. This problem

was analyzed using Program PYWALL 2.0. The trench is 19.7 ft (6 m) wide and 20 ft


deep (6.1 m) (Fig. 5). It is embedded in two soil layers and the groundwater pumped out

of the excavation side. The contractor will place struts and wales at the height of the

water table (Fig. 6), which are assumed to compress no more than 0.2 in (5 mm).

- 4.6 m

+1.5 m

Sand, γ ’=0.9 T/m3

φ =25o

2

Cu,ave=1.05 T/m2

6 m

6.1 m

- 16 m

- 5.1 m

-

0 m

- 4.6 m

+1.5 m

Sand, γ ’=0.9 T/m3

φ =25o

Stiff Clay Cu=6.0 T/m

2

6 m

6.1 m

- 16 m

- 5.1 m

0 m

Figure 5 Profile of Trench

Figure 6 Profile of Sheet Wall and Soil Layers


The sheet piles used to construct the wall are 49.6-in. (1.26 m) wide steel AZ26 sections,

with moment of inertia equal to 1680 in4 (69,940 cm4), elastic section modulus equal to

200 in3 (3,280 cm3), and area equal to 38.6 in2 (249 cm2). The wall was divided into 100

increments of 5-in. (127 mm) in length. The program was asked to generate the

triangular-distribution earth pressure and the p-y curves. The soil input parameters are

provided in Table 1.

Table 1 Soil Input Parameters for Trench Sheet Wall Problem Soil type Layer

thickness (in.)

Total Unit Weight (lbs/in3)

Cohesion (lbs/in2)

Friction Angle (deg.)

E50 K (lbs/in3)

Sand 260 0.0686 0 25 0 20 Stiff Clay 429 0.0682 8.68 0 0.007 300

A rough hand check of the earth pressure behind the wall at the bottom of the excavation

is done to check the program output. The depth of the soil above the water line is

approximately 4.9 ft. (1.5 m) and the depth below to the bottom of the excavation is

approximately 15.1 ft (4.6 m). The active earth factor, Ka, is calculated to be:

2 2tan (45 / 2) tan (45 25 / 2) 0.406Ka φ= °− = °− ° =

Thus, the pressure behind the wall is:

3 3 3 2 2118.5 4.9 56.1 15.1 62.4 15.1 1522 10.6alb lb lb lb lbK ft ft ftft ft ft ft in

⎛ ⎞× × + × + × = =⎜ ⎟⎝ ⎠

To determine the distributed load produced by the earth pressure, the pressure is

multiplied by the width of the sheet pile section, 49.6-in. (1.26 m), resulting in an earth

pressure of 525.8 lb/in. The maximum earth pressure at the bottom of the excavation

from the PYWALL output is 524 lb/ft (Fig. 7), which is in close agreement with the hand

computations.


Figure 7 Earth Pressure Distribution from PYWALL

Other output graphs from the PYWALL software are shown in Figs. 8 to 11. The

maximum deflection in the wall is 0.9 in. at a depth of approximately 18.5 ft. The

maximum moment of 3,030 in-kips occurs at a depth of 16.7 ft. Therefore, the maximum

stress in the section is:

2max 3

3030 15.2 /200

M in kips kip inS in

σ −= = =

This stress is well below the maximum allowable stress of 50 kip/in2 for the sheet pile

section. The maximum shear (35.4 kips) and the maximum reaction (37.9 kips) per 49.6-

in. sheet wall unit occur at the height of the supports. The structural engineer will design

the struts and wales based on these results.


Figure 8 Deflection of Sheet Pile Wall from PYWALL

Figure 9 Bending Moment in Sheet Pile Wall from PYWALL


Figure 10 Shear in Sheet Pile Wall from PYWALL

Figure 11 Sheet Pile Wall Reaction from PYWALL


6. Concluding Comments

Several steps have been undertaken in-house by Ensoft to verify the output of

Program PYWALL. The user, if desired, may easily perform some of the elementary

computations shown below.

1. With regard to the static equilibrium of the lateral forces on a single pile, the

values of soil resistance can be computed and plotted along the length of the

pile. With the lateral loads at the top of the pile, a check on the equilibrium of

lateral forces can be made. A satisfactory check has been made by estimation;

a more comprehensive check can be made by use of numerical integration of

the distributed loads. The program will also conduct such checks internally to

ensure the equilibrium of forces.

2. The final internal check relates to the computed movement of the system. The

first step is to refer to the computer output to confirm that the distributed load

(soil resistance) and the distributed deflections along the length of the pile are

consistent with the associated p-y curves. If equations were used to compute

the values of p and y, it is necessary to interpret the equations at a sufficient

number of points to shown that the soil criteria for lateral load was followed.

The second step with respect to lateral load is to employ the diagram in Step 1

and to use principles of mechanics to ascertain that the deflection of the

individual piles was computed correctly.

While employing the steps shown above have confirmed the internal functioning

of Program PYWALL, the application of the program to results of field experiments is

useful. As noted earlier, the book by Reese & Van Impe (2001)1 presents a discussion of

the development of the methods used in Program PYWALL and applies the methods to

several cases. Although the program has been used with apparent success in many

analyses, new information is being developed and new versions may be written from time

to time. No warranty, expressed or implied, is offered as to the accuracy of results from

the program. The program should not be used for design unless caution is exercised in

interpreting the results and independent calculations are available to verify the general 1 Reese, L. C., & W. F. Van Impe, Single Piles and Pile Groups Under Lateral Loading, Balkema, Rotterdam, 2001, 463 pages.


correctness of the results. All users are requested to inform ENSOFT, INC. immediately

of any errors that are found in the coding for study and correction.

6.1 REFERENCES

American Petroleum Institute, “Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms, API Recommended Practice 2A (RP 2A),” Seventeenth Edition, April 1, 1993.

Baguelin, F., J. F. Jezequel, and D. H. Shields, The Pressuremeter and Foundation Engineering, Trans Tech Publications, 1978.

Bhushan, K., L. J. Lee, and D. B. Grime, “Lateral Load Test on Drilled Piers in Sand,” Preprint, ASCE Annual Meeting, St. Louis, Missouri, October 26-30, 1981.

Broms, B. B., “Design of Laterally Loaded Piles,” Proceedings, American Society of Civil Engineers, Vol. 91, No. SM3, May, 1965, pp. 77-99.

Det Norske Veritas and Riso National Laboratory, Guidelines for Design of Wind Tunnels, 2001, 253 pages.

Det Norske Veritas, “Rules for the Design, Construction, and Inspection of Offshore Structures,” Veritsveien 1, 1322 Hovek, Norway, 1977.

Federal Highway Administration, Ground Anchors and Anchored Systems, Geotechnical Engineering Circular No. 4, June 16, 1999.

George, P. and D. Wood, Offshore Soil Mechanics, Cambridge University Engineering Department, 1977.

Georgiadis, M., "Development of p-y Curves for Layered Soils," Proceedings, Geotechnical Practice in Offshore Engineering, American Society of Civil Engineers, April, 1983, pp. 536-545.

Jamiolkowski, M., “Design of Laterally Loaded Piles,” General Lecture, International Conference on Soil Mechanics and Foundation Engineering, Tokyo, Japan, 1977.

Matlock, H., "Correlations for Design of Laterally-Loaded Piles in Soft Clay," Paper No. OTC 1204, Proceedings, Second Annual Offshore Technology Conference, Houston, Texas, Vol. 1, 1970, pp. 577-594.

Matlock, H. and A. T. Haliburton, "Finite-Element Method of Solution for Linearly Elastic Beam Columns," Research Report No. 56-1, Center for Highway Research, The University of Texas at Austin, Austin, Texas, September, 1966.


Matlock, H. and W. B. Ingram, "Bending and Buckling of Soil Supported Structural Elements," Paper No. 32, Proceedings, Second Pan American Conference on Soil Mechanics and Foundation Engineering, Brazil, July, 1963.

Matlock, H. and L. C. Reese, "Generalized Solution for Laterally Loaded Piles," Transactions, American Society of Civil Engineers, Vol. 127, Part I, 1962, pp. 1220-1251.

Matlock, H. and E. A. Ripperger, “Measurement of Soil Pressure on a laterally Loaded Pile,” Proceedings, American Society for Testing Materials, Vol. 58, 1958, pp. 1245-1259.

Nyman, K. J., “Field Load Tests of Instrumented Drilled Shafts in Coral Limestone”, Unpublished Masters Thesis, The University of Texas at Austin, May 1980, 181 pages.

O’Neill, M. W. and S. M. Gazioglu, “Evaluation of p-y Relationships in Cohesive Soil,” Proceedings, Symposium on Analysis and Design of Pile Foundations, ASCE, San Francisco, October 1-5, 1984, pp. 192-213.

O’Neill, M. W. and J. M. Murchison, “Evaluation of p-y Relationships in Cohesionless Soils,” Proceedings, Symposium on Analysis and Design of Pile Foundations, ASCE, San Francisco, October 1-5, 1984, pp. 174-191.

Parker, F., Jr. and L. C. Reese, "Lateral Pile-Soil Interaction Curves for Sand," Proceedings, The International Symposium on the Engineering Properties of Sea-Floor Soils and Their Geophysical Identification, The University of Washington, Seattle, Washington, July, 1971.

Peck, R. B, Hanson, W.E. and T. H. Thornburn, Foundation Engineering, 2nd Edn, Wiley, New York, 1974.

Poulos, H. G., and E. H. Davis, Pile Analysis Foundation and Design, Wiley, New York, 1980.

Price, G. and I. F. Wardle, "Lateral Load Tests on Large Diameter Bored Piles," Contractor Report 46, Transport and Road Research Laboratory, Department of Transport, Crowthorne, Berkshire, England, 1987, 45 pages.

Reese, L. C., "Analysis of a Bridge Foundation Supported by Batter Piles," Proceedings, Fourth Annual Engineering and Geology and Soils Engineering Symposium, Moscow, Idaho, April, 1966, pp. 61.

Reese, L. C., "The Analysis of Piles under Lateral Loading," Proceedings, Symposium on the Interaction of Structure and Foundation, The Midland Soil Mechanics and Foundation Engineering Society, University of Birmingham, Birmingham, England, July, 1971, pp. 206-218.


Reese, L. C., “Handbook on Design of Piles and Drilled Shafts under Lateral Load,” a report prepared for Federal Highway Administration, U.S. Department of Transportation, Research, Development and Technology, McLean, VA, FHWA-IP-84-11, July, 1984, 360 pages.

Reese, L. C., W. R. Cox, and F. D. Koop, "Analysis of Laterally Loaded Piles in Sand," Paper No. OTC 2080, Proceedings, Fifth Annual Offshore Technology Conference, Houston, Texas, 1974 (GESA Report No. D-75-9).

Reese, L. C., W. R. Cox, and F. D. Koop, "Field Testing and Analysis of Laterally Loaded Piles in Stiff Clay," Paper No. OTC 2313, Proceedings, Seventh Offshore Technology Conference, Houston, Texas, 1975.

Reese, L. C. and H. Matlock, "Numerical Analysis of Laterally Loaded Piles," Proceedings, Second Structural Division Conference on Electronic Computation, American Society of Civil Engineers, Pittsburgh, Pa., 1960, pp. 657.

Reese, L. C., and W. F. Van Impe, Single Piles and Pile Groups Under Lateral Loading, Balkema, 2001, 463 pages.

Sullivan, W. R., “Development and Evaluation of a Unified Method for the Analysis of Laterally Loaded Piles in Clay,” Unpublished Masters Thesis, The University of Texas at Austin, May, 1977.

Tschebotarioff, G. P., “Large scale earth pressure tests with model flexible bulkhead,” Final Report, Bureau of Yards and Dock, Department of Navy, pp 1-112, 1948.

Welch, R. C. and L. C. Reese, "Laterally Loaded Behavior of Drilled Shafts," Research Report No. 3-5-65-89, conducted for Texas Highway Department and U.S. Department of Transportation, Federal Highway Administration, Bureau of Public Roads, by Center for Highway Research, The University of Texas at Austin, May, 1972.

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Pywall v3 Validation Notes