Seismic Rotational Displacement of Gravity Walls by Pseudodynamic Method

Prediction of the rotational displacements, induced by earthquake is a key aspect of the seismic design of retaining walls. In this paper, the pseudodynamic method is used to compute rotational displacements of the retaining wall supporting cohesionless backfill under seismic loading. The proposed method considers time, phase difference, and effect of amplification in shear and primary waves propagating through the backfill and the retaining wall. The influence of ground motion characteristics on rotational displacement of the wall is evaluated. Also the effects of variation of parameters like wall friction angle, soil friction angle, amplification factor, shear wave velocity, primary wave velocity, period of lateral shaking, horizontal, and vertical seismic accelerations on the rotational displacements are studied. Results are provided in graphical form with a comparison to the available pseudostatic result to validate the proposed theory. Present results give higher values of rotational displacements of the wall when compared with the available results by pseudostatic analysis.     

Seismic Rotational Displacements of Gravity Walls by Pseudodynamic Method with Curved Rupture Surface

This paper presents the use of pseudodynamic method to compute the rotational displacements of gravity retaining walls under passive condition when subjected to seismic loads. The concept of Newmark sliding block method for computing the rotational displacements under seismic condition and the limit equilibrium analysis have been combined in this paper to evaluate the performance of a gravity retaining walls under seismic conditions. One of the main features of the paper is the adoption of a new procedure to evaluate seismic passive earth pressure considering composite curved rupture surface (which is the combination of arc of a logarithmic spiral and straight line) and the dynamic nature of earthquake loading, which is useful to predict rotational displacements accurately. It also determines the threshold seismic acceleration coefficients for rotation using Newmark’s sliding block method. It is shown that the assumption of planar failure mechanism for rough soil-wall interfaces significantly overestimates the threshold seismic accelerations for rotation and underestimates the rotational displacements.     

Seismic Displacement Criterion for Soil Retaining Walls Based on Soil Strength Mobilization

This paper presents a seismic displacement criterion for conventional soil retaining walls based on the observations of a series of shaking table tests and seismic displacement analysis using Newmark’s sliding-block theory taking into account internal friction angle mobilization along the potential failure line in the backfill. A novel approach that relates the displacement of the wall and the mobilized friction angle along the shear band in the backfill is also proposed. A range of horizontal displacement-to-wall height ratios (δ3h/H) between 2 and 5% representing a transitional state from moderate displacement to catastrophic damage were observed in the shaking table tests on two model retaining walls. This observation is supported by both Newmark’s displacement analysis and a new approach that relates the movement of the wall to the mobilization of the friction angle along the shear band in the backfill. A permissible displacement of the wall as defined by the displacement-to-wall height ratio, namely, δ3h/H, equal to 2% was found to be of practical significance in the sense that peak friction angle of the investigated sand is retained along the shear band in the backfill. It is also suggested that δ3h/H = 5% be used as a conservative indicator for the onset of catastrophic failure of the wall associated with fully softened soil strength along the shear band in cohesionless backfill.     

Simulating Seismic Response of Cantilever Retaining Walls

Many failures of retaining walls during earthquakes occurred near waterfront. A reasonably accurate evaluation of earthquake effects under such circumstance requires proven analytical models for dynamic earth pressure, hydrodynamic pressure, and excess pore pressure. However, such analytical procedures, especially for excess pore pressure, are not available and hence comprehensive numerical procedures are needed. This paper presents the results of a finite-element simulation of a flexible, cantilever retaining wall with dry and saturated backfill under earthquake loading, and the results are compared with that of a centrifuge test. It is found that bending moments in the wall increased significantly during earthquakes both when backfill is dry or saturated. After base shaking, the residual moment on the wall was also significantly higher than the moment under static loading. Liquefaction of backfill soil contributed to the failure of the wall, which had large outward movement and uneven subsidence in the backfill. The numerical simulation was able to model quite well the main characteristics of acceleration, bending moment, displacement, and excess pore pressure recorded in the centrifuge test in most cases with the simulation for dry backfill slightly better than that for saturated backfill.     

Seismic Stability of Soil Retaining Walls Situated on Slope

Many soil retaining walls, which were used to stabilize highway embankments constructed on hillside, were severely damaged during the major earthquake (Chi-Chi earthquake, ML = 7.3) on September 21, 1999 in Taiwan. We investigated two typical cases of soil retaining wall damage using survey, soil borings and soil tests. To this end we developed a new pseudo-static method to evaluate the seismic stability of retaining walls situated on slope. Sliding failure along the wall base and bearing capacity failure in the foundation slope were considered in the new pseudo-static method. Results of the analysis showed that seismic stability of the wall against bearing capacity failure may be greatly overestimated when the inertia of soil mass is not taken into account. The analytical results also showed that sliding failure along the wall base occurs prior to the bearing capacity failure of the wall situated on a gentle slope at Site 1. The opposite is true for the wall situated on a steep slope at Site 2. For soil retaining walls constructed on slope, sliding failure of the wall may occur under small input horizontal ground acceleration when the passive resistance in front of the wall is not effectively mobilized. This highlights the importance of improving the strength of backfilled soils in the passive zone when constructing soil retaining walls on slope. The results obtained in the present study also suggest a modification of the current design considerations for soil retaining walls situated on slope.     

Seismic Earth Pressures on Cantilever Retaining Structures

An experimental and analytical program was designed and conducted to evaluate the magnitude and distribution of seismically induced lateral earth pressures on cantilever retaining structures with dry medium dense sand backfill. Results from two sets of dynamic centrifuge experiments and two-dimensional nonlinear finite-element analyses show that maximum dynamic earth pressures monotonically increase with depth and can be reasonably approximated by a triangular distribution. Moreover, dynamic earth pressures and inertia forces do not act simultaneously on the cantilever retaining walls. As a result, designing cantilever retaining walls for maximum dynamic earth pressure increment and maximum wall inertia, as is the current practice, is overly conservative and does not reflect the true seismic response of the wall-backfill system. The relationship between the seismic earth pressure increment coefficient (ΔKAE) at the time of maximum overall wall moment and peak ground acceleration obtained from our experiments suggests that seismic earth pressures on cantilever retaining walls can be neglected at accelerations below 0.4 g. This finding is consistent with the observed good seismic performance of conventionally designed cantilever retaining structures.     

Numerical Study of Impact of Soil Anisotropy on Seismic Performance of Retaining Structure

Recent laboratory investigations indicate that the stress–strain–strength responses of granular soils are appreciably affected by the fabric orientation of the soil relative to the frame of principal stresses. Especially, a sand specimen exhibiting a dilative response during triaxial compression may show a contractive response during triaxial extension under otherwise identical conditions. This observation is of practical importance for applications concerning essentially undrained loading conditions, because the effective mean normal stress at failure, and consequently, the shear strength, associated with an undrained contractive path are considerably lower than those following a dilative path. This raises a question about the impact of soil anisotropy on seismic performance of retaining structures subjected to active and passive earth pressures, because the directions of principal stresses in retained soils for the two cases are very different. This note presents a set of fully coupled finite-element analyses incorporating an anisotropic sand model. The analyses reveal that the impact of fabric anisotropy could be significant when the retaining structure is under passive earth pressure conditions.     

Seismic Design of Flexible Cantilevered Retaining Walls

In this paper, the seismic behavior of embedded cantilevered retaining walls in a coarse-grained soil is studied with a number of numerical analyses, using a nonlinear hysteretic model coupled with a Mohr-Coulomb failure criterion. Two different seismic inputs are used, consisting of acceleration time histories recorded at rock outcrops in Italy. The numerical analyses are aimed to investigate the dynamic behavior of this class of retaining walls, and to interpret this behavior with a pseudostatic approach, in order to provide guidance for design. The role of the wall stiffness on the dynamic response of the system is investigated first. Then, the seismic performance of the retaining walls under severe seismic loading is investigated, exploring the possibility of designing the system in such a way that during the earthquake the strengths of both the soil and the retaining walls are mobilized. In this way, an economic design criterion may be developed, that relies on the ductility of the system, as it is customary in the seismic design of structures.     

Exhumed Geogrid-Reinforced Retaining Wall

An instrumented geogrid-reinforced wall constructed on a highly compressible foundation was deconstructed 16 months after its completion, providing a unique opportunity to exhume and examine the instrumented geogrids that were used to construct the wall. The objectives of this post mortem study were: (1) to inspect the condition of the strain gauges that were attached to the geogrid layers before construction and to verify the reliability of their output; (2) to develop a procedure in which the residual (plastic) strains along exhumed geogrid panels could be determined; and (3) to assess the in situ strain and force distribution along geogrid panels based on the measured residual strains from the exhumed geogrids. After exhumation, it was observed that many of the attached strain gauges failed due to full or partial debonding from the geogrid, thus rendering outputs which potentially underestimated the actual strain. Combining aperture measurements of virgin and exhumed geogrids, all from the same manufacturing lots, enabled the assessment of residual strains following stress relaxation. Laboratory simulation of loading and unloading, including creep and relaxation, yielded a relationship between the measured residual strains and the in situ strain and force distribution; i.e., the residual strain fingerprint provided insight into the behavior of the geogrids within the wall prior to its deconstruction. The mobilized maximum tensile strains in the geogrid panels along the height of the wall were roughly uniform, in the range 4±1%. These findings imply that if the same type of reinforcement had been used throughout the height of the wall, the mobilized force along the height would have been relatively uniform. The back-calculated maximum force in the geogrids indicated that the factor of safety on the long-term strengths of the geogrids ranged from about 1.4 on the stronger/stiffer geogrid to about 1.8 on the weaker/softer geogrid.     

Performance of a Cantilever Retaining Wall

Earth pressure cells, tiltmeters, strain gauges, inclinometer casings, and survey reflectors were installed during construction of a reinforced concrete cantilever retaining wall. A data acquisition system with remote access monitored some 60 sensors on a continual basis. Analyses of the data indicated development of the active condition after translation of about 0.1% of the backfill height. The wall rotated into the backfill as a rigid body, but the top of the stem deflected away from the backfill, approximately equal in magnitude and opposite in direction to the displacement from rigid body rotation. Loading on the wall back-calculated from strain gauge readings was consistent with active earth pressure. The maximum lateral force, about the same as the design value, occurred during compaction of the backfill. Observations that differed from standard assumptions included the passive earth pressure in front of the shear key being less than 10% of the design value and vertical stress below the heel being greater than the toe. Compaction-induced lateral stresses on the stem were sometimes twice the vertical stress.     

Time-Dependent Back Analysis of a Multianchored Pile Retaining Wall

A multianchored pile retaining wall was constructed to protect the cut made for the cut and cover section of the twin Trojane Tunnel. Deformation monitoring surveys were conducted and measurements of movements were carried out throughout the construction cycle of the wall and beyond. In order to determine design parameters for the soil strata embedded in a complex geological sequence, the soil-wall interaction was back analyzed using the finite element method. The technical note describes the process of selection of material parameters through careful assessment of the laboratory data and the results of the numerical back analyses. Once selected, the parameters were verified on the other cut and cover sections of the same tunnel and later used in routine design. Generally, a good agreement between predicted and observed behavior was achieved suggesting the adequate determination of the geotechnical model and the soil parameters.     

Seismic Response Modification Factors for Reinforced Masonry Structural Walls

The current North American design standards provide seismic force modification factors for the rectangular masonry structural walls category only; no similar provisions for flanged and end-confined masonry structural walls exist. This study demonstrates that seismic force reduction factor (R) values calculated for rectangular walls was close to 5.0, which is consistent with the value stipulated by the ASCE 7, and was 36 and 90% higher for the corresponding flanged and end-confined walls. The deflection amplification factor (Cd) values calculated for rectangular walls were higher than specified in the ASCE 7 for the special reinforced masonry wall category. Values of the ductility-related force modification factor (Rd) for flanged and end-confined walls were, respectively, at least 30 and 100% higher than those of rectangular walls specified in the National Building Code of Canada (NBCC). Quantification of the seismic response parameters within this study is expected to facilitate adoption of the flanged and end-confined wall categories in North American masonry codes as a cost-effective technique to enhance the seismic performance of masonry construction.     

Case History of Geosynthetic Reinforced Segmental Retaining Wall Failure

A geosynthetic reinforced segmental retaining wall was collapsed during a monsoon season in Korea, three months after the completion of wall construction. The circular type global slope failure was the dominant failure mode. The as-built design was examined for its appropriateness in meeting the current design requirements and the global slope stability. A comprehensive stress-pore pressure-coupled finite-element analysis was additionally conducted with due consideration of both positive and negative pore pressures in saturated and unsaturated zones. A number of relevant tests were also carried out on the backfill and the reinforcement collected from the site. The investigation revealed among other things that the inappropriate design and the low-quality backfill were mainly responsible for the wall failure, although the primary triggering factor was the rainfall infiltration. The results of the stress-pore pressure-coupled finite-element analysis provided sound evidences as to the wall performance over the rainfall period, supporting the field observation. Practical implications of the findings from this study are also discussed in view of reinforced wall design.     

Reliability Analysis of Partial Safety Factor Design Method for Cantilever Retaining Walls in Granular Soils

Uncertainties in the geotechnical design variables and design equations have a significant impact on the safety of cantilever retaining walls. Traditionally, uncertainties in the geotechnical design are addressed by incorporating a conservative factor of safety in the analytical model. In this paper, a risk-based approach is adopted to assess the influence of the geotechnical variable and design equation uncertainties on the design of cantilever retaining walls in sand using the “partial factor of safety on shear strength” approach. A random model factor based on large-scale laboratory test data from the literature has been incorporated into the reliability analyses to quantify the uncertainty in the geotechnical calculation model. Analyses conducted using Monte Carlo simulation show that the same partial factor can have very different levels of risk depending on the degree of uncertainty of the mean value of the soil friction angle. Calibration studies show the partial factor necessary to achieve target probability values of 1 and 0.1%.     

Optimum Design of Cantilever Retaining Walls Using Target Reliability Approach

In this paper, an approach for reliability-based design optimization of reinforced concrete cantilever retaining wall is described. A parametric study is conducted to assess the effect of uncertainties in design parameters on the probability of failure of cantilever retaining walls. In total, ten modes of failure are considered, viz. overturning of the wall about its toe, sliding of the wall on its base, eccentricity, bearing capacity failure below the base slab, and shear and moment failure in the toe slab, heel slab, and stem. The analysis is performed by treating backfill and foundation soil properties, geometric properties of wall, and reinforcement and concrete properties as random variables. These results are used to develop a set of reliability-based design charts for different coefficients of variation of friction angle of backfill soil (5 and 10%) and targeting reliability index (βt) in the range of 3–3.2 for all failure modes. A comparative study is also presented, which shows that optimized sections have less areas of cross section compared to those obtained from specifications on dimensioning of retaining walls available in literature.     

Correction for Geometry Changes during Motion of Sliding-Block Seismic Displacement

The sliding-block model is often used for the prediction of permanent coseismic displacements of natural slopes and earth structures. This model assumes motion in an inclined plane but does not consider the decrease in inclination of the sliding soil mass as a result of its downward motion, which is the usual condition in the field. The paper studies the above effect and proposes an empirical equation correcting the predictions of the sliding-block model. The investigation is performed by using a recently developed multiblock model. The equation correcting the predictions of the sliding-block model depends on the slip length, the difference in inclinations of the upper and lower part of the slip surface, the seismic displacement predicted by the sliding-block model and the maximum value of the applied horizontal acceleration.     

Transmission of Shear Forces in Sheet Pile Interlocks

An experimental study was conducted to investigate the transmission of shear forces in sheet pile interlocks. This transmission strongly determines the safety of retaining walls made up of U-sheet piles. The limits are given by no and full transfer of the shear at the interlock between the piles. The bending stiffness in the first case is only about one-third compared to that of the second case. Operating values for real systems given in literature and code vary in a broad range within those limits. By estimating the characteristic of the shear force F versus the relative displacement x of small elements at different positions y along the interlocks, it was possible to explain the different results. It was found that F(x,y) depends not only on the coordinates but also on several uncertain, unknown factors. The uncertainty results mainly from the unknown penetration process. The process is determined by the velocity of the penetration, which itself is influenced by the state of the soil inside the clutches, the parameters of the vibrator, and a noncentered penetration of one clutch against the other. Furthermore, the behavior of the wall during excavation at one side and in service is not predictable.     

Vertical Stability of Anchored Concrete Soldier–Pile Walls in Clay

The problem of vertical stability in flexible anchored retaining walls is analyzed and the pattern of the behavior under conditions of poor vertical support is described, on the basis of results from case histories, small-scale tests, and numerical modeling. The possibility of shear stress mobilization in the soil-to-wall interface of anchored concrete soldier–pile retaining walls is discussed. A finite element procedure to model excavations supported by soldier–pile retaining walls is described and applied to a numerical case study. Finite element analyses are performed, emphasizing the consequences of vertical instability due to buckling of the soldier piles and the role of interface resistance in vertical equilibrium. The understanding of some results of the numerical analyses, which are highly influenced by the complexity of the interaction between the different parts of the structure, is obtained by reassessing the vertical equilibrium issue in the light of limit analysis. This approach makes it possible to estimate the pile resistance corresponding to the limit situation of excavation collapse. The finite element model is used to confirm this resistance. Some conclusions are drawn.     

Seismic Displacement of Slopes Reinforced with Piles

The seismic stability of slopes reinforced with a row of piles is analyzed using the kinematic theorem of limit analysis within the framework of the pseudostatic approach. An existing method which is based on the theory of plasticity is used to determine the lateral forces provided by the piles. Expressions for calculating the yield acceleration coefficient are derived. Then, based on Newmark’s sliding block concept, the permanent displacement induced by an earthquake shocking can be calculated by the integrals of seismic records. An example is investigated to illustrate the validity of this method and the effects of piles on a restraining slope’s dynamic deformation.     

Effect of Live Load Surcharge on Retaining Walls and Abutments

In the conventional design of retaining walls and bridge abutments, the lateral earth pressure due to live load surcharge is estimated by replacing the actual highway loads with a 600 mm layer of backfill. This original recommendation was made several decades ago when the highway truck loads were much lighter. A number of researchers have shown that the pressure exerted on the wall due to live load surcharge is greater near the surface and is diminished nonlinearly throughout the height of the wall. The heavier highway loads and the demonstrated nonlinear earth pressure distribution require a need for a more rational method for obtaining the equivalent height of backfill. This paper discusses theoretical background, an analytical approach to estimation of actual earth pressure, a number of innovative approaches to obtain a simplified pressure distribution, an extensive parametric study, calibration procedures for the traditional method, and recommendations.