compaction‐induced earth pressures under k0‐conditions
TRANSCRIPT
COMPACTION-INDUCED EARTH PRESSURES
UNDER ^ - C O N D I T I O N S
By James M. Dtincan,1 F. ASCE and Raymond B. Seed,2 A. M. ASCE
ABSTRACT: Analytical models and procedures are presented for the evaluation of peak and residual compaction-induced lateral earth pressures either in the free field or adjacent to vertical, nondeflecting soil-structure interfaces. A hys-teretic model for the stresses generated by multiple cycles of loading and unloading is presented, along with recommendations regarding the determination of suitable model parameters. This model is then adapted to incremental analytical methods for the evaluation of peak and residual earth pressures resulting from the placement and compaction of soil. Compaction loading is considered as a transient moving surficial load of finite lateral extent. Simplified hand calculation procedures are presented for cases in which all soil layers are identically compacted. Finally, a series of case studies are presented in which analytical results are compared with full-scale field measurements in order to verify these analytical methods.
INTRODUCTION
The calculation of the forces exerted by soils against structures was one of the earliest problems considered in soil mechanics. Since the early lateral earth pressure theories of Couplet in 1726 (11), Coulomb in 1776 (10), and Rankine in 1857 (22), a number of increasingly complex theories and analytical procedures have been developed to calculate the earth pressures acting against structures and the deflections resulting from these pressures. Analytical procedures currently available are generally well able to estimate these pressures and deflections for situations involving uncompacted backfill. As early as 1934, however, Terzaghi noted that compaction significantly affected lateral earth pressures and resulting structural deflections (32). Today, despite progress made in understanding the phenomenon of compaction-induced stresses, it remains true that compaction of soil induces soil stresses which are not yet amenable to accurate and reliable analysis with existing theories and procedures.
This has far-reaching consequences within the discipline of geotechnical engineering because the strength and mechanical behavior of a soil depend to a large extent on the levels of stresses within the soil mass . Compaction can significantly increase these stresses. An ability to analyze such compaction effects is thus necessary in order to properly model the response of compacted soils to both static and dynamic loads, with applications in virtually every area of geotechnical engineering. Compaction-induced earth pressures and /o r the resulting structural stresses and deformations can be of serious concern in the design and analysis
:W. Thomas Rice Prof, of Civ. Engrg., Virginia Polytechnic Inst, and State Univ., Blacksburg, VA 24061.
2Asst. Prof, of Civ. Engrg., Stanford Univ., Stanford, CA 94305. Note.—Discussion open until June 1, 1986. Separate discussions should be
submitted for the individual papers in this symposium. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on February 6, 1985. This paper is part of the Journal of Geotechnical Engineering, Vol. 112, No. 1, January, 1986. ©ASCE, ISSN 0733-9410/86/0001-0001/$01.00. Paper No. 20262.
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of many types of soil-structure systems such as retaining walls, buried structures and pipes, flexible culverts, reinforced earth walls, etc. Compaction-induced stresses also influence resistance to both liquefaction and hydraulic fracturing within a soil mass, as well as stress distributions and deformations of compacted earth and rockfill dams and embankments.
This paper presents new models and analytical procedures for the calculation of peak and residual compaction-induced stresses either in the free field or acting against vertical nondeflecting structures, as well as for the interaction between compaction-induced and overburden-in-duced stresses. Initially, these analytical methods are based on a hys-teretic model for stresses induced by multiple cycles of loading and unloading under K0-conditions. This model is then extended to the consideration of field conditions in which compaction loading may be modeled as a transient, moving, surficial load of finite lateral extent. Incremental numerical analyses and a simplified hand calculation method are presented. Finally, several case studies are presented in which analytical results are compared with field measurements of compaction-induced stresses in order to verify the accuracy and usefulness of these methods.
The models and analytical methods presented are suitable only for situations in which the noncompaction-related stresses (overburden-in-duced stresses) result from essentially K0-conditions: conditions wherein no lateral deformations occur, and the major and minor principal stresses are oriented horizontally and vertically. These methods are therefore suitable for the calculation of lateral stresses resulting from the placement and/or compaction of horizontal layers of soil either in the free field or adjacent to vertical, nondeflecting structures. Situations not conforming closely to these conditions, such as nonvertical or nonplanar soil-structure interfaces, nonlevel ground or fill surfaces (e.g., embankments), deflecting (yielding) structures, etc., may be analyzed using modified versions of these models and analytical methods adapted to finite element analysis procedures (26-28).
REVIEW OF PREVIOUS STUDIES
A large number of laboratory and full-scale field studies of compaction-induced stresses and deformations have been performed during the past 50 yrs (e.g., Refs. 2, 4-8, 12-15, 21, 23, 24,' 29-32). Unfortunately, much of the data currently available pertaining to compaction-induced earth pressure measurements is of limited value as, even with recent advances in techniques for the measurement of in-situ earth pressures, it remains extremely difficult to obtain reliable measurements with an assured accuracy of better than ±20%, even under ideal conditions (2,6,9,17,34,35,37). Nonetheless, a sufficient database does exist to permit evaluation of analytical procedures for the calculation of compaction-induced stresses and deformations (26,28).
Based on the field data currently available, the following general observations can be made regarding compaction-induced stresses and deformations:
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1. The compaction of soil represents a process of load application and removal which can result in significant increases in residual lateral earth pressures. These earth pressures may be many times greater than the theoretical at-rest values, and may approach passive earth pressure magnitudes (4,7,8,30).
2. The depth to which compaction increases lateral earth pressures appears to be a function of the dimensions and vertical thrust of the compaction roller, varying from on the order of 2 to 3 m for small hand-operated vibratory rollers (7,8,23), to as much as 15 m for very heavy compaction equipment (26).
3. At depths where available overburden pressures are sufficient that possible passive failure does not limit residual lateral earth pressures, a high percentage (40-90%) of the peak lateral earth pressure increases induced during compaction may remain as residual pressures (7,8,23,29).
4. The compaction of soil against deflecting structures can significantly increase structural deflections (4,7,8,12,13,23,32), generally increases near-surface residual lateral pressures to greater than at-rest values, and generally decreases lateral pressures at depth, apparently as a result of increased structural deflections (4,7,8,13,15). The mode of structural deflections can, however, significantly influence this pattern (12,13,26).
5. In previously compacted soils (soils with previously "locked-in" compaction stresses), additional compaction loading can result in much smaller increases in peak earth pressures during compaction than in un-compacted soils, and a negligible fraction of these peak increases may be retained as residual earth pressure increases upon the completion of compaction (23,29).
Several theories and analytical methods have been proposed to explain and/or analyze the residual lateral earth pressures induced by soil compaction. Common to all of these is the idea that compaction represents a form of overconsolidation wherein stresses resulting from a temporary or transient loading condition are retained to some extent following removal of this peak load. Rowe (1954) proposed that compaction could be considered the application and removal of a surficial surcharge pressure (25). Based on the results of bi-directional direct shear tests in which he noted that small strain reversals resulted in a negligible relaxation of stresses, Rowe theorized that virtually all peak soil stresses induced by the surcharge loading would be retained after surcharge removal, and suggested that the coefficient of lateral earth pressure in a soil following compaction could be expressed as
K£ = K011 + ̂ J (1)
where K0 is the coefficient of earth pressure at rest, h is the overburden pressure, and h0 is the effective transient overburden pressure representing the peak loading condition during the compaction process. Sowers et al. (1957) proposed a similar theory based on sliding planes within the soil mass and strain reversal (30).
Broms (1971) proposed an empirical analytical procedure based on the concept of hysteretic loading and unloading behavior (3). This empirical
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/.*r»
°h s K 0 o» '
/Crh = K,crv
- > CT'h
FIG. 1.—Broms' Proposed Model
procedure, which was limited to consideration of placement and compaction of horizontal layers of soil adjacent to a nondeflecting vertical wall, was the first to provide good qualitative agreement with field data for conditions to which it could be applied. The model upon which Broms' method is based is illustrated in Fig. 1. An element of soil at some depth is considered to exist at some initial stress state (point A). An increase in vertical effective stress (loading) results in no lateral stress increase unless and until the K0-lme is reached (point B), after which further loading results in an increase in horizontal stress as a'h = K0a'v . A subsequent decrease in vertical effective stress (unloading) results in no decrease in lateral stress unless and until a limiting condition is reached (point D), after which further unloading results in a decrease in horizontal stress as a'h = KX(j'v. The nature of Kj will be discussed later.
Calculation of compaction-induced lateral stresses by Broms' method involves incremental analysis of the stresses resulting from the placement and compaction of each layer of fill. Compaction at any point is modeled as application of the peak, transient increase in vertical effective stress (Av'v) caused by the compaction vehicle as determined by simple Boussinesq (1) elastic analyses, followed by subsequent removal of this transient vertical load. The peak and residual horizontal effective stresses due to this transient compaction loading, as well as those due to surcharge increases as a result of fill placement, are then determined by the model shown in Fig. 1.
MULTI-CYCLE K0-LOADING AND UNLOADING
General Hysteretic K0-Loading Model.—The simple, idealized case of compaction-induced lateral stresses acting against a vertical, frictionless, nondeflecting wall in level layers of fill wherein compaction is accomplished by cyclic application and removal of a uniform, vertical sur charge loading of infinite lateral extent, is fully analogous to one-dimensional cyclic overconsolidation loading/unloading, because principal effective stresses remain horizontal and vertical and no lateral displacements occur. The development of a hysteretic model for the stresses generated by this type of loading (hereafter referred to as K0-loading/ unloading) thus provides a framework for the evaluation of compaction-
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TABLE 1.—Hysteretic i(0-Loading/Unloading Model Parameters
Parameter (1) a
3 K0
•Ki,*'
c'
Name (2)
Unloading coefficient
Reloading coefficient Coefficient of at-rest
lateral earth pressure for virgin loading
Frictional component of limiting coefficient of lateral earth pressure
Effective stress envelope cohesion intercept
Recommended limits
(3)
0 < a s 1
0 < p < 1 0 < Ko < 1
Ka — Kix^ £ Kp
Method of estimation based on <$>'
(4)
See Fig. 2 for relationship between a and sin 4>'
Assume (3 = 0-6 K0 = 1 - sin 4>'
K1A. = tan2 (45 + 4>'/2)
Note: Kp = Coefficient of passive lateral earth pressure.
induced stresses for this simple idealized case. The following presents a brief summary of such a model as well as a
description of the variables involved. A full discussion of the development of this hysteretic model and recommendations for parameter determination are presented by Seed and Duncan (26). The model is unfortunately complex, but it does provide excellent agreement with observed laboratory K0-test behavior, and is readily simplified to a computationally tractable form for the analysis of compaction-induced stresses by finite element methods (26-28). The discussion which follows can be slow reading; first-time readers may wish to skip ahead at this point to the section describing case studies.
Five material property parameters are required for the hysteretic model, and these are a, p, K0, K̂ ^ , and c'. These parameters are described in Table 1. The parameters K^* and c' together determine the limiting coefficient of at-rest lateral earth pressure (K{), which is assumed to be controlled by passive soil failure based on the familiar Mohr-Coulomb failure criteria as
\<Vlim °V (2)
Ideally, these five parameters should be determined by performing K0-loading/unloading tests, though reasonable estimates of four of the parameters may be derived from a knowledge of <$>' and c', as indicated in Table 1 and Fig. 2, and 0.6 appears to be a reasonable estimate of p providing for only minimal error in the absence of specific K0-test data.
Table 2 and Fig. 3 define the terms used in the following description of the hysteretic Ko-model. The following seven "rules" define the model:
1. Virgin loading, defined as loading to a vertical effective stress exceeding all previous stress magnitudes, follows the K0-line as
vi< = K0(Tv (3)
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\V> r* \5 20 25 30 35 40 45 50
FIG. 2.—Suggested Relationship between sin 4>' and
FIG. 3.—Basic Components of Hysteretic K0-Loading/Unloading Model
where K0 — 1 - sin 4>', as suggested by Jaky (19) and supported by Mayne and Kulhawy based on data from 118 K0-tests reported in the literature (20). Virgin loading establishes a new maximum past loading point (MPLP).
2. Virgin unloading, defined as any unloading occurring at a vertical effective stress less than that achieved since the most recent establishment of a new MPLP, follows a stress path defined by Eq. 4 below, and establishes a new current minimum unloading point (CMUP).
oil = KoO-»
where Ki, = K0(OCR)a
(4a)
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TABLE 2.—Hysteretic K0-Loading/Unloading Model Definitions
Hysteretic model terms ' (D
Existing stress state
Maximum past loading point ((T?i,MPLP / CTi>,MPLp)
Current minimum unloading point ( O ^ C M U P / OVCMUp)
Recent maximum loading point (fft.RMLP 1 cri>,RMLp)
Recent minimum unloading point (ffli.RMUP / ° \ ' ,RMUp)
Reloading point
A
P
a*
Definitions (2)
Existing lateral and vertical effective stresses
Maximum past lateral and vertical effective stresses
Lateral and vertical effective stresses at stress state corresponding to minimum oj achieved since last MPLP
Lateral and vertical effective stresses at stress state corresponding to maximum ts'h achieved during most recent loading cycle
Lateral and vertical effective stresses at stress state corresponding to minimum u'h achieved during most recent unloading cycle
Point of intersection between reloading stress path and virgin i?0-lme
Difference in horizontal effective stresses between MPLP and CMUP
Fraction of A regained in fully reloading from CMUP to R
Modified unloading coefficient
and OCR = Q~p,MPLP
0"i>,ESS
(4c)
3. All unloading is subject to the passive failure limiting condition as
a/, s= Kio-; (5)
where Kx is a function of both c' and <j)' as shown in Eq. 2 and Table 1. 4. Virgin reloading, defined as the first reloading cycle after estab
lishment of a new CMUP, follows a linear stress path from the CMUP to the reloading point R, which is established as (see Fig. 3):
V*,r = <CMUP + (3A .
where A = al /t,MPLP 0"/, /CMUP
(6a)
(6b)
(6c)
Virgin reloading thus follows a linear stress path whose slope increases with an increasing degree of unloading prior to reloading, as shown in Fig. 4. Virgin reloading establishes a new reloading point (R).
5. Nonvirgin reloading follows a linear stress path from the RMUP to
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FIG. 4.—Typical Stress Paths for Hysteretic K0-Model
R, then follows the i*C0-line to the MPLP. Further loading constitutes virgin loading. When any reloading achieves a stress level higher than R but less than the MPLP, the new stress point (which occurs along the Ko-line because P < 1 ) becomes the new R for subsequent reloading cycles.
6. Nonvirgin unloading from a stress point on the K0-lme (implying that the most recent reloading exceeded the past R and established a new R, but did not exceed the MPLP) follows a stress path defined by
Oh Cp.KMLP
Cp.ESS (7)
where a* is such that the unloading path passes through the CMUP as
In O'h.RMLP
^0O ' i ,CMUP,
In CTi>,RMLP
(8)
\C Tu,CMUP/
Unloading that continues below the CMUP constitutes virgin unloading (originating at the MPLP). There is, however, an overriding constraint that a* a a. If a* is less than a (implying that previous unloading followed a stress path that was significantly affected by the ^- l imi t ing condition), then: (1) a* is equal to a; (2) unloading is according to Eq. 7; (3) unloading sets a new "pseudo CMUP," which performs as CMUP except that it does not establish a new R; and (4) unloading to a a'h less than the true CMUP establishes a new true CMUP and thus a n e w R. This constraint on a* models an apparent partial "loss of memory" on the part of the soil as a result of shearing during unloading along the i n l i ne .
7. Nonvirgin unloading from a stress point above the i«C0-line follows an a*-type stress path as described below and illustrated in Fig. 5. The point at which unloading begins (point C) is first projected vertically down to C on the K0-line, and the CMUP (point B) is projected vertically downwards the same distance to B'. An <x*-type unloading path from C through B' is then calculated as in No. 6 above. Once again a* is constrained so that a* > a. The actual unloading path is then "parallel" to the calculated path through C'B', where any point on the actual un-
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FIG. 5.—KrLoading Following Moderate Reloading
— i 1 1 1 1 1 r j y Test Dota:(Componello and Vaid,l972)
CT-JIksc)
FIG. 6.—Hysteretic Model versus K0-Test Data: (a) Monterey Sand; (b) Undisturbed Haney Clay
loading path CDB can be found by projecting vertically up from the calculated path by a distance BB'.
Figs. 6(a) and 6(b) illustrate the accuracy with which this hysteretic model is able to model the stress paths for two multi-cycle K0-tests on sand and clay, respectively. At no point does the modeled horizontal effective stress differ from the actual measured horizontal effective stress by more than a few percentage points, and deviations are not progressively cumulative but rather tend to be self-correcting with successive load cycling.
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ANALYSIS OF FIELD COMPACTION-INDUCED STRESSES
This hysteretic model may be applied to analysis of compaction as represented by a transient, moving surficial load of finite lateral extent by directly modeling loading due to increased overburden as an increase in vertical effective stress (ACT/), and by modeling compaction loading in terms of the peak virgin, compaction-induced horizontal stress increase (Aal,,vc,p) defined as the horizontal effective stress which would have been induced at the point of interest by the most critical positioning of the compaction plant if the soil had been previously uncompacted (if the soil had no "locked in" residual stresses due to previous compaction). This modeling of ACT//0C/P applies whether or not the soil, in fact, has such residual compaction-induced stresses. The hysteretic model is then "driven" during a given compaction loading cycle by an "equivalent" peak vertical load increment calculated as
A<e,p = ——? (9)
During a given compaction increment, ACT/,,^ is first applied and then removed, as compaction is considered to result in no net increase in residual vertical stresses for conditions considered in this paper.
This modeling of compaction on the basis of Aarl,/VCiP is convenient because it is a value which has been shown to be readily calculated by simple, linear-elastic analyses (26). Moreover, case studies based on field data indicate that transforming the value to ACT/,,,,,,, by Eq. 9, and then using ACT/,,,,,,, to drive the hysteretic model, results in the calculation of appropriate true peak and residual lateral stress increases (ACT/,P and Aa^r respectively).
It is important to note that peak compaction loading must be based on directly calculated lateral stress increases rather than directly calculated vertical stress increases multiplied by some constant (e.g., K0 or KA), as was generally done in earlier analytical methods, because for surficial loading of a finite lateral extent, the relationship between ACT/, and ACT/ is far from constant as illustrated in Fig. 7. In this figure, which shows ACT/ and ACT/, at several depths due to a surficial point load, note
\ 0 \ ^GROUND SURFACE
0.6
'0.8
I 1 I I I 1.0 0.0 0.1 0.2 0.3 0.4
r/B
FIG. 7.—ACT,, and Ao-„ Due to Surficial Point Load
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that ACT,; is negative where Acr̂ , is greatest, and exceeds Acr£ at other locations.
Determining Acr/,^,,.—Seed and Duncan (26) present a study and recommendations for the calculation of A(TX,VC,P for various situations. The main conclusions may be summarized as follows:
1. Either in the free field, or at or near vertical, nondeflecting soil/ structure interfaces, &<r'XtVCiP resulting from surficial compaction loading can be calculated directly by simple elastic analyses, including finite element methods as well as closed form solutions. Poisson's ratio (v) for surficial compaction loading may be chosen according to the empirically derived relationship
1 v = v0 + - (0.5 - v0) (10a)
K0
where v„ = , (10b) 1 + K0
and K0 - 1 - sin $' (10c)
2. The calculation of &a{/VCtP for typical surficial compaction plant geometries is a three-dimensional problem not well suited to two-dimensional finite element procedures as these are not well able to account for the "spreading" of stresses with depth. Three-dimensional finite element methods are well able to calculate k(j'hlW,p, but require an excessive amount of engineering time for most applications.
3. The limited body of available field data indicates that the loading imposed by a typical vibratory roller can be modeled as approximately two to four times the static weight of the roller.
4. k<Ti,,vc.p acting at a vertical, nondeflecting soil-structure interface due to concentrated surficial loading can be taken as twice the value that would be calculated at the same point by closed-form elastic solutions if the point occurred in the free field.
Fig. 8 illustrates typical profiles of ACT^W/P acting against a vertical wall as a result of a roller (represented by a line load) operating at varying minimum distances from the wall. Fig. 8(a) illustrates Avl,jVC/P for a situation in which the soil is not underlain by a rigid base. When the soil is underlain by a rigid base, attenuation of £xj'hjVCrP with depth beyond the maximum point is somewhat less pronounced, and is followed by an increase with depth as the rigid base is approached as shown in Fig. 8(b), though the rigid base does not affect the upper portions of the kv'h,vc,P profiles.
Incremental Analysis Procedure.—The proposed hysteretic model may be incorporated in an incremental analytical procedure which can be used to evaluate the peak and residual lateral earth pressures resulting from the placement and compaction of level layers of soil either in the free field or adjacent to a vertical, nondeflecting wall. This incremental procedure will be illustrated by means of an example problem: calculation of lateral earth pressures acting against a 10-ft high, vertical, nondeflect-
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(a) (b)
FIG. 8.—Typical Profiles of Aai,K,p against Vertical Wall: (a) No Rigid Underlying Base; (b) Rigid Base at 6 ft
ing wall behind which backfill will be placed and compacted. Soil will be placed in 6-in. lifts, and each lift will be compacted with the single drum roller described in Fig. 8. The roller will approach to within X = 1 ft of the wall.
The first step in performing such an analysis is to determine suitable soil parameters for the hysteretic model. The parameters chosen should be suitable for modeling the post-compaction properties of the soil, as each lift will be subjected to several passes of the roller and post-compaction properties will control the analysis. For this example problem, the following parameters will be used to model the soil: K0 = 0.38; Klti,> = 4.20; a = 0.65; (3 = 0.6; c' = 0; and 7 = 115 pcf. The hysteretic model parameters correspond to a post-compaction friction angle of 4>' = 38°.
The next step is to determine the profiles of kv'h,VC/P versus depth induced by compaction of each new fill layer. In this case, as all layers are compacted with the same roller approaching to within the same distance of the wall, the same ba'hiVC,r profile [Fig. 8(b), for x = 1 ft] may be used for all layers. Note that this neglects the effects of a rigid base underlying the new fill but that this has little effect on the final results for this particular problem.
Finally, an incremental analysis is performed in which the vertical and horizontal effective stresses at the midpoint of each soil layer are modeled using the proposed hysteretic loading/unloading model. Placement of a new fill layer results in a permanent increase in vertical stress (Acri). Multiple passes of the compactor at the surface of any given fill layer are modeled with a single loading/unloading cycle in which stresses at the midpoints of all layers in place at the time of the compaction loading are subjected to application and subsequent removal of an "equivalent" vertical stress as given by Eq. 9, based on the predetermined profile of &a'hiVCiJ, for that stage of fill compaction. Analysis proceeds with
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Earth Pressure Against Wall (PSF) 0 200 400 600
>
Earth Pressure Against Wall ( PSF) 0 200 400 600
I - 4 -
a. S 6
10
\ yr - \ \ \ 4
\ 1 - \ m
\
- \ \
\
i
- Simplified Hand Solution
Incremental Solution
L
^ ii
l i t (6)
FIG. 9.—Example Problem Results: (a) Calculated Peak and Residual Earth Pressure: Compaction of Final Layer of Backfill; (b) Final Pressure Distributions Based on Incremental Analysis and Hand Solution
alternating increments of fill placement and compaction loading increments.
All of this has been coded in the computer program NCOMP (26), and some results of an incremental analysis using this program for the example problem are presented in Fig. 9(a), which shows the calculated peak lateral pressures during the last compaction loading increment, as well as the final residual lateral earth pressures acting against the wall following completion of backfilling and compaction.
Simplified Hand Calculation Procedure.—For situations in which the same, or at least very similar, profiles of Ao-̂ W/P versus depth may be used for all layers, a simple hand calculation procedure may be employed which results in good agreement with the incremental procedure described above. The recommended hand calculation procedure is as follows:
1. All calculations are based on final fill geometry. First, the single profile of peak lateral compaction pressure (Aa^,,,) versus depth must be determined. The resulting values of Acr^p should then be multiplied by a factor F (which will be between zero and one), determined as
5° F = -
4 0.25 (11)
2. The resulting scaled ba'Kvc,v profile should then be added to the at-rest lateral pressure profile {<j'hi0 = K^a'v) such that a profile of final, residual lateral stresses {(j'Kr) versus depth results, where
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v'hrT - K0a'v + F • Aff^, , , (12)
3. The near surface portion of the resulting a'Kr profile should then be reduced so that o^r s K^l at all depths.
4. Below the depth of the maximum remaining value of aj,ir, the residual horizontal effective stress should be further modified and modeled as increasing linearly with depth at a rate defined as
Aa,; = K2 • ACT; (13a)
where K2 = X0(l - F) (13b)
until the K0-lateral earth pressure profile is intersected. At greater depths the lateral earth pressure is simply equal to K0 times a'v.
The results of this simple hand calculation procedure for the example problem discussed previously are shown with a dashed line in Fig. 9(b). Agreement between this simple method and the more complicated incremental analysis procedure is generally good when use of a single Acr^p profile for all fill stages is appropriate.
CASE STUDIES
A number of case studies have been performed involving comparison between field measurements of compaction-induced stresses and calculated values in order to verify the accuracy and usefulness of these analytical models and procedures. The following is a brief summary of several of these.
Test Wall, Stockholm, Sweden.—A series of full-scale tests performed by Rehnman and Broms (23) provides a well-documented set of case studies with verifiably reliable measurements of compaction-induced stresses suitable for use in evaluating the accuracy of the analytical models proposed. These tests involved measurement of lateral earth pressures acting against a braced, reinforced concrete test wall instrumented with 12 Glotzl hydraulic pressure cells inset in the wall with their faces flush with the concrete, as shown in Fig. 10. Five additional pressure cells
Q =7.5 tons
FIG. 10.—Peak Point Loading Configuration and Pressure Cell Layout: Stockholm Test Wall
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TABLE 3.—Hysteretic Model Parameters Used for Analyses of Full-Scale Tests: Stockholm Test Wall
Hysteretic model parameters
(1)
<$>' (degrees) 7 (tons/m3) K, a
P Ki,^ c'
Gravelly Sand Backfill
Loosely dumped (2)
34 1.74 0.44 0.62 0.6 3.5 0.0
Compacted (3)
42 2.02 0.33 0.72 0.6 5.0 0.0
Silty Fine Sand Backfill
Loosely dumped (4)
32 1.50 0.47 0.55 0.6 3.3 0.0
Compacted (5)
37 1.84 0.40 0.67 0.6 4.0 0.0
were similarly mounted in a concrete base slab at the toe of the wall, and comparison between measured and calculated overburden pressures for these five cells verified the accuracy of the rneasurements obtained.
Two types of backfill were used for these tests: a gravelly sand and a
Acrh'( tons/m )
1.0 \5 2.0 2.5 Acrh '(tons/m2)
1
AAXA "" \ \ \ AA/
/ / / „
A4/ 4
1 AA'.AAI
I
(A
- 1
Peak
Residua i i
PROFILE B
Field Dala A A
A A
-
Analysis
1
(a)
A o " k ( t o n s / m 2 )
1.5
Peak Acr^ for y previously
• —uncompacted '. soil
/ /
Field Data Analysis
Peak: O / " " "
•
Ao-|(( tons/m2) 0.5 1.0 1.5
FIG. 11.—Measured Peak and Residual Lateral Earth Pressure Changes, Stockholm Test Wall: Gravelly Sand Backfill: (a) Loosely Dumped Fill; (h) Fill Placed and Compacted in Layers
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silty fine sand. Testing involved application and removal of wheel loads at the surface of the completed backfills. These tests were performed four times, testing each type of backfill in both a loosely dumped state and in a condition achieved by placing and compacting the fill in layers. Based on the data provided by Rehnman and Broms, and the guidelines proposed in Table 2, the soil properties and hysteretic model parameters listed in Table 3 were used to model these four backfill conditions. The values of a. presented in this table represent mean values based on the relationship between a and <$>' proposed in Fig. 2. Concentrated loads were applied to the completed surfaces of the four backfills by positioning a Michigan 175A-Series 1 front loader with its scoop filled so that its front wheels represented a pair of 7.5-ton loads as illustrated in Fig. 10. The resulting peak pressure increases were measured during load application, and the residual pressure increases were measured following removal of the loader.
Figs. 11(a) and 12(a) show the measured peak and residual increases in lateral pressures induced by applying surficial point loads to loosely dumped fills of both types. Also shown in these figures are the peak
A<Th(tons/m ) Aerh(tons/m )
- 0 0.5 1.0 1.5 2.0 2.5 „0 0.5 1.0 1.5 1 1 T
PROFILE B
Field Data Analysis
Ao-h ' ( tons/m2 )
T 1 1 1— U f i \ ^PeakAoL for -A \d? N. V previously
i \ v uncompacled / I \ soil
Field Data Analysis
FIG. 12.—-Measured Peak and Residua! Lateral Earth Pressure Changes, Stockholm Test Wall: Silty Fine Sand Backfill: (a) Loosely Dumped Fill; (b) Fill Placed and Compacted in Layers
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and residual lateral pressure increases calculated by analyses based on the proposed hysteretic loading/unloading model. As the loosely dumped backfills represented "previously uncompacted soils," the peak lateral pressure increases were simply equal to Aal,iVC,v • The residual lateral pressure increases were then calculated based on the peak compaction pressure profile (Acrl,tVCfP versus depth), again using the computer program NCOMP.
In addition to the two tests on loosely dumped backfills, Rhenman and Broms performed a second pair of identical tests on previously compacted backfills of both types. For these tests the backfill was placed in lifts of between 20 and 40 cm and compacted with a Dynapac CM20 vibratory plate compactor. Figs. 11(b) and 12(b) show both the calculated and measured peak and residual increases in lateral pressure induced by application and removal of the twin surficial point loads subsequent to completion of fill placement and compaction for both backfill types. Also shown, for purposes of comparison, are the calculated peak lateral pressure increases at pressure cell profile B for the loosely dumped fills, as presented previously in Figs. 11(a) and 12(a). The program NCOMP was used first to model the incremental placement and compaction of the two backfills, which induced residual compaction-induced stresses, and then to model the subsequent application and removal of the twin surficial point loads. Note that the presence of previously "locked in" compaction-induced stresses resulted in significantly smaller increases in peak lateral stress due to application of the point loads, as this represented "reloading," and that an almost negligible fraction of these peak increases were retained following load removal. This has the practical implication that surface loads can have significantly less effect on u'h if a fill was previously compacted than they would if the fill was loosely dumped. This behavior was well modeled in the analyses based on the proposed hysteretic model.
Agreement between the calculated and measured lateral pressure increases is very good at profile B for all backfill conditions. At profile A, however, the calculated peak pressure increases exceed the measured values for the previously compacted backfills because small wall deflections (which are not accounted for by the program NCOMP) were caused by the peak lateral pressure increase which was greatest in the vicinity of profiles B. As loading-induced lateral pressure increases were relatively small at profile A, which occurs some distance (laterally along the wall) from the zones of maximum peak lateral stress increase, the deflection-induced decrease in lateral stresses was of major significance at profile A in the stiff, compacted backfills, and in fact decreases in lateral pressure corresponding to the peak loading condition were measured at several depths at profile A.
The consistently good agreement between the calculated and measured earth pressures for these field tests provides strong support for this type of analysis based on the hysteretic model, as well as the use of "equivalent" peak vertical stress increases based on directly calculated peak "virgin" lateral stress increases (AcrlhVC,p) to model the peak loading induced by a surficial compaction load of finite lateral extent.
TRRL Wall, Crowthorne, England.—Tests performed by Carder et al.
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(7) at the TRRL Experimental Retaining Wall Facility represent another well-documented study with verifiably reliable measurements of compaction-induced stresses. A reinforced concrete trough 22 m (72 ft) long was backfilled with a clean medium sand, and the resulting pressures against the side walls were measured at two test sections. Backfill was placed in 0.15-m (0.5-ft) lifts, and each lift was compacted with a 1.3-Mg twin-roll vibratory roller operating parallel to the walls and approaching to within 0.15 m (0.5 ft) of the walls.
The wall at one test section was a 1-m (3.3-ft) thick reinforced concrete wall 2-m (6.6-ft) high, and at the other test section the wall was a 2-m (6.6-ft) high steel wall braced with hydraulic jacks. Earh pressures on the faces of both walls were measured using flush-mounted (inset) pressure cells of three types: hydraulic, pneumatic, and stiff strain-gauged diaphram. Pressure distributions measured by arrays of each cell type on the face of the metal wall were compared with the total lateral force exerted on the wall measured by means of load cells on the bracing jacks. Based on this comparison, all hydraulic and diaphram cell measurements were scaled by factors of 1.01 and 0.85, respectively, and the pneumatic measurements will be discarded. The remaining scaled measurements are of unusually high reliability.
The program NCOMP Was used to analytically model the incremental placement and compaction of backfill against the nonyielding concrete wall section. Appropriate profiles of Ao-̂ TO/P versus depth were generated
Lateral Pressure (kPa) 5 10 15 20
FIG. 13.—Incremental Solution, Broms' Solution, Hand Solution, and Measured Pressures: TRRL Concrete Wall
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by modeling the dynamic thrust of the vibratory roller as 2.5 times the static roller weight, as discussed earlier. Based on the reported post-compaction triaxial soil friction angle of 38.7°, the following parameters were used to model the soil: 7,,, = 19.6 kN/m3 (124.7 pcf); K0 = 0.37; K\A' = 4.33; c' - 0; and (3 = 0.6. Analyses were performed using three values of a (0.58, 0.72 and 0.85), corresponding to the mean and mean plus and minus one standard deviation values from Fig. 2. The final results of these analyses, along with the actual pressure measurements, are shown in Fig. 13. Once again, agreement between the analytical results and field measurements is very good.
Fig. 13 also shows dashed curves representing classical at-rest earth pressure theory and (B) Broms' method. Broms' method is inconsistent due to the fact that it models peak lateral pressure increases resulting from concentrated surficial loading on the basis of a constant (K0) times the peak vertical stress increase, rather than using the peak lateral stress increase (ACT^BC/P), which can be either larger or smaller than K0 times the peak vertical stress increase. Broms' procedure can be modified by adopting the directly calculated ACT „̂CIV (using Eq. 9) as a basis for modeling peak loading, in which case the resulting modified method, which assumes no relaxation of lateral stress with unloading, corresponds to the proposed hysteretic model with a fixed value of a = 1. This would then represent a consistent upper bound solution as shown by the dashed curve (C) in Fig. 13.
Curve D in Fig. 13 shows the results of the proposed simplified hand calculation, again using a = 0.72. This simplified procedure provides good agreement with both the incremental analyses and the field measurements.
CONCLUSION
The proposed hysteretic model for multicycle K0-loading provides good agreement with available multicycle K0-test data, and also represents a basis for incremental analyses of compaction-induced soil stresses resulting from the placement and compaction of level layers of fill either in the free field or adjacent to vertical, nondeflecting soil-structure interfaces. Incremental analyses of such conditions, based on this hysteretic model, provide good agreement with field measurements of compaction-induced earth pressures for a number of case studies, supporting the accuracy and usefulness of these analytical methods.
In performing such analyses, it is important that compaction loading be modeled on the basis of the peak, virgin compaction-induced lateral stress increase {<j'hlVC,v) transformed to an "equivalent" peak vertical stress increase by Eq. 9, rather than on the basis of a directly calculated peak vertical stress increase subsequently multiplied by K0, KA or some other coefficient. Model parameters should represent post-compaction soil conditions. Suitable parameters may be determined either from K0-test data, or based on empirical correlations with the soil friction angle (if)').
Simple hand calculations provide good agreement with the more complex incremental analysis procedures, as well as with field measurements, for situations in which it is appropriate to use similar profiles of
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k<r'h,vc,p versus depth for analysis of compaction of all layers. In addition to thus providing a basis for analysis of compaction-in
duced stresses for the relatively simple conditions considered herein, extended versions of these models and analytical procedures, adapted to finite element methods , provide a basis for the analysis of compaction-induced stresses and deformations for both more general and more complex conditions.
ACKNOWLEDGMENT
Financial support for these studies was provided by a grant from Nik-ken Sekkei of Japan and the Univ. of California at Berkeley. The research was also supported with an Exxon teaching fellowship awarded to the second writer. This support is gratefully acknowledged.
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2. Boyce, S. C , and Kulhawy, F. H., "Laboratory Determination of Horizontal Stress in Cohesionless Soil," Geotechnical Engineering Report No. 83-1, Cornell Univ., Ithaca, NY, 1983.
3. Broms, B., "Lateral Earth Pressures Due to Compaction of Cohesionless Soils," Proceedings, 4th Budapest Conference on Soil Mechanics and Foundations Engineering, 1974, pp. 373-384.
4. Broms, B., and Ingleson, I., "Earth Pressures Against Abutment of Rigid Frame Bridge," Geotechnique, Vol. 21, No. 1, 1971, pp. 15-28.
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6. Carder, D. R., and Krawczyk, J. V., "Performance of Cells Designed to Measure Soil Pressure on Earth Retaining Structures," Transport and Road Research Laboratory Report No. LR 689, 1975.
7. Carder, D. R., Pocock, R. G., and Murray, R. T., "Experimental Retaining Wall Facility-Lateral Stress Measurements with Sand Backfill," Transport and Road Research Laboratory Report No. LR 766, 1977.
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13. Coyle, H. M., and Bartoskewitz, R. E., "Earth Pressure on Precast Panel Retaining Wail," Journal of the Geotechnical Engineering Division, ASCE, Vol. 102, No. GT5, 1976, pp. 441-456.
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21. Prescott, D. M., Coyle, H. M., Bartoskewitz, R. E., and Milberger, L. J., "Field Measurements of Lateral Earth Pressures on a Pre-cast Panel Retaining Wall," Texas Transportation Institute Research Report No. 169-3, 1973.
22. Rankine, W. J. H., "Theory on the Stability of Loose Earth Based on the Elipse of Stresses," Philosophical Transactions of the Royal Society, No. 147, 1857.
23. Rehnman, S. E., and Broms, B. B., "Lateral Pressures on Basement Wall. Results from Full-Scale Tests," Proceedings, 5th European Conference on Soil Mechanics and Foundation Engineering, Vol. 1, 1972, pp. 189-197.
24. Rinkert, A., "Earth Pressure from Frictionless Soils. A Report on Half-Scale Tests," Royal Swedish Geotechnical Institute, Proceedings No. 17, Stockholm, Sweden, 1959.
25. Rowe, P. W., "A Stress-Strain Theory for Cohesionless Soil with Applications to Earth Pressures at Rest and Moving Walls," Geotechnique, Vol. 4, No. 2, 1954, pp. 70-88.
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27. Seed, R. B., and Duncan, J. M., "SSCOMP: A Finite Element Analysis Program for Evaluation of Soil-Structure Interaction and Compaction Effects," Geotechnical Engineering Research Report No. UCB/GT/84-02, Univ. of California, Berkeley, CA, 1984.
28. Seed, R. B., and Duncan, J. M., "FE Analyses: Compaction-Induced Stresses & Deformations," Journal of Geotechnical Engineering, ASCE, Vol. 112, No. 1, 1985, pp. 23-43.
29. Sherif, M. A., and Mackey, R. D., "Pressures on Retaining Wall with Repeated Loading," Journal of the Geotechnical Engineering Division, ASCE, Vol. 103, No. GT11, 1977, pp. 1341-1345.
30. Sowers, G. F., Robb, A. D., Mullis, C. H., and Glenn, A. J., "The Residual Lateral Pressures Produced by Compacting Soils," Proceedings, 4th International Conference on Soil Mechanics and Foundation Engineering, London, England, 1957, pp. 243-247.
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