The effect of arching pressure on a vertical circular shaft

Tunnelling and Underground Space Technology 37 (2013) 10–21

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Tunnelling and Underground Space Technology

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The effect of arching pressure on a vertical circular shaft

Kyoung-Yul Kim a, Dae-Soo Lee a, Jaeyeon Cho b, Sang-Seom Jeong b,⇑, Sungjune Lee c

a Korea Electric Power Research Institute, Daejeon, South Koreab Department of Civil and Environment Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 120-749, South Koreac Department of Civil Engineering, Cheongju University, Cheongju 360-764, Republic of Korea

a r t i c l e i n f o a b s t r a c t

Article history:Received 15 August 2012Received in revised form 15 January 2013Accepted 11 March 2013Available online 13 April 2013

Keywords:Vertical circular shaftArching effectEarth pressureCentrifuge model testFull-scale field test

0886-7798/$ - see front matter � 2013 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.tust.2013.03.001

⇑ Corresponding author. Tel.: +82 19 362 4074.E-mail address: [email protected] (S.-S. Jeong)

The lateral earth pressure of vertical circular shaft is investigated by using experimental tests and a the-oretical analysis. The emphasis was quantifying on the magnitude and distribution of a lateral earth pres-sure measured by three-dimensional arching effect. A framework for determining the earth pressuredistribution on the basis of both centrifuge model and full-scale field test results is introduced. Throughthese studies, it is found that the lateral earth pressure decreases within active displacement (dh/H:0.2 � 10�2, dh: horizontal displacement, H: Height of vertical shaft) of wall at deep excavation and thearching effect is more significant for deep excavation than for shallow excavation. It is also found thatthe lateral earth pressure acting on a vertical circular shaft considering arching effect is 80% smaller thanthat calculated by Rankine theory, and thus represents a significant improvement in the prediction ofrealistic earth pressure for vertical circular shaft subjected to arching pressure.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

In South Korea, an increasing need for underground excavationand the application of the vertical circular shaft is becoming animportant issue in engineering practice. Here the vertical shaft isgenerally embedded in soft or hard rocks through weathered soilvarying thicknesses ranging up to 15 m. Since 1980, a number ofhuge excavation projects such as underground space for construct-ing power stations, subways, high-speed railways, and many life-line constructions have been performed in urban areas (Jeongand Seo, 2004). Although there have been considerable advance-ments in construction techniques involving vertical shaft, it is stillvery important for tunnel engineers to control the lateral earthpressure. Additionally, proper estimation of earth pressures is akey factor in design of vertical shafts. Because of three dimensionalarching effects, i.e. convex arching and/or inverted arching, theearth pressure acting on a circular type of vertical shaft is less thanother types. Thus, the circular vertical shaft is generally used.

Much work has been done to study the lateral earth pressureacting on a rigid wall by many researchers. Terzaghi (1920) re-ported fundamental studies on characteristics of earth pressureacting on retaining wall. Berezantzev (1958) reported that the ac-tive earth pressure acting on a gravel-backfilled cylindrical retain-ing wall, however it could not consider the earth pressure changeswith varying wall shapes. In addition, a few previous studies havebeen performed for the earth pressure acting on a cylindrical

ll rights reserved.

.

retaining wall in sands (Terzaghi, 1943; Steinfeld, 1958; Prater,1977). Moreover, recent studies by Coates (1981) determined thatthe earth pressure acting on a vertical shaft lining. Also, Handy(1983) and Wang (2000) reported that the friction between backfilland the retaining wall was caused by earth pressure in a curvedfailure surface. However, most of previous studies were based ontwo-dimensional plain strain condition and thus, it may not repre-sent the behavior of actual vertical shaft which does not take intoaccount the actual lateral earth pressure acting on a vertical circu-lar shaft.

To overcome this limitation, some research has been performedby centrifuge model test for a vertical circular structure. Koniget al., (1991) conducted a test to investigate the three-dimensionalearth pressure distribution, and Toyosawa et al., (2006) analyzedlateral earth pressure distribution for plane retaining wall using acentrifuge model test.

Handy (1983) analyzed soil arching action behind retainingwalls, and Wang and Yen (1973) carried out this analysis for slopes.Nakai et al. (1997) performed a series of physical model tests undera 1 g conditions and carried out numerical analysis of these tests toinvestigate the arching effect. They found that the results obtainedfrom the model tests were in good agreement with those obtainedfrom the numerical analysis. Recently, Kim et al. (2009) reportedthat the earth pressure was reduced by horizontal/vertical three-dimensional arching effect. However, these studies do not predictthe characteristics of the earth pressure considering arching effectat each excavation stage.

As discussed above, since Terzaghi (1920) started to examinethe effect of lateral earth pressure acting on a plane wall, much

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(b) Slip surface

(a) Mode of yielding (Wong and Kaiser, 1988)

Fig. 1. Behavior of the soil around vertical circular shaft: (a) mode of yielding and(b) slip surface.

K.-Y. Kim et al. / Tunnelling and Underground Space Technology 37 (2013) 10–21 11

work has been done in the area of soil–structure interaction ofplane retaining walls. Relatively little work has been done on flex-ible and circular walls such as vertical shaft, and hardly anythingon earth pressure distribution of vertical circular shaft. Soil-circu-lar wall behavior is complicate since many complex constructionsequences, different soil conditions, initial conditions, and archingeffect are involved. Additionally, previous studies are not applica-ble to the multi-layered and/or c–/ soils.

The objective of this study is to investigate the actual magni-tude and distribution of lateral earth pressure acting on the verticalcircular shaft considering the three-dimensional arching effect inweathered soil. In order to achieve the objective, new theoreticalmethod is suggested for estimating the earth pressure in multi-lay-ered c–/ soils. Comparisons are made between the soil-verticalshaft behavior observed by centrifuge test and full-scale field testsand that computed by the theoretical methods.

2. Theoretical earth pressure formula of vertical circular shaft

The behavior of a vertical shaft is affected and near the surfacedominated by gravitational forces (Wong and Kaiser, 1988). It is atruly three-dimensional problem and all three stress components(r0t , r0m, r0r). The stress concentrations near a vertical shaft wouldcause yielding due to the stress difference between vertical (r0m)and radial (r0r) around a shaft (Fig. 1a). In order to accurately deter-mine the lateral earth pressure on a vertical shaft, it is necessary toconsider an accurate shape for the slip surface in the formulationfor the earth pressure. In this study, it is assumed that the slip sur-face for a vertical shaft is plane and slope at an angle of b = 45� + //2 is used to calculate the earth pressure on the shaft (Fig. 1b).

The three-dimensional earth pressure acting on a vertical circu-lar shaft in c–/ soil is calculated by considering convex (lateraldirection) and inverted (vertical direction) arching effect (Fig. 2).A comprehensive study of earth pressure acting on vertical shafthas been reported by Kim et al. (2009). Therefore, only the coeffi-cient of tangential and radial earth pressure will be briefly summa-rized here.

2.1. The coefficient of tangential earth pressure

The coefficient of tangential earth pressure (k) is defined to bethe ratio of tangential stress to vertical stress. The earth pressureon vertical shafts decreases with the increase of tangential stressacting on the failure surface, thus with increase of k value. Wongand Kaiser (1988) suggested that k value is not 1.0 at elastic state;but will reach 1.0 at plastic state. In this study, k is assumed to be1 – sin/ (Lee et al., 2007).

2.2. The coefficient of tangential earth pressure

The coefficient of radial earth pressure is defined as the ratio ofradial stress to vertical stress. Rankine (1857) suggested the coeffi-cient of active earth pressure (Ka) without considering wall frictionangle (d). Paik and Salgado (2003) assumed miner principle stressdirection is changing in concave shape, such as elliptic, catenaryand parabolic due to fictional resistances of wall, and the coeffi-cient of earth pressure (Kwa) as follows:

kwa ¼3ðN cos2 hþ sin2 hÞ3N � ðN � 1Þ cos2 h

ð1Þ

where N ¼ tan2ð45þ /=2Þ; h ¼ tan�1 ðN�1�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðN�1Þ24N tan2 dp

2tand

� �, d is the

wall friction angle (�).As shown in Fig. 3, the equilibrium condition of horizontal force

acting on the differential soil element gives

Z 2p

0NwRdhdzþ

Z 2p

02r0t sin

dh2

� �r dzþ

Z 2p

0sf

cos bsin b

ðr þ RÞdhdz

¼Z 2p

0Nf

cosð90� bÞsin b

ðr þ RÞdhdz ð2Þ

In Eq. (2), Nw is the lateral stress acting on wall surface of ele-ment and is same as rh, and sf is defined as shear strength at failuresurface. Nw and r0t will be expressed as

Nw ¼ r0h ¼ kwar0m ð3Þ

r0t ¼ ð1� sin /Þr0m ð4Þ

where r0m is the vertical stress at certain depth z. If dh is very small,then Eq. (5) can be obtained by substituting Eqs. (3) and (4) into Eq.(2):

Nf ¼Rkwar0m þ rð1� sin /Þr0m þ c cos b

sin b ðr þ RÞr þ R

� tan btan b� tan /

ð5Þ

(b) Vertical arching pressure

(a) Lateral arching pressure

Fig. 2. Lateral and vertical arching effect of vertical circular shaft: (a) lateral arching pressure and (b) vertical arching pressure.

12 K.-Y. Kim et al. / Tunnelling and Underground Space Technology 37 (2013) 10–21

From Fig. 3a, the equilibrium of vertical stress gives

r0mAþ Adzc ¼ ðr0m þ drmÞAþ 2pRsw dzþ 2pðr þ RÞfsf sin b

þ Nf sinð90� bÞg dzsin b

ð6Þ

where A is the area of differential soil element, sf is the shearstrength at failure surface, and sw is the shear strength at wallsurface.

The first order differential Eq. (7) can be obtained by substitut-ing Eq. (5) into Eq. (6).

dr0mdzþ Sr0m ¼ T ð7Þ

Eq. (7) can be solved with the boundary condition, r0m ¼ 0 whenz = 0. Then, r0m is

r0m ¼ q� TS

� �e�s�z þ T

Sð8Þ

For parameter T and S can be written as

T ¼ c� 2pA

cw þ cðRþ rÞ 1þ 1tan b

þ 1þ tan b� tan /tan b� tan /

� ��

S ¼ 2pA

kwa þ R tan dþ ðkwaRþ krÞ þ 1þ tan b� tan /tan b� tan /

� ��

where c is the soil unit weight (kN/m3), / is the soil friction angle(�), c is the cohesion factor (kPa), R is the radius of vertical circularshaft (m), r is the width of plastic region in certain depth (m), A isthe horizontal area of loose area (m2), b is the angle of slip surface(45� + //2), and q is the surcharge load.

Therefore, the total soil pressure (pi) can be expressed as

Pi ¼ kwar0m ð9Þ

where kwa is a coefficient of radial earth pressure and r0m is the ver-tical effective overburden pressure.

(a) Section view

(b) 3D view

Fig. 3. Equilibrium of stress at soil: (a) section view and (b) 3D view.


3. Centrifuge model test

3.1. Testing program

A series of centrifuge model tests were performed to investigatethe soil pressure of vertical circular shaft in sand. Two model testswere performed on 1/75th scale models to analyze characteristicsof earth pressure acting on the vertical circular shaft, as summa-rized in Table 1. The model tests were performed at a radial accel-eration of 75g.

Model vertical shaft was made of aluminum alloy with a hollowcircular section, 200 mm embedded length, and 80 mm outerdiameter (Fig 4b). It was equivalent to reinforced concrete vertical

shaft of length 15 m, and outer diameter 6 m at prototype scale. Toinvestigate the lateral earth pressure at each excavation stage, testmodel was divided two sections.

The soil used in the model test had a specific gravity (Gs) of 2.65and was classified as SP in the Unified Soil Classification System.The sand layer was prepared from the sand hopper to form a uni-formly dense sand bed with 81–82% relative density approxi-mately. Table 2 presents the material properties used in thecentrifuge models. To observe the plastic region in soil sample, adifferent color was adopted at each soil layer.

After completing sample preparation, the sample box wasmounted on the platform of the centrifuge. The lateral earthpressure acting on the vertical shaft was monitored during the

Table 1Centrifuge model tests.

Soil Vertical shaft

c (kN/m3) / (�) Water content (%) G (kPa) Diameter (cm) H (cm) H/D

Test 1 12.66 36.95 2.0 75 8.0 20.0 2.5Test 2 12.65 36.95 2.0 75 8.0 20.0 2.5

(a) Soil sample box (b) Model vertical shaft (c) Sand hopper

Fig. 4. Testing apparatus: (a) Soil sample box, (b) model vertical shaft and (c) sand hopper.

Table 2Properties of the test soil.

D10 (mm) 0.091D20 (mm) 0.098D60 (mm) 0.140D90 (mm) 0.175Coefficient of uniformity, Cu 1.53Specific gravity, Gs 2.65Unified soil classification system SP


excavation. To simulate the excavation step, incremental activewall displacement (dh/H, dh: horizontal displacement, H: Heightof vertical shaft) was chosen to be 1.0 mm/140 s using a multi-gearmotor. Terzaghi (1920) suggested that active earth pressure occursat about 0.1%H of active wall displacement. This value is applicableto 15 mm wall displacement in this test.

3.2. Testing apparatus

The geotechnical centrifuge used in this study was located atDaewoo Institute of Construction Technology (DICT). DICT’s

Table 3Main properties of geotechnical centrifuge equipment.

Centrifuge radius Platform radius (m)Nominal radius (m)

Usable payload dimension Platform width (m)Nominal depth (m)Usable height (m)

Performance Maximum payload (kN)Acceleration at max. payloaAcceleration range (g)Speed range (rpm)

Electrical slipring Signal, power, and video lin

Rotary joint OilWaterAir

geotechnical centrifuge was manufactured by Actidyn companyin France and corresponds to an Actidyn system C65-2, with a plat-form radius of 3.0 m and a maximum capacity of 120 g ton. Thespecification of DICT’s centrifuge is summarized in Table 3.

A small soil sample box 700 mm long, 400 mm wide, and200 mm high was made with a steel frame (Fig. 4a). Model verticalshaft was made of aluminum alloy with a hollow circular section,400 mm embedded length, 20 mm outer diameter, and 3 mmthickness. They are equivalent to reinforced concrete piles oflength 15 m, outer diameter 6 m at prototype scale.

A sand hopper was designed to form a uniform soil bed with therequired density (Fig. 4c). It is automatically controlled by a com-puter system according to the traveling velocity of the hopper andthe height and quantity of pluviation.

A variety of instrumentations were installed to monitor dis-placements and earth pressures during the testing. The displace-ment of vertical shaft wall was measured by two linear variabledifferential transformers (LVDTs) located on both sides of the shaftsurface shown in Fig. 5. Pre-calibrated Kyowa earth pressure trans-ducers were installed on the external surface of vertical cylinderwall to measure the lateral earth pressures acting on the verticalshaft, and their locations in the model are also shown in Fig. 5.

3.02.7

0.81.00.8

12d (g) 100

10–23025–265

es 46, 12, 2

20 MPa working pressure Each two ports2 MPa working pressure

(a) Section view

(b) Plan view

(c) Vertical circular shaft model

Fig. 5. Sectional and plan views of the soil sample box and vertical shaft model.


3.3. Test results and discussion

Some typical results from centrifuge model tests are presentedhere. The data are presented in terms of prototype units scaled up

according to the relevant scaling relationships (Schofield, 1980).The validation of initial condition (displacement of verticalshaft = 0) for earth pressure was examined by a comparison witha K0 condition. Fig. 6a and b shows a comparison of the measured

16

12

8

4

0

Dep

th(m

)

0 20 40 60 80

Lateral earth pressure (kPa)

K0=0.390mm

(a) Test 1

16

12

8

4

0

Dep

th(m

)

0 20 40 60 80


K0=0.390mm

(b) Test 2

Fig. 6. Comparison of measured and calculated earth pressure at rest (at acceler-ation 75g).

0 0.2 0.4 0.6

δh/H (x10-2 )

0

20

40

60

80

Late

rale

arth

pres

sure

(kPa

)

(a) Upper section

0 0.2 0.4 0.6

δh/H (x10-2 )

0

20

40

60

80

Late

rale

arth

pres

sure

(kPa

)AP1AP2AP3AP4AP5AP6AP7AP8

(b) Lower section

Fig. 7. Earth pressure distributions in Test 1: (a) upper section and (b) lowersection.


and calculated earth pressures. It is shown that agreement be-tween the K0 and initial condition of test is generally good (coeffi-cient of determination, R2 = 0.96, 0.99).

Figs. 7 and 8 show the results from two typical tests with mea-sured earth pressure under the condition of active wall displace-ment. As shown in Figs. 7a and 8a, it is noted that the lateralearth pressure on upper section of the vertical shaft (AP1–AP4)at first excavation step gradually decreases, until a wall displace-ment is reached at about 0.2. This curve demonstrated the reduc-tions in lateral earth pressure with gradual increase of walldisplacement. When the active wall displacement (dh/H:0.2 � 10�2) is occurred, the earth pressure was about 30% (AP4) de-creases in initial earth pressure. At this time, the earth pressure onlower section (AP5–AP8) of vertical shaft is measured in a constant.In the second excavation step, where the earth pressure in lowersection of the vertical shaft, large reductions of earth pressureare occurred in Figs. 7b and 8b. When the active wall displacement(dh/H: 0.2 � 10�2) is occurred, the earth pressure was about 80%(AP8) decreases of initial earth pressure. Additionally, an earthpressure acting on the upper part (AP1–AP4) of vertical shaft tends

to increase as the active displacement of lower part increases. Fur-thermore, an increase of lateral earth pressure in the active dis-placement from 0 to 0.2 results in about 10–30%. Similarmagnitude of earth pressure as initial condition (before the firstexcavation) is measured when the active wall displacement wasincreased from 0 to 0.6.

Fig. 9 shows the distribution of plastic deformation in soil sam-ple. It is noted that plastic region in the soil sample is about 1D(D = diameter of vertical shaft) and then, the settlement of soilsample was about 13 mm (97.5 cm in full scale). Fig. 10 shows acomparison of the test result and theoretical solution proposedby Kim et al. (2009). All the measured data have a relatively smal-ler earth pressure than the result of the proposed solution. How-ever, earth pressure at the bottom, 14 m in depth, occurredrelatively high, because soil container used in test is the particu-larly strong steel structure, earth pressure caused by soil looseningcould not be dissipated at the bottom section. In most of previousstudies, it is verified that the overall lateral earth pressure acting

0 0.2 0.4 0.6

δh/H (x10-2)

0

20

40

60

80La

tera

lear

thpr

essu

re(k

Pa)

(a) Upper section

0 0.2 0.4 0.6

δh/H (x10-2)

0

20

40

60

80

Late

rale

arth

pres

sure

(kPa

)

AP1AP2AP3AP4AP5AP6AP7AP8

(b) Lower section

Fig. 8. Earth pressure distributions in Test 2: (a) upper section and (b) lowersection.

Fig. 9. Failure surface (mode

16

12

8

4

0

Dep

th(m

)

0 20 40 60 80


K0=0.390mm (Test1)theory (Kim)δh/B=0.2x102 (Test1)δh/B=0.2x102 (Test2)

Fig. 10. Comparison of earth pressure distributions.


on the vertical circular shaft was reduced approximately 80% com-pared with the initial condition.

From the test results, it is note that the lateral earth pressure atdeep depth decreased within active displacement (dh/H:0.2 � 10�2), beyond which it continue to increase toward the initialcondition as displacement increase. This finding is similar fromwhat Tatiana and Mohamed (2010) discussed about active dis-placement for a wall. On the other hand, test vertical shaft is exca-vated into a relatively shallow excavation, there is very littlereduction of earth pressure. The reason for this behavioral differ-ence between deep and shallow excavation step is explained bythe fact that the weight re-distribution caused by the arching effectwill produce more pressure reduction in the deep depth than shal-low depth. Conclusively, the arching effect is generally more signif-icant for deep excavation than for shallow excavation and theobserved values by the centrifuge model have a smaller earth pres-sure when compared with the calculated by existing method (Kimet al., 2009).

4. Field test

Full-scale field test was conducted at the test site in order toinvestigate the lateral earth pressure acting on vertical circularshafts. This test was performed to provide a basis for a design

l height 200 mm, 75 g).

(a) Configuration of test shaft

(b) Shaft embedment

Fig. 11. Configuration of test shaft and shaft embedment.


guideline that would be applicable to a vertical shaft installed inweathered soils. Based on the soil condition, the applicable limitingdepth of vertical shaft is confined as up to 15 m to identify the

three-dimensional arching effect. Special attention is given to theanalyzing lateral earth pressure acting on full-scale vertical shaft(Fig. 11a) as excavation proceeds.

Table 4Summary of field and laboratory test results.

Soil Depth (m) N value Gs W.C. (%) E (MPa) / (�) c (kPa) Sieve analysis (%)

#4 #10 #40 #100 #200

Top soil 0–6.2 17/30–50/18 2.59 8.3 – 20.96 – 98.0 82.1 23.1 8.7 5.9Weathered soil 6.2–13.1 16/30–50/10 2.62 18.3 23.3 25.31 126.4 99.1 84.5 37.7 15.9 8.6Weathered rock 13.1–23.6 50/1–50/0 – – 33.8 (66.9) 31.8 294.0 –Soft rock 23.6–25.5 – – – – – –

14

12

10

8

6

4

2

0

Dep

th(m

)

0 20 40 60 80 100


MeasuredTheory (Kim)Rankine

(a) P-1

14

12

10

8

6

4

2

0

Dep

th(m

)

0 20 40 60 80 100


MeasuredTheory (Kim)Rankine

(b) P-2

Fig. 12. Measured and calculated earth pressure: (a) P-1 and (b) P-2.

Fig. 13. Stress applied on circular cylinder.


4.1. Geotechnical conditions at test site

A comprehensive geotechnical investigation was carried out todefine the soil profile and properties at the test site as accuratelyas possible. The in situ field tests included the standard penetrationtest (SPT), pressure meter testing (PMT) and borehole shear test.Undisturbed soil samples were retrieved for laboratory testingfrom the boring. Relatively disturbed specimens were also re-trieved from the SPT sampler. Laboratory testing was performed

to determine the particle size distribution, water content in rela-tion to Atterberg limits.

A generalized soil profile for this site is presented in Fig. 11b.The soil profile near the surface consists of layers of top soil,weathered soil and weathered rock underlain by soft rock. Thewater table was located 9.7 m below the natural ground surfaceduring the tests. The surface soils consist of poorly graded sandand silt sand classified as SP or SM according to the Unified SoilClassification System (USCS). The undrained shear strength wastypically 126.4–294 kPa. The underlying weathered soil layer con-sists of a well graded residual soil classified as SW or SM (USCS).Table 4 shows the summary of field and laboratory test results.

4.2. Test program and setup

A schematic representation of an instrumented vertical shaft isalso shown in Fig. 11b. The circular shaft had an outer diameter of6 m and a wall thickness of 80 mm. The depth of the shaft belowground level was 13.6 m. Excavation was performed by the back-hoe shovel. The reinforcing structure consisted of 12 H-pile(300 � 200 � 9 � 14 mm) with a ring wale (300 � 200 � 9 �14 mm). During the construction of H-pile, S.G.R. (Space GroutingRocket) method was adopted for the stability of the soil.

Many instrumentation was used to monitor the response of thevertical shaft-soil system. Automated equipment including soilpressure gauge, vibrating wire-stress meter, inclination, void waterpressure and ground water level measurement device were in-stalled. Earth pressure was measured at 1 m below the top ofH-pile using 10 soil pressure gauges, which were attached at twolocations (P-1 and P-2). Two vibrating wire-stress meter wasinstalled along the ring wales to measure the earth pressure. Thegauges, shown in Fig. 11, were sealed with a JIG to preventmechanical damage. Data from the various sensors were collectedsimultaneously using a computer controlled data acquisitionsystem.

4.3. Test results and discussion

The observed lateral earth pressures are compared with thepredicted values of theoretical methods. Fig. 12a and b shows

14

12

10

8

6

4

2

0

Dep

t h(m

)

0 20 40 60 80 100Lateral earth pressure (kPa)

ConvertedTheory (Kim)Rankine

(a) P-1

14

12

10

8

6

4

2

0

Dep

th(m

)

0 20 40 60 80 100


ConvertedTheory (Kim)Rankine

(b) P-2

Fig. 14. Converted and calculated earth pressure: (a) P-1 and (b) P-2.

14

12

10

8

6

4

2

0

Dep

th(m

)

0 20 40 60 80 100Lateral earth pressure (kPa)

Measured (P-1)Measured (P-2)Converted (P-1)Converted (P-2)Theory (Kim)Rankine

Fig. 15. Comparison of test result for vertical circular shaft.


representatively the predicted and measured earth pressure at twodifferent locations (P-1 and P-2). A reasonably good agreementbetween the measured ones and the solution presented by theexisting theories are obtained. In addition, maximum lateral earthpressure acting on the vertical shaft occurred within the depth ofshaft diameter below the ground level. However, the calculatedresults by Rankine theory have a relatively 80% lager earth pres-sure as the depth increased than the results of previous theory(Kim et al., 2009) and measured one.

These results clearly demonstrate that the distribution patternof the earth pressure acting on the vertical shaft is significantlydominated by three-dimensional arching effect. Therefore, theRankine theory may not reflect the nature of the arching effect ofsoil for the general case, and thus it requires validation beforebeing used in practice.

As mentioned above, two vibrating wire-stress meter was in-stalled along the ring wales to investigate the earth pressure actingon the vertical shaft. As shown in Fig. 13, the ring wale axial stressas pressure acting on the circular cylinder can be converted toearth pressure. The earth pressure is calculated from the followingequation;

2piR ¼ 2F ð10Þ

where pi is the soil pressure, R is the radius of vertical shaft, F is thering beam axial stress. In this analysis (+) stress value means activeearth pressure and (�) value means passive earth pressure.

Fig. 14 shows the converted and predicted earth pressures dis-tribution. The calculated results of existing method (Kim et al.,2009) closely approach the converted data from the measuredone. Although a reasonably good agreement between the theoret-ical and the measured one was obtained, the existing method(Kim et al., 2009) has a larger lateral earth pressure those of themeasured values at the same depth. In this case, it is also shownthat maximum lateral earth pressure acting on the vertical shaftoccurred within the depth of 4–6 m below the ground level. How-ever, the calculated results by Rankine theory have a significantly70% lager lateral earth pressure at the deep depth than the resultsof previous theory (Kim et al., 2009) and converted one. The three-dimensional arching effect is generally more significant for deepdepth than for shallow depth and the previous method consideringarching effect has a considerably smaller earth pressure whencompared with the results by Rankine theory.

Fig. 15 shows the lateral earth pressure distributions obtainedfrom the measured and predicted data. It is shown that the predic-tions by considering three-dimensional arching effect are in goodagreement with the general trend observed by field measurementsand has a considerably smaller earth pressure than the earth pres-sure calculated by the Rankine theory. This is because the Rankinetheory based on the two-dimensional plane stress ignores three-dimensional arching effect and, thus, overestimates the lateralearth pressure with increasing depth. This clearly demonstratesthat for vertical circular shaft, there exists three-dimensionalarching effect, so that this set of prediction and measured resultsprovides the reducing of lateral earth pressure.

4.4. Reduction ratio of lateral earth pressure

In the present design of vertical shaft, geotechnical engineershave traditionally calculated the active earth pressure againstwalls using Rankine theory. It was assumed that the distributionof active earth pressure exerted against the wall is triangular. How-ever, many experimental results (Tsagareli, 1965; Matsuo et al.,1978; Fang and Ishibashi, 1986) show that the distribution ofactive pressure acting on a wall depends on the mode of wall

Table 5Summary of Rf values for vertical circular shaft.

Soil Values z/D

0.2 0.5 0.7 1 1.7

c–/ soil Measured earth pressure (kPa) 18.16 24.26 19.80 13.71 10.89Rankine earth pressure (kPa) 21.09 37.5 45.7 51.56 70.31Rf 13.89 35.31 56.67 73.41 84.5


movement and is non-linear, different from the assumption madeby Rankine. The non-linearity of the active earth pressure distribu-tion results from arching effects (Handy, 1983). Especially, properestimation of earth pressures is a key factor in design of verticalcircular shafts. Because of three dimensional arching effects, i.e.convex arching and/or inverted arching, the earth pressure actingon a circular type of vertical shaft is less than other types. This sec-tion presents a correlation between Rankine earth pressure and re-duced lateral earth pressure based on the results of full-scale fieldtest performed in this study.

As mentioned above, in the case of the vertical circular shaft,there is no criterion to evaluate ‘‘earth pressure’’ for vertical shaft.Therefore, the measured versus the predicted by Rankine theorywere compared using an Rf value (reduction factor) defined as

Rf ¼Predicted earth pressure�Measured earth pressure

Predicted earth pressure

� 100% ð11Þ

A conservative Rf value ranges from 0% to 100% and Table 5summarizes the magnitude of Rf with varying excavation depths(z/D). Based on the Rf value results of Table 5, it is found that theRf values show a significant reduction in the prediction of real earthpressure.

5. Conclusions

The main objective of this study was to investigate a lateralearth pressure acting on a vertical circular shaft embedded inweathered soil. A limited study of the response of centrifuge andfield tests was performed to examine the three-dimensional arch-ing effect for lateral earth pressure. When applied to vertical circu-lar shaft constructed in weathered soil, comparative studies haveclearly demonstrated the important arching effect of vertical circu-lar shaft. Based on the findings of this study, the following conclu-sions can be drawn:

1. The test results show that the magnitude and distribution of alateral earth pressure acting on a vertical circular shaft is notlinear with increasing excavation depth. Experimental observa-tions confirm that more realistic distribution of lateral earthpressure is introduced for a vertical shaft embedded in weath-ered soil.

2. Through a comparison of theoretical calculation and full-scaletest with field measurements, it is found that for test shaft acoupled three-dimensional arching effect is important. The lat-eral earth pressure acting on the vertical circular shaft wasmaximum 80% reduction in a certain depth. Therefore, a com-monly used method like the Rankine equation for calculatingthe lateral pressure can substantially overestimate the lateralpressure in real situations.

3. Based on Rf value, the arching effect is generally more signifi-cant for deep excavation depth than for shallow excavationdepth and the measured data has a smaller earth pressure whencompared with the results by existing theories. When test shaftwere excavated into a relatively shallow depth, there was verylittle arching effect caused by small active earth pressure actingon vertical shaft and weight re-distribution.

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The effect of arching pressure on a vertical circular shaft