Investigation of Footing Restraint on Stability of Large-scale Reinforced Soil Wall Tests

RICHARD J. BATHURST

Professor, Civil Engineering Department, Royal Military College of Canada, Kingston, Ontario, K7K 5LO

SYNOPSIS

The paper reviews selccted results frolll two I:lrge-st:ale retainiJlgwail testscalTiedolll ill the RM(' Hetaining Wall 'Icst rildlity. The teslscolllpris\",1 two geogrid reinforced structures 3m in height that were taken to collapse under st:lged uniform surch:llgc pressurc applied to the hori7.0ntal hackfill s : rlace. The tests were carefully monitorcd and illllstrated that initial failme of thc compositc system was duc to soil shcar failure. The failurc location was con­trolledhythefadng treatmcnt whichwas ascgmcntal struCtUlC inoncwall amI a full height panel structure in the second. Themcasureosurchargc prcssure at soil failure was compared to prcdicted capacity usin!! conventional Ii III it -cquilihriumlllcthods of design. 'nle obselvcd maximulII surchargc capacitics of the walls arc significantly greater than those predicted hy tl)eory. The S()\II'ce of the discrepanq· is identified usillg a 3Dwedge analysis which explicitly includes the restraint offered by the footing at the base of each wall facing and side wall friction due to the test facility. Obselved maximum surchargc loads are corrected for side wall friction to demonstrate that in a tllle plane strain condition with realistic footing restraint the footing provides a significant portion of wall c:lpacity. A major condusion of the paper is that footing restraint is likely an important contributor to conselvativeness in current limit eqUilibrium -based methods of analysis in North America.

INTRODUCTION

Large -scale models of geosynthetie reinforced soil retaining walls have been carried out at the Royal Military College of Canada (RMC) over a period of several years. The purpose of the program has been to careful­ly measure a wide range of performance features of these systems dur­ingconstruction, at working load levels and at collapse under staged uni­form surchargingofthe hackfillsllrface. The tests have been carried Ollt under carefully controlled laboratory conditions in order to minimize the numher of variables within and hetween tests. The result is a high­quality database of results that can be used to investigate the accuracyof current analysis and design methods and to calibrate numerical models.

RMC RETAINING WALl. TEST FACILITY

This paper is focused on the results of two tests that were carried out in the RMC Retaining Wall lest Facility. The facility was conceived to pro­vide a general purpose large-scale apparatus to test a variety of rein­forced soil wall systems. The inside dimensions of the test facility at the time of this study were 3.8m high x 6m long x 2.4m wide. Experimen tal wall facings are constructed at the front of the test facility and the back of the test facility is used to mountextensometers attached to the inter­nal reinforcement layers. The facility side walls are comprised of a com­posite plywood/plexiglas/polyethylene sheeting that assists to reduce sidewall friction. Thesoilsurface c;tn besurcharged hy inflating airhags at the top of the facility. The current surcharging arrangement allows a vertical pressure of up to 1O() kPa to be applied to the soil surface.

The test facility is illustrated in Figure I. 'The two test configurations that are the focus of the paper are illustrated in Figure 2. The retained soil was a well-compacted coarse angular sand.

389

ANCHOR BOLTS

Figure I RMC Retaining Wall 'Iest Facility

.lru:J:kU\cntall'anel Wall Confieyru1i.!m

FRONT EDGE OF TEST FACILITY

'Ille incremental panel wall test is illustrated in Figure 2a.ln this meth­od each row of panels was placed sequentially as the height of the re­tained suil was increased and each row was temporarily supported until the soil hehind the wall had reached the top of each row of panels. The wall facings were constructed with 0.75m high articulated panels and each panel was connected to a separate strip of geogrid reinforcement extending 3m into the soil backfill. 'The reinforcement layer spacings

backfill soil

J- 3m-l

T 4 panels O.75m high =3m

i

a) incremental panel wall

reinforced soil

.T sIngle panel =3m

1 6m

b) full height panel wall

instrumented section

instrumented section

Figure 2 Reinforced soil retaining wall test configurations

and length are a standard configuration that has been adopted for all tests completed to date that used panel facings (a total of seven). The purpose of the incremental construction is to mobilize tensile load in the reinforcement layers as construction proceeds from the bottom to the wall crest. The design was based on a British code (BE3/781978) in ef­fect during the development of the test facility and assumed that the re­inforcement was a relatively stiff uniaxial polymeric geogrid material.

The facing units were stacked in three separate columns. The outside columns were 0.7m wide and the inside column was 1m wide. Only the central column of panels was instrumented and each column was an­chored by independent layers of reinforcement that provided complete coverage at each elevation across the width of the facility. The instrum­ented panels were rigid hollow aluminium panels, O. 75m highx 1m wide x 400mm thick, while the outside panels were constructed of wood. The strategy adopted here was to de -couple as far as possible the influence of side wall friction effects on the behaviour of the central instrumented column. The results of direct shear box tests carried out on the sand/side wall interface material used in this investigation showed that the fully­mobilized friction angle was 10 -15 degrees. The base of each column of panels was supported on a pinned connection with no horizontal or ver­tical degree of freedom. This boundary condition was adopted for sim­plicity and is a common boundary condition for retaining wall facing units that are usually seated on a rigid footing to ensure proper align­ment and to minimize differential settlements between panels (e.g. Ba­thurst 1991a).

Full Height Panel Wall Configuration

The full height panel wall test configuration is illustrated in Figure 2b. In this test the panel facing units were bolted together to form three in­dependent 3m high facing panels. The panelswere braced externally for the duration of construction (i.e. until the retained soil had been placed and compacted to the top of the wall). The reinforcement arrangement and boundary condition at the base of the facing units was identical to that described for the incremental panel wall.

A uniformly graded coarse angular sand material with some fine gravel has been used for all retaining wall tests carried out at RMC. The grain

390

size distribution for the sand has a uniformity coefficient Cu =5.0 and a coefficient of curvature Cc = 1. The compacted bulk unit weight was 18 kN/m3 and itwas placed at a moisture content of 1 to 3%. The results of direct shear box tests carried out at two different laboratories on com­pacted RMC sand gave a peak (secant) friction angle of <P = 53 degrees (Jewell 1987, Bathurst et aL 1987). The high strength of the sand is con­sidered to be due to the angularity of the constituent sand particles. This material would be considered an ideal material in a field application due to its high friction angle, permeability and ease of compaction.

Reinforcement

The earliest geogrid reinforced soil retaining wall models constructed in the RMC facility were built using a high strength extruded uniaxial polyethylene geogrid (Tensar SR2, Table 1). However, the composite structures could not be failed with the surcharge capacity at hand when this product was employed (Bathurst and Koerner 1987, Bathurst et al. 1987, 1988). For this reason, the tests reported in this paper were car­ried out using a weaker and more extensible biaxial polypropylene geo­grid material (Tensar SSI) oriented with its weakest direction in the plane strain direction of the wall. In practice this material has not been used for retaining wall construction but its use in the current study en­sured that collapse of the structure could be anticipated based on con­ventional design theory as described later in the paper.

Constant load (creep) tests were carried out on virgin samples of rein­forcement material. The in-isolation creep tests were carried out in a temperature controlled room at the same ambient temperature as the RMC laboratory. The results of tests are illustrated in Figure 3a. The data was used to generate isochronous load-strain data for the poly­meric material representing the stiffness of the material at selected elapsed times after application of a constant load using the method de­scribed by McGown et al. (1984). The construction of the l00hour iso­chronous load -straincUive for the SSI material in the weak direction is illustrated in Figure 3b. Using the same reinforcement material as in the current study, Yeo (1985) has demonstrated that under increasing staged tensile loading the cumulative strain in the geogrid is equivalent to that which results from the maximum load applied in a single incre­ment. This obselvation together with the data in Figure 3 has been used to estimate the tensile load in the reinforcement layers from directly measured strains during staged surcharging of the RMC test walls.

TABLE 1--

Mechanical Properties of Geogrid Materials (ASTM D4595 Tensile Properties of Geotextiles by the Wide Width

Strip Method)

Material Stiffness (kN/m) (@ 2% strain)

Tensar SR21

Tensar SS12

transverse (strong) longitudinal (weak)3

1096

292 204

Peak Load (kN/m)

79

20 12

1 high density polyethylene uniaxial geogrid 2 polypropylene biaxial geogrid 3 SSI oriented in weak direction for RMC test walls

SOURCE: Manufacturer's literature.

Strain(%) @Peak Load

17

14 14

-#. -c ·m .... -en

-E

30~---------------------. P

20

10

6.25 kN/m

5

3.75

2.5 1.25

O'+--+--~--~----~----~--~ o 200

100

400 600

time (hrs) a) constant load (creep) test data

800 1000

8~----------------------~

Z 4.9 ~ -CL. "'0 ca

4

o 2.8

2

0~--~--1---~---r---.---; o 0.05 0.10

strain, e (mm/mm) b) 100 hour isochronous 10ad-strainculVe

Figure 3 100 hour isochronous load-strain behaviour of geogl'id reinforcement

Instrumentation

0.15

Since the RMC test facility is indoors where construction quality can be carefully controlled and instrumentation protected, a comprehensive instrumen tation program is possible. In addi tion, expensive instrumen­tation can be recovered between tests. The instrumentation arrange-

391

extensometer '::;:,<5::: _H-~~--""""";;';;;;;;;;;""","'" ......

Geokon pressure: ~11 ~ , ',.

displacement potentiometer

l?ad T nng I

3m

1 Figure 4 Instrumentation arrangement for incremental panel

wall test

ment for the incremental panel wall test is illustrated in Figure 4. Approximately 300 electronic devices have been routinely installed in RMC test walls. The data acquisition system was controlled by a micro­computer that was programmed to record the response of all instru­ments at a selected time -interval (typically 8 hours). However, several critically located devices were monitored continuously and were pro­grammed to trigger full-channel acquisition if significant changes in device output were sensed. In this way significant events in the testing program were captured such as tertiary creep in the reinforcement just prior to wall collapse. A detailed description of the instrumentation used in the RMC tests can be found in the paper by Bathurst (1990). Of particular interest to this investigation are the load cells/rings mounted at the footing that permitted continuous monitoring of horizontal and vertical reactions developed at the base of the wall.

PREDICTED MAXIMUM DESIGN LOAD USING CONVENTIONAL LIMIT-EQUILIBRIUM METHODS

Current methods of analysis and design of geosynthetic reinforced soil retaining wall structures are based on conventional geotechnical con­cepts of earth pressure theory and Coulomb materials (e.g. FHWA 1989, AASHTO 1990). By definition, limit-equilibrium based meth­ods of analysis can be used to predict collapse conditions for earth re­tainingwall structures. In practice, factol's of safety are applied to fully­mobilized stabilizing forces to ensure safe design and failure of the polymeric reinforcement is defined by strain -limited (serviceability) criteria. The advantage of tests of the type carried out at RMC is that the accuracy oflimit-equilibrium models can be examined directly since a collapse condition was achieved in each test. The essential features of current design methodologies recommended by US federal agencies and the Canadian Foundation Engineering Manual for the class of structures described here have been reviewed in an earlier paper (Ba­thurst 1991b). These structures are treated as conventional gravity structures in which the reinforced soil zone is assumed to act as a mono­lithic body whose mass ensures adequate resistance to translational slid­ing at the base of the reinforced zone and overturning about the toe. Similarly, the length and height of the reinforced soil zone measured from the front of the structure must not lead to collapse of the founda­tion soils (bearing capacity failure). These collapse mechanisms are called external stability failure mechanisms and are treated in the same manner as any rectangular gravity wall structure in geotechnical engi­neering. More challenging are the calculations associated with internal stability of the reinforced zone. The density, strength and length of the reinforcement in the reinforced soil zone must be adequate to ensure that the reinforced soil zone acts as a monolithic body. Internal stability calculations are based on a "tie-backwedge" approach in which an ac­tive failure plane is assumed to propagate up into the soil from the heel ofthe facing units at an angle of 45+4>/2 degrees from the horizontal where 4> is the peak friction angle of the purely frictional soil. The ap-

proach is illustrated in Figure 5. Each layer of reinforcement is required to carry a portion of the distributed lateral earth pressure calculated from active earth pressure theory expressed as follows:

T max = Sv Ka (yz + q) (1)

The contribu tory area Sv is calculated using the mid - elevation between layers. Th.e tensile capacity Teap of the reinforcement must be adequate over the hfe of the structure so that T max is not exceeded. Based on the assumption ofa 100hrpost-construction design life and the data illus­trated in Figure 3, the maximum tensile load is 2.8 kN/m and 4.9 kN/m b~sed?? 5% ~nd .10% strain criteria respectively. The 5% strain (ser­vlceablhty) crltenon can be found in AASHTO (1991) and FHWA (1989) guidelines. At the time of the RMCwall constructions the strain l~mit criterion was 10% and this value appears in other current guide­hnes (e.g. GRI GG4, 1991, NCMA 1993). The 10% strain value was used in the design of the experiment to ensure collapse of the wall with the surcharge capacity at hand. These empirically established strain­limited criteria are adopted in North American practice to ensure that wall facing deformations are not excessive.

In practice, partial factors are applied to in-isolation tensile capacity values to account for mechanical damage and chemical degradation. In addition, an overall factor of safety is used to further reduce Teap to ac­count for overall uncertainties in soil properties, geometry and bound­ary loadings. In this experimental program these partial factors can be taken as unity since the test facility and construction method creates a benign environment for the polymeric reinforcement with respect to mechanical and chemical degradation. Constant load tests carried out on exhumed geogrid samples from earlier tests have demonstrated that the load -strain - time properties of these materials placed in the RMC test facility do not change as a result of method of construction (Bush and Swan 1987). This is not surprising since the soil particle sizes are small and the granular material is placed carefully and compacted using a light-weight vibrating plate tamper.

In order f~r the internal active wedge to remain in horizontal equilibri­um the remforcement must have adequate anchorage capacity within the resistance zone. In conventional practice a Coulomb model is adopted to compute anchorage capacity:

FigureS

z

1

Tcap> Tmax

Calculation of tensile force required in reinforcement layers

392

(2)

Theparameters in equation (2) can be referenced to Figure 6. Thecoef­ficient a is a measure of the effiCiency of load transfer between the an­chorage zone soils and the geogrid reinforcement. A minimum value of 0.5 is recommended by AASHTO but manufacturers literature quote numbers as high as 0.9. Regardless of the choice of coefficient, pullout capacity failure is not a possibility in these tests due to the long embed­ment length Le employed in the standard test configurations.

l!sing gen~ric calculati~ns for external and internal stability it is pos­SIble to estImate the maxImum surcharge pressure required to achieve a factorofsafetyofunity for the failure mechanisms described above. The calculations for this paper were carried out using simple computer codes. The essential computational details of these codes are described in the paper by Bathurst and Simac (1993).The results of calculations show that ~actors of safety against base sliding, overturning and pullout are exce.sslvely la~ge even when a 100 kPa pressure is applied to the top of the tnal walls (I.e. factors of safety> 10). The rigid concrete base slab that forms the base of the test facility precluded any investigation of bearing capacity failure. The only possible failure mechanism that could be generated according to theory was over-stressing of the reinforce­ment as illustrated in Figure 7.

The data in Figure 7 shows the factor of safety against over-stressing of the reinforcement plotted against surcharge pressure. The data reveals that according to conventional theory the wall would exhibit unaccept­able performance at the end of construction based on a 5% strain crite­rion. Based on a 10% strain criterion, the maximum acceptable sur­charge load would be achieved at a surcharge pressure of20kPa which is well within the capacity of the RMC Retaining Wall Test Facility. The re­inforc.ement layer with the minimum factor of safety against over­stressmgwas the second layer from the bottom. These predicted capaci­ties represent the best possible estimates based on current methods of analysis and unusually accurate input parameters.

MEASURED RESPONSE

Incremental Panel Wall Test

Measured displacements from one layer of reinforcement are pres­ented in Figure 8. The displacement -load - time history oftheo ther re-

Tpull > Tmax

Figure 6 Calculation of reinforcement pullout capacity

2.0~----------------------------~

1.5 >-a; 1 0% strain criterion m en - 1.0 0 ~

0 t5 <tS -

0.5

5% strain criterion

0+----+----~--~----~--_4

o 20 40 60 80 100

surcharge pressure (kPa)

Figure 7 Factor of safety against reinforcement over-stressing

inforcement layers and panels was qualitatively similar. The data shows that as the surcharge load increased there were corresponding increases in wall deformations and that the time-dependent (creep) deforma­tions of the composite system due to the reinforcement increased with magnitude of surcharge. Duringthe application of the 70 kPa surcharge load, time-dependent deformations increased dramatically until a well-developed shear plane (soil failure) occurred within the rein­forced soil zone. Thereafter, load was shed to the extensible geosynthe-

6 54 1

extenso meter 32 i 3m

1 wall collapse

soil failure

distance behind

panel 100

LAYER 3

80

~--------------------------~~--pa~nel I E 1 .07m ..s60 surcharge c: 0 OkPa ~40

I E 12 ~20 l u

0

2 .25m

3 .40m

~t=S====~4 j .80m .. 1.2m 6 3.0m

-20+----.---.----.---.---~----.-~

o

Figure 8

500 1000 1500 2000 2500 3000 3500

elapsed time (hrs)

Horizontal geogrid displacements recorded by extensometers during incremental panel wall test

393

monitoring point

120~--------------------------------4.

geogrid rupture -----11-[",

surcharging

o

end of construction

12

400 800

elapsed time (hrs)

1200 1600

Figure 9 Panel displacements during full height panel wall test

tic reinforcing layers and visco -elastic creep of these polymeric materi­als led to ultimate collapse of the wall many hours after soil failure. Additional performance data for this wall can be found in the papers by Bathurst et al. (1989) and Karpurapu et al. (1991).

Based on the observed performance of the wall, the failure surcharge load was 70 kPa which is significantly greater than the predicted design value of 20 kPa based on a 10% serviceability strain criterion applied to the reinforcement.

Full Height Panel Wall Test

Qualitatively similar results were reported for outward facing move­ments of the full height panel wall (Figure 9) as for the incremental pan­el wall test. This structure also exhibited time dependent deformations that increased with surcharge magnitude resulting in soil failure at 80 kPa surcharge followed thereafter by reinforcement failure. In this test the surcharge was released just as the reinforcement in the topmost lay­er was observed to rupture. This allowed the internal state of the rein­forced zone to be visually examined by carefully removing the surcharg­ing arrangement. The internal failure surface was observed to exit at the surface of the backfill at about the location predicted by Rankine theory. The collapse pressure was 80kPa as opposed to 70kPa for the nominally identical test constructed with segmental units. The difference may not be unexpected since the single panel structure was constructed with a more rigid facing treatment. An important observation made during ex­cavation was that rupture ofthe reinforcement occurred at the rigid con­nection between the topmost layer and the facing. This failure mecha­nism is not surprising since the soil surface immediately behind the wall was shown to have settled about 65mm (Le. 2%ofthe height of the wall). Additional performance data for this trial wall can be found in the paper by Bathurst and Benjamin (1990).

Strains at Failure

Strains recorded using strain gauges mounted directly on the reinforce­ment layers and extensometers are summarized in Figure 10 for both walls at incipient soil failure. The data shows that the peak strains for all but the bottom layer fall between 5% and 10% which is consistent with the range of strain -limited values assumed in the initial conventional analysis presented at the beginning of the paper. There is an important difference in the location of the peak strains, however, as illustrated for the top two layers. The peak strains for the flexible facing structure are located within the soil mass while for the full height panel structure the peak strains are located at the connections confirming visual observa­tions made during wall excavation.

Footing Reactions

It is reasonable to expect that the under-predictions of wall surcharge capacity may be due to boundary edge effects which include test facility sidewall friction and toe restraint. Measured toe reaction components Rv and Rh are illustrated in Figure 11. The magnitudes of toe reactions are plotted together with the sum of the weight of the active wedge W and the distributed surcharge load Q acting at the top of the failed wedge observed at wall collapse. The reaction forces are significant

12 Layer 4

f---I (top)

'j: 8 I c ~ .~ incremental

4 I-Jr-- full height panel

0 0 0.5 1.0 1.5 2.0 2.5 3.0

8

* Layer 3

c 4 .~

I incremental "Iii

I full height panel

0 --0 0.5 1.0 1.5 2.0 2.5 3.0

8

e Layer 2

c 4 'e incremental "Iii

full height panel

0 0 0.5 1.0 1.5 2.0 2.5 3.0

1.0 Layer 1

~ 1----1 (bottom) c 0.5 'e

I incremental

"Iii full height panel

0 0 0.5 1.0 1.5 2.0 2.5 3.0

distance from facing (m)

Figure 10 Strain in geogrid reinforcement layers at incipient soil failure

394

when compared to the de-stabilizing vertical force W. For example. approximately 25% of the combined vertical load of the failed soil and surcharge load is transmitted to the footing in each test at collapse.

THREE-DIMENSIONAL WEDGE STABILITY ANALYSIS

In order to quantify the contribution of boundary effects on wedge sta­bility at collapse it is necessary to investigate vertical and horizontal sta­bility of the 3D wedge of soil observed in each trial wall. For the pur-

Q

Rh-+

Rv a) footing reactions

100

80

E --z 60 e

"0 «I .Q

40 Q)

B 20 Rv

0 Rh

0 10 20 30 40 50 60 70 80

surcharge (kPa)

b) incremental panel wall

100

80 E --z 60 e "0 «I .Q 40 Rv Q)

B 20

Rh 0

0 10 20 30 40 50 60 70 80

surcharge (kPa)

c) full height panel wall

Figure 11 Measured footing reactions

poses of this paper, failure of the wall is taken as the condition at incipient soil failure rather than reinforcement rupture. The outward wall deformations of the two walls at soil failure were in excess of 2% of the height of the wall and visual distress was apparent to the observerin both cases. The theoretical model presented below is based on a 3D wedge analysis reported by Bathurst and Benjamin (1987) for unrein­forced soil structures constructed in the RMC test facility. In this earlier investigation, an unreinforced wall was taken to failure in order to cali­brate the test facility for side wall friction effects. The experiment con­sisted of an unreinforced, externally supported, 3m high single panel wall taken to failure by allowing the face to slowly rotate about the toe. The analytical model is modified here to incorporate reinforcement forces.

Theoretical Development

The theoretical developments to follow can be related to the 3D wedge (free body diagram) illustrated in Figure 12. The quantities Sand N are the shear and normal forces acting on the internal shear plane and F 1,

F2, F3, and F 4 are the tensile forces developed in the reinforcement at soil failure. The quantities Xq andXsw represent sidewall friction force components generated due to the surcharge load and the soil wedge re­spectively. These forces are generated by soil arching between the test facility side walls. The orientation of the critical soil failure plane is ~ which is at or close to 45 + Q>/2 degrees. Clearly, if side wall friction is not present, this class of problem becomes a variant of the classical Cou­lomb wedge problem.

Thesidewall resisting force Xswdue to wedge self-weight is assumed to act parallel to the internal failure plane. Parametric analysis showed that numerical solutions were insensitive to the orientation of this vec­tor over the range from vertical to ~.

The unit side wall friction fsw can be expressed as:

(3)

Here qz=Yz and is the vertical stress due to soil self-weight acting at depth z below the top of the wall. Ksw is the coefficien t of side wall earth pressure and Q>sw is the side wall friction angle. Integration of equation (3) over the height of the wedge H and considering two side wall gives:

KswyH3 Xsw = 3 tan <l>sw tan (~ -~) (4)

The additional side wall friction generated due to surcharge loading is represented by a force vector Xq acting upwards. The attenuated verti­cal stress qz acting at depth z can be described by:

(5)

where:

2Ksw C2 = --w- tan <l>sw sin ~ (6)

and w represents the length of the wedge in the direction parallel to the facing unit (2.4min this investigation). Solution of equations [3), [5) and [6) lead to:

H

Xq = C2 wq tan(~ -~) t (H - z)e -C2z dz (7)

Forces acting at the soil failure surface are described by the Coulomb

395

relationshipS= NtanQ>. The sum of the horizontal restraining forces due to toe restraint and the reinforcement can be expressed as:

4

PAh = Rh + I Fi i=1

(8)

The horizontal and vertical toe forces can be equated through an equiv­alent wall friction angle A. where tan A. = Rv /P Ab. Here the quantities Rv and PAh are equivalent to vertical and horizontal components of the to­tal active earth force PA in classical Coulomb wedge theory. Horizontal and vertical eqUilibrium ofthewedge in Figure 12 leads to the following solution:

PA = W + qBw - Xq - XSw[sin ~ + ~ COS~]

sinA. + ~ COSA.

where:

A cos~ + sin~ tan<l>

B = H tan (~ - ~) D = sin~ - cos~ tan<l>

W = yHBw. 2

The solution to PA is obtained when dPA/d~=O.

Selection of Parameters

(9)

With the exception of the side wall earth pressure coefficient Ksw, all variables in the above equations are known or can be estimated with confidence from independent direct shear box test data and isochrono­us load-strain data for the reinforcement. Direct shear box tests were carried out to determine the mobilized friction angle Q>sw between the sand and facility side walls. The surface of the side walls was covered with three layers of polyethylene sheeting lubricated with machine oil. These tests showed that Q>sw was in the range of 10 to 15 degrees and that shearing resistance was mobilized essentially instantaneously. Hence, any assumed value of Q>sw can be assumed to be operative for the dura­tion of both large-scale models including construction, surcharging and incipient failure. The back-calculated equivalent wall friction angle A. was 58 degrees and 51 degrees for the full height panel and incre­mental panel walls respectively at soil failure. A reasonable estimate of Ksw is 0.3 to 0.4 based on previous test facility calibration work on an un­reinforced retaining wall test reported by Bathurst and Benjamin (1987) and related work by Jewell (1987). Nevertheless, a wider range of solutions using Ksw = 0 to 0.5 is examined.

Results of Wedge Stability Analyses

A range of possible solutions to the horizontal and vertical component of PAine quat ion [9) is presented in Figures 13 and 14 for the walls at soil failure.Selecting Q>=53 degrees,Ksw =0.35, and Q>sw = 15 degrees gives values for force components P A cos A. and PA sin A. that fall within mea­sured data for both walls. A peak friction angle of 53 degrees is consis­tent with results of direct shear box tests discussed earlier. However, un­der conditions approaching plane strain the peak friction angle of 53 degrees interpreted from direct shear box tests may actuallyunder-es­timate the peak friction angle. Jewell (1987) argues that the peak fric­tion angle for the RMC sand maybe as high as 55-56 degrees in which case the sidewall friction effects are even less than those computed here. The Ksw=O condition identified on the figures corresponds to the ideal condition of no side wall friction (i.e. true plane strain condition). As

may be expected the measured and vertical and horizontal restraining forces PA cos A and 1',\ sin A fall below these values illustrating that side wall friction does contribute to the surcharge capacity of the test walls. Using the best estimate of cj>, cj>sw and Ksw reveals that the contribution of side wall friction to wedge stability ranges from 12% to 14% of the equivalellt restraining force I' A developed by both walls at soil failure.

3m

T z

N tan <t>

Figure 12 Three-dimensional wedge stability

396

This range is consistent with the results of an unreinforced wall test re­ported by Bathurst and Benjamin (1987) that showed that the side wall contribution tostability in the RMC Retaining Wall Facilitywas 14% of the active earth force developed against an externally supported unrei n­forced wall with similar toe restraint.

Adjusted Maximum Surchar~ Pressures

The surcharge pressure q required to give the measured values of I' A cos A and PA sin A in Figures 13 and 14 underideal plane strain condi­tions can now be calculated. This simply requires setting Xsw = Xq=O in equation (9) and finding q such that PA components match measured toe forces at failure. The calculated values to give the best match be­tween measured values and computed values with side wall friction arc summarized on Table 2. The effect of side wall friction is to increase the maximum surcharge pressure by about 17% for the incremental panel wall test and about 18% for the full height panel wall test.

The summary data in Table 2 also shows that the predicted maximum surcharge pressure is approximately 1/3 of the maximum (corrected) surcharge pressure for each structure. The difference between pre­dicted surcharge capacity and the corrected observed values can be as-

E -... z ~ <J) Q)

e Q Iii C 0 N 0g

.r::. '0 E :::l <J)

cj>sw = 10 degrees

cj>sw = 15 degrees 60~----------------------------,

55

50

45

40

35 measured range at soil failure

30

ct>

50°

53°

56°

0 0.1 0.2 0.3 0.4 0.5

Ksw a) horizontal forces (PA cos A)

--- --

500

---measured range at soil failure - - __

40+--'--.--.--.---~-r--.--.--r-~

o 0.1 0.2

Ksw

b) vertical forces (I' A sin A)

0.3 0.4 0.5

Figure 13 Stability analysis for incremental panel wall at soil failure

<l>sw = 10 degrees

<l>sw = 15 degrees 60

E 55 --z <I> e-

rn 50 50° Q)

~ .E Iii 45 ',:::':: 'E ~~ :~ 53° 0 N . ..:: '8 40 --~ --'0 -- SSO ---E 35 :l measured range at soil failure rn

30 0 0.1 0.2 0.3 0.4 0.5

E --z e-rn Q)

~ .E :s c 0 N '§ ~

'0

Ksw a) horizontal forces (PA cos i..)

100

95

90

85

80

75

70

65

60 ---------

E 55 :l ---measured range at soil failure - -

rn 50

0 0.1 0.2 0.3 0.4

b) vertical forces (P A sin i..)

Figure 14 Stability analysis for full height panel wall at soil failure

0.5

signed to toe restraint which is not considered in current methods of de­sign.

SUMMARY

The performance of two carefully constlUcted and monitored geogrid reinforced soil retaining walls has been presented and the influence of boundary effects at the toe of the structures and side walls of the RMC Retaining Wall Test Facility studied. The principal points that can be drawn from this investigation are summarized below:

1. A 3D wedge analysis has been developed that is an extension of the classical Coulomb wedge method. The analysis explicitly includes all boundary forces due to toe restraint and test facility side walls and the stabilizing influence of the reinforcement layers. The model has been demonstrated to give an accurate prediction of measured toe forces using reasonable input parameters.

2. The maximum predicted surcharge pressure based on current tie­back wedge methods of analysis is 20 kPa which is approximately a third of the (colTected) observed capacity of the test walls. The source of conservativeness in the prediction of maximum surcharge

397

pressure for the walls constructed at RMC can be assigned to the additional restraint offered to the retaining wall structures due to the footing support.

3. Based on the the results of reinforcement strain measurements taken at incipient soil failure, the 10% strain criterion applied to isochronous load-strain data does result in a reasonable estimate of reinforcement forces in the top three layers at soil failure. How­ever, this concurrence may be fortuitous and the actual strain at fail­ure in other structures may be influenced by the stiffness of the re­inforcement employed and soil materials.

TABLE 2--Comparison of maximum surcharge pressures

Experimental

Measured Corrected (<I>sw=O)

Incremental panel wall 70kPa 60kPa

Full height panel wall 80kPa 68kPa

Theory

Tie-back wedge method

0-20 kPa

0-20 kPa

IMPLICATIONS TO CURRENT DESIGN METHODOLOGY

Based on the experimental results presented in the paper it can be ar­gued that current me thods of analysis and design have a built in factor of safety of three against failure due to surcharging. This conclusion is re­stricted to structures of the type investigated (i.e. short height, heavily surcharged retaining walls constructed with high quality granular fill and facing units that can transmit shear). However, it is not unreason­able to believe that a portion ofload-carrying capacity due to toe re­straint is present in every reinforced soil wall constructedwith panel fac­ings. This toe restraint offers an additional margin of safety not considered in routine calculations.

Unfortunately, Coulomb wedge analyses that can explicitly consider load support at the wall toe may be impractical for design purposes. In order to ensure a determinate system the net reinforcement loadat fail­ure and the equivalent wall friction angle i.. must be assumed a priori. In addition, wedge analyses of the type presented here do not provide any information on the distribution of load between reinforcement layers.

A method to estimate in advance the magnitude of i.. is even less clear since vertical load transfer to the facing units is not frictional in nature but, rather, is due to local volumes of reinforced soil hanging up on the mechanicalgeogrid/panelconnectionsthatprotrudeintothereinforced soil zone. The amount of load shedding is also a function of the relative vertical compliance of the facing system. As demonstrated clearly in this experimental program, the relative downward movement of the re­tained soils against the back of relatively rigid facing systems causes additional load on the connections and finally greater vertical load on the footing. The relative downward movement of soil is due to soil com­pactionandsettlementduringconstructionandpost-constructionout­ward panel rotation. In the field, this mechanism leads to greater strains and forces in the reinforcement close to the connections which cannot be predicted by conventional theory. The development of high connec­tion strains/forces observed in this experimental program has also been observed in the field after construction of a 7m high propped panel wall (Bathurst 1991a). In fact, full height panels are not recommended for routine construction by the FHWA for the reasons cited here.

For incremental construction, including the use of modular blockfacing systems, the development of high connection forces is less of a problem because the wall facing and fill surface proceed together during

construction (e.g. Bathurst et al. 1993, Simac et al. 1993). The strain data illustrated in Figure 10 for the two top reinforcement layers shows that peak strains occur within the reinforced soil zone rather than at the connections. Similarrelative trendsforconnectionstrains have been re­ported by the author and co-workers for walls constructed with a stiffer reinforcement (Bathurst et al. 1987, Bathurst 1990).

The inherent conservativeness of current methods of design is com­pounded by the use of other partial factors applied to the laboratory in­dex tensile strength of the reinforcement to account for mechanical damage and chemical attackandoverall uncertainty. In the paper by Ba­thurst (1991b) it is demonstrated that in some extreme cases the engi­neermay be required to use only 2% of the laboratory tensile strength of the geogrid reinforcing product for internal stability calculations against over-stressing based on default partial factors of safety found in AASHTO guidelines.

ACKNOWLEDGEMENTS

The author would like to acknowledge the contribution of DJ. Benja­min (formerly a graduate student at RMC) who supervised the exper­imental work reported in the paper. The financial support of the De­partment of National Defense through the ARP program is gratefully acknowledged.

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