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Development of engineering procedure for evaluating lateral earth pressures for seismic design of cantilever retaining walls W.I. Cameron & R.A. Green University of Michigan, Ann Arbor, Michigan, USA

ABSTRACT: The purpose of this research is to develop a seismic design procedure for determining the lateral earth pressures on flexible cantilever retaining structures. Non-linear numerical analyses are being conducted using the computer program FLAC (Fast Lagrangian Analysis of Continua) to evaluate the effect of soil-structure system flexibility on the magnitude and distribution of lateral earth pressures for global and internal stability. The methodology of the research and some of the preliminary results are presented. Keywords: earth retaining wall, seismic design, earthquakes 1 INTRODUCTION Earth retaining structures constitute an integral part of the infrastructure in the United States and around the world, extensively being used for bridge abutments, cuts along highways, port facilities, etc. The stability of these retaining structures is vital to reduce earthquake losses and for post-earthquake emergency response. Estimating the lateral earth pressures induced by earthquake shaking is a key aspect of the seismic design of the earth retaining structures. The magnitude and distribution of the seismically induced lateral earth pressures on retaining walls is a complex soil-structure interaction problem that depends on the flexibility of the wall, the soil stiffness, the deformation of the wall, and the characteristics of the ground motions. For cantilever retaining walls, the magnitude and distribution of the seismically-induced lateral earth pressures acting on the stem of the wall are very important for an adequate structural design. A typical sketch of a cantilever retaining wall is shown in Figure 1. Current seismic design methods for determining the lateral earth pressures of cantilever retaining walls do not consider the flexibility of the soil-structure system. Although some studies have been conducted to evaluate the flexibility of the wall, little research has contributed to the improvement of the current design approaches. The goal of this research is the development of an improved procedure for estimating the seismic earth pressures to which flexible cantilever retaining walls are designed to ensure global stability (e.g. sliding and overturning) and internal stability (e.g. structural adequacy of the stem and base of the wall). The effect of the flexibility of the soil-structure system on the magnitude and distribution of lateral earth pressures acting along the stem and heel sections of cantilever retaining walls are being evaluated. Because the flexibility of the soil-structure system is not only a function of the properties of the wall and soils but also a function of the characteristic of the ground motions to which the system is subjected, a portion of the research is also focusing on characterization of the frequency content of the earthquake ground motions. The methodology of the proposed research and some of the preliminary results are presented.

a) Earth pressures on stem of the wall stem section

b) Earth pressures on heel section

backfill structural block

stem

heel section

heel

toe base

Figure 1. Sketch of design lateral earth pressures on cantilever retaining wall for a) internal stability and b) global stability.

2 BACKGROUND Contrary to the design of massive gravity retaining structures, the design of cantilever retaining walls requires the consideration of both internal and global stability. For the global stability of cantilever retaining wall, the lateral earth pressures are assumed to act on a vertical section (or heel section), which extends from the heel of the wall through the backfill to the ground surface, as shown in Figure 1b. It is standard design practice to assume that the critical earth pressures for global and internal stability of cantilever retaining structures are synonymous. However, the critical load cases for global and internal stability do not necessarily occur at the same time, nor do they necessarily have the same amplitudes. For global stability evaluations, the critical load case corresponds to the dynamic pressures that are imposed on the wall as it moves away from the backfill (i.e. active condition). For internal stability considerations, recent studies (Green & Ebeling 2002, Green et al. 2003) have showed that higher pressures act on the wall as it moves towards the backfill, which is of no concern for the global stability of the wall, but constitutes the critical load case for internal stability. In current design approaches for earth retaining structures, the Mononobe-Okabe method (Mononobe & Matsuo 1929, Okabe 1924) is commonly used for determining the lateral earth pressures induced by earthquake loading. The Mononobe-Okabe (M-O) method is based on limit equilibrium and is an extension of Coulomb’s theory developed for static conditions, wherein the M-O method takes into account the inertial forces acting on the soil mass during earthquake loading. The M-O method, as illustrated in Figure 2, was developed for global stability of massive gravity walls. One of the fundamental assumptions of the M-O method is that the retaining wall and failure soil wedge act as rigid bodies. This assumption has been shown to be reasonable for large gravity type retaining structures (e.g. Seed & Whitman 1970). The applicability of the M-O method for determining the critical design pressures for cantilever retaining walls is questionable. First, the flexibility of the soil-structure system violates one of the fundamental assumptions (i.e. the wall and failure soil wedge acts as rigid monoliths). Second, the M-O method was developed for global stability of massive gravity retaining walls, not for estimating the design pressures required for internal stability or structural detailing of the cantilever retaining walls. Regarding the implementation of the M-O method, the assumption that critical earth pressures for global and internal stability of cantilever retaining structures are synonymous is not appropriated. Many studies have been conducted for assessing the validity of the M-O approach for different types of retaining walls. The significance of the flexibility of cantilever retaining walls on dynamically induced earth pressures was highlighted by both centrifuge model tests (Ortiz et al. 1983, Steedman 1984, Anderson et al. 1987) and detailed numerical dynamic response analyses (Al-Hamoud 1990, Green & Ebeling 2002). These studies also showed a significant residual increase in the static earth pressures at the end of shaking. Finally, regarding the observed performance of cantilever walls during earthquakes, Whitman (1996) stated that “Experience with

W kh failure plane

H W(1-kv)

φ

δ

PAE

αAE

R

PAE = kh = kv = W = R = φ = αAE = δ =

resultant of lateral earth pressure coefficient of horizontal inertial force coefficient of vertical inertial force weight of failure soil wedge shear resistance force angle of internal friction angle of failure plane angle of interface friction

Figure 2. Illustration of the failure mechanism of the M-O method for active conditions.

cantilever walls is mixed, with enough suggestions of difficulties to provide a warning that lateral earth pressures during earthquakes may be larger than generally assumed.” 3 OBJECTIVES AND APPROACH OF RESEARCH The objective of this research is to develop an improved engineering procedure for determining the lateral earth pressures for the seismic design of flexible cantilever retaining structures. The influence of the flexibility of the soil-structure system on the magnitude and distribution of lateral earth pressures acting along the stem and heel sections of the wall is investigated for both internal and global stability evaluations. Considerations of the effect of ground water condition on the retained backfill and/or foundation soils are beyond the scope of this research. The research involves the following three phases: 1) characterization of frequency content of earthquake ground motions, 2) numerical analyses of the dynamic response of cantilever retaining systems, and 3) development of an improved engineering procedure for determining the seismic design earth pressures for global and internal stability evaluations of cantilever retaining walls that takes into account the flexibility of the soil-structure systems. 4 METHODOLOGY OF RESEARCH

4.1 Characterization of frequency content of ground motions The objective of this phase is to select/develop a simplified index for quantifying the characteristic frequency of the ground motions as a function of earthquake magnitude, site-to-source distance, and tectonic/geologic settings. Recorded and/or synthetic earthquake records for Western United States (WUS) and Central/Eastern United States (CEUS) representing a wide range of magnitude and site-to-source distance combinations are being collected and evaluated for frequency content characterization. Various approaches proposed in literature for quantifying the characteristic period of ground motions are being investigated, including: 1) period corresponding to the peak response spectral acceleration (Seed et al. 1968), 2) period corresponding to the peak response spectral velocity (Wiggins 1964), 3) period corresponding to the peak "smoothed" response spectral acceleration (Rathje et al. 1998), 4) mean period (Rathje et al. 1998), which is computed from the Fourier amplitude spectrum of the acceleration time history of the ground motion, 4) TV/A for median Newmark-Hall design spectra (Green & Cameron, 2003; Cuesta et al. 2003), and 5) others. Preliminary analyses suggest that TV/A may be the best index for quantifying the characteristic period of the ground motion. TV/A is defined as the period corresponding to the intersection of the constant spectral acceleration and velocity regions of the 5% damped Newmark-Hall design spectrum for that is constructed by using the actual peak ground acceleration and velocity of the

0.25

TV/A

Station Piedmont Jr High (phj045)

0.20 Pseudo spectral acceleration (g)

0.15

Newmark-Hall type spectrum

0.10

response spectrum

0.05 0.00

0.0

0.5

1.0

1.5 2.0 Period (sec)

2.5

3.0

Figure 3. Illustration of the parameter of TV/A for quantifying the characteristic period of a free-field rock outcrop motion recorded during the 1989 Loma Prieta earthquake.

earthquake motions, as illustrated in Figure 3. TV/A is calculated using the following equation:

TV / A = 2 ⋅ π ⋅

αV ⋅ PGV α A ⋅ PGA

(1)

where PGV= peak ground velocity; PGA= peak ground acceleration; αV and αA = amplification factor for horizontal ground motions for the constant velocity and acceleration regions, respectively, for the 5% damped Newhall-Hall design spectrum. TV/A was used by Green & Cameron (2003) to develop a preliminary correlation for one-dimensional site amplification of peak ground accelerations. The results of the study indicated a fairly good correlation between amplification of ground motions and the ratio of the low-strain fundamental period (Tn) of the soil profile and TV/A. The use of TV/A for quantifying the characteristic period of the ground motions has several advantages over the others indices evaluated for this research: 1) TV/A is relatively easy to compute from acceleration time histories of ground motions by using the corresponding PGA and PGV, 2) TV/A is synonymous to the Ts for the NEHRP design spectra (NEHRP 2001), and 3) existing attenuation relations for PGA and PGV can be used to determine TV/A as a function of earthquake magnitude (M) and site-to-source distance (R). 4.2 Numerical modeling of seismic response of walls The objective of this phase is to perform a parametric study of the seismic response of the cantilever retaining systems in which the magnitude and distribution of lateral earth pressure induced on cantilever retaining walls as a function of the characteristic frequency of the earthquake ground motions and the geometry/properties of the soil-structure system are examined. The nonlinear numerical analyses of the seismic response of the cantilever retaining systems are being performed using the two-dimensional finite difference computer program FLAC (Itasca 2000). FLAC is capable of modeling large deformations and non-linear soil behavior and allowing incremental construction of the wall to ensure proper initial stress conditions in the wall-soil system. Additionally, the explicit time marching algorithm in FLAC allows stable solutions to be computed for unstable physical processes (e.g. sliding and/or overturning of earth retaining walls). The numerical model used for this research is similar to that used by Green & Ebeling (2002) in their preliminary analyses of the dynamic response of cantilever retaining walls. An elastoplastic constitutive model with the Mohr-Coulomb failure criterion is used to model the soils. Cantilever retaining walls are modeled using elastic beam elements with interfaces elements along the wall surfaces that are in contact with the soil. The wall-backfill system is constructed incrementally to simulate the build-up in the initial lateral earth pressures on the wall. Finally, the acceleration time histories of interlayer ground motions are used as the input motion along the base of the FLAC model.

For the elasto-plastic constitutive model in conjunction with the Mohr-Coulomb failure criterion, four parameters are required: total unit weight (γt), effective internal friction angle (φ), small strain shear modulus (G), and bulk modulus (K). For the parametric study, typical values for these parameters are assumed for the backfill and foundation soils. The model of elastic beam elements for the cantilever retaining structures requires four parameters: total unit weight (γ), cross-sectional area (Ag), elastic Young’s modulus (E), and moment of inertia (I). These parameters are being obtained from the structural design of the reinforced-concrete wall. The interaction between the soil and retaining wall are modeled by using interface elements along the wall surface that is in contact with the soil. The interface elements allow the permanent relative movement of the wall and soil to occur. The interface element is represented by springs to model the normal stiffness (kn) and shear stiffness (kn), slider to model the shear resistance (S), and tensile element to model the tensile strength (T) of cohesive soils. These parameters are being calibrated to the hyperbolic-type interface model proposed by Gomez et al. (2000a, b). Free-field acceleration time histories of outcrop ground motions recorded on rock or stiff soil sites are used in the analyses. However, the outcrop motions records are not input directly into the FLAC model. First, a modified version of SHAKE91 (Idriss & Sun 1992) is being used to compute the interlayer motions at the depth corresponding to the base of the FLAC model. 4.3 Development of engineering design procedure One of the key aspects of this phase is to define parameters for quantifying the flexibility of the soil-structure system. It is hypothesized that the flexibility of the system can be quantified in terms of the fundamental period of the soil-structure system relative to the characteristic period of ground motions. For example, wall flexibility can be due to relatively low stiffness of the structural wall members and/or to the flexibility of the foundation soils. However, even a wall having relatively flexible structural members can respond dynamically as a rigid monolith if the characteristic wave length of the ground motion is long compared to the height of the wall (e.g. Steedman & Zeng 1990). This is because at a given instant in time the wall and failure wedge will experience fairly uniform accelerations with depth. On the contrary, if the characteristic wave length of the ground motion is short compared to the height of wall, the acceleration of the wall and driving soil wedge will vary as a function of depth, resulting in a complex laterally induced pressure distribution on flexible walls. Therefore, both the properties of the soil-structure system and the characteristics of the ground motions determine whether a wall will respond dynamically as a rigid monolith, as assumed in the M-O method, or as a flexible system. The results of the numerical analyses are being used to calculate the magnitude and distribution of the dynamic lateral earth pressures induced along the stem and heel section of the wall. The dynamic earth pressures computed by FLAC are compared with those predicted using the M-O method. The permanent relative displacements of the wall are computed by subtracting the total displacements in the free-field zone from the total displacements of the wall at the same depth. Finally, the identified trends in the results of the parametric study will be used to develop an improved design procedure, wherein the influence of characteristics of the input ground motions, the flexibility of the retaining structure, and maximum tolerable permanent displacement of the wall will be correlated to the seismically induced lateral earth pressures on cantilever retaining walls. It is desired to develop an improved design procedure for estimating the design lateral earth pressures for flexible cantilever retaining walls that uses the maximum tolerable permanent displacement of the wall as a specified input parameter, analogous to the RichardsElms displacement-controlled design method for rigid gravity walls (Richards & Elms 1979). 5 PRELIMINARY RESULTS Preliminary numerical analyses were performed on a 6.1-m high cantilever wall retaining a medium dense granular backfill (φ=35°) and supported on dense foundation soils (φ=40°). A freefield rock outcrop motion (SG3351) recorded during the 1989 Loma Prieta earthquake (moment magnitude, Mw=6.9) was scaled to different peak ground accelerations to perform a series of analyses. The results of the preliminary analyses showed that the lateral earth pressures induced

1.0

away from backfill

0.5 kh

0.0

10

20

30

-0.5 toward the backfill

-1.0 291.6

stem

residual force

218.7 PFLAC (kN/m)

at-rest (Ko) conditions static KA conditions

145.8 72.9 0.0

40 Time (seconds)

0

10

20

30

40 Time (seconds)

Figure 4. Time histories of coefficient of horizontal inertial forces (kh) at approximately the center of the structural block and resultant of induced earth pressures (PFLAC) on the stem of the wall.

on the stem of the wall were in very good agreement with those predicted by the M-O method during the early stages of shaking. However, at higher levels of acceleration, the computed lateral earth pressures were greater than those predicted by the M-O method. As shown in Figure 4, the dynamic pressures increased significantly during shaking, exceeding those values corresponding to at-rest (Ko) condition. At the end of shaking, the residual earth pressures, which were not released during slippage of the wall away from backfill, tended to be very close to the Ko-condition values. Figure 4 also shows the coefficient of horizontal inertial force (kh) corresponding to the acceleration computed at the center of the structural block (consisting of the wall and backfill contained within). The differences in the lateral earth pressures computed by FLAC and those predicted by the M-O method can be understood by examining the failure mechanism presented in Figure 5. The failure mechanism of the soil behind the structural block consisted of several wedges, rather than a single rigid failure wedge as assumed in the M-O method. At larger values of kh directed away from the backfill, the induced inertial forces on the structural block caused it to simultaneously bend, rotate, and slide away from the backfill and at the same time the small wedge of soil (referred to as a graben in Fig. 5) moves vertically downward. As the direction of kh reversed (i.e. changes direction from away to toward the backfill), the graben prevents the wall from returning to its initial undeformed shape, locking-in the elastic stresses produced from the bending and rotation of the wall. The increase in locked-in stresses continued until the residual stresses graben

Figure 5. Failure mechanism of the wall analyzed (deformations magnified by factor of 3).

Measured force (N)

890 801 712 623 534 449

residual force at the end of shaking

356 267 178 0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

Time (seconds) Figure 6. Results of a centrifuge test of retaining wall on flexible foundation (modified from Anderson et al. 1987).

imposed on the stem reach a value corresponding to Ko-condition (as shown in Fig. 4), while the dynamically induced inertial stresses were superimposed on the locked-in stresses. The tendency of the increase in residual pressure was in good agreement with the results of centrifuge tests conducted by Anderson et al. (1987), as shown in Figure 6. The results of the preliminary FLAC analyses were used to evaluate the magnitude and distribution of the dynamic lateral earth pressures induced along the stem and heel section of the wall. As the wall moved away from the backfill, the distribution of lateral pressures acting on the stem and heel sections of the wall was triangular in shape, the same as for the static active case, with the resultant force acting at approximately one third of the height of the wall above the base. As the wall moved toward the backfill, the distribution of the pressure was relatively uniform along the stem of the wall, with the resultant acting at approximately mid-height of the wall. As a result of the higher point of action of the resultant force, the maximum moment around the bottom the wall stem occurred as the wall moved toward the backfill. 6 CONCLUSIONS The results of this research will contribute to minimize the seismic risk by providing engineering practitioners with an improved design tool for flexible retaining systems. The improved design procedure will be used for determining the seismic pressures on flexible cantilever retaining structures for both global and internal stability evaluations. The simplified procedure will overcome some of the limitations of the currently used design methods by taking into account the flexibility of the soil-structure system. 7 REFERENCES [1] Green, R.A. & Ebeling, R.M. 2002. S Seismic analysis of cantilever retaining walls, phase I. ERDC/ITL TR-02-3, Information Technology Laboratory, U.S. Army Corps of Engineers, ERDC, Vicksburg, MS. [2] Green, R.A, Olgun, C.G., Ebeling, R.M. & Cameron, W.I. 2003. Seismically induced lateral earth pressures on a cantilever retaining wall. Proc. 6th US Conference and Workshop on Lifeline Earthquake Engineering, Long Beach, California, ASCE, TCLEE Monograph No. 25: 946-955. [3] Mononobe, N. & Matsuo, H. 1929. On the determination of earth pressure during earthquakes. Proc. World Engineering Congress, 9: 177-185. [4] Okabe, S. 1924. General theory of earth pressures and seismic stability of retaining wall and dam. Journal Japan Society of Civil Engineering, 10(5): 1277-1323.

[5] Seed, H.B. & Whitman, R.V. 1970. Design of earth retaining structures for dynamic loads. ASCE Specialty Conf. on Lateral Stresses in the Ground and Design of Earth Retaining Structures: 103-147. [6] Ortiz, L. A., Scott, R. F. & Lee, J. 1983. Dynamic centrifuge testing of a cantilever retaining wall. Earthquake Engineering and Structural Dynamics, 11: 251-268. [7] Steedman, R.S. 1984. Modeling the behaviour of retaning walls in earthquakes. Ph.D. thesis, Engineering Dept. Cambridge Unversity. [8] Anderson, G.R., Whitman, R.V. & Germaine, J.T. 1991. Seismic response of rigid tilting response of centrifuge-modeled gravity retaining wall to seismic shaking: description of tests and initial analysis of results. Report R87-14, Dept. Civil Engineering, MIT, Cambridge, MA. [9] Al-Hamoud, A. 1990. Evaluating tilt of gravity retaining walls during earthquakes, Sc.D. thesis, Dept. Civil Engineering, MIT, Cambridge, MA. [10] Whitman, R.V. 1996. Designing retaining structures against the effects of earthquakes. Proc. Vancouver Geotechnical Society Symposium, June 7, Vancouver, Canada. [11] Seed, H.B., Idriss, I.M. & Keifer, F.W. 1968. Characteristics of rock motions during earthquakes. Earthquake Engineering Research Center, Report No. EERC-68-6, Berkeley, CA. [12] Wiggins, J.H. 1964. Effect of site conditions on earthquake intensity. Journal of Structural Division, ASCE, 90(ST2): 279-313. [13] Rathje, E.M., Abrahamson, N.A. & Bray, J.D. 1998. Simplified frequency content estimates of earthquake ground motions. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 124(2): 150-159. [14] Green, R.A. & Cameron, W.I. 2003. Influence of ground motion characteristics on site response coefficient. Proc. 2003 Pacific Conference Earthquake Engineering, Paper 090, New Zealand. [15] Cuesta, I., Aschheim, M.A. & Fajfar, P. 2003. Simplified R-factor relationships for strong ground motions. Earthquake Spectra, EERI, 9(1): 25-45. [16] NEHRP 2001. NEHRP recommended provisions for seismic regulations for new buildings and other structures. Part 1-Provisions: FEMA 368, Part 2-Commentary FEMA 369, Federal Emergency Management Agency, Washington DC. [17] Itasca 2000. FLAC (Fast Lagrangian Analysis of Continua) user’s manuals. Itasca Consulting Group, Inc., Minneapolis, MN. [18] Gomez, J.E., Filz, G.M. & Ebeling, R.M. 2000a. Development of an improved numerical model for concrete-to-soil interfaces in soil-structure interaction analyses. Report 2, Final Study, ERDC/ITL TR-99-1, U.S. Army Corps of Engineers, ERDC, Vicksburg, MS. [19] Gomez, J.E., Filz, G.M. & Ebeling, R.M. 2000b. Extended load/unload/reload hyperbolic model for interfaces: parameter values and model performance for the contact between concrete and coarse sand. ERDC/ITL TR-00-7, U.S. Army Corps of Engineers, ERDC, Vicksburg, MS. [20] Idriss, I.M. & Sun, J.I. 1992. SHAKE91: a computer program for conducting equivalent linear seismic response analyes of horizontally layered soil deposits. University of California, Davis. [21] Steedman, R.S. & Zeng, X. 1990. The influence of phase on the calculation of pseudostatic earth pressure on a retaining wall. Géotechnique, 40(1): 103-112. [22] Richards, R. & Elms, D.G. 1979. Seismic behavior of gravity retaining walls. Journal of Geotechnical Engineering Division, ASCE, 105(GT4): 449-464. Wanda I. Cameron, PhD Candidate University of Michigan Dept. Civil and Environmental Engineering Geotechnical Engineering Group 2350 Hayward Street 48109 – Ann Arbor, MI – USA Tel. : 1 734 763-2478 Fax : 1 734 764-4292 E-mail: [email protected]

Prof. R. A. Green, Supervisor University of Michigan, E-mail: [email protected]