Simplified Approach for the Seismic Response of a Pile Foundation

Pseudostatic approaches for the seismic analysis of pile foundations are attractive for practicing engineers because they are simple when compared to difficult and more complex dynamic analyses. To evaluate the internal response of piles subjected to earthquake loading, a simplified approach based on the “p-y” subgrade reaction method has been developed. The method involves two main steps: first, a site response analysis is carried out to obtain the free-field ground displacements along the pile. Next, a static load analysis is carried out for the pile, subjected to the computed free-field ground displacements and the static loading at the pile head. A pseudostatic push over analysis is adopted to simulate the behavior of piles subjected to both lateral soil movements and static loadings at the pile head. The single pile or the pile group interact with the surrounding soil by means of hyperbolic p-y curves. The solution derived first for the single pile, was extended to the case of a pile group by empirical multipliers, which account for reduced resistance and stiffness due to pile-soil-pile interaction. Numerical results obtained by the proposed simplified approach were compared with experimental and numerical results reported in literature. It has been shown that this procedure can be used successfully for determining the response of a pile foundation to “inertial” loading caused by the lateral forces imposed on the superstructure and “kinematic” loading caused by the ground movements developed during an earthquake.     

Seismic Rotational Stability of Waterfront Retaining Wall Using Pseudodynamic Method

Design of waterfront retaining walls under seismic conditions is an important topic of research among the geotechnical engineering fraternity, and recently there have been studies in which the stability of rigid waterfront retaining walls has been assessed. However, an important aspect of seismic rotational stability of such walls is still missing from the literature archives. The present study shows the importance of rotational displacements for the design of the rigid waterfront retaining wall. Consideration has been made for the calculation of the hydrodynamic pressure as well as the seismic forces, both due to the seismic pressure and seismic wall inertia. These seismic forces have been calculated using the pseudodynamic approach. The free water condition has been considered in the analysis, and thus the hydrodynamic pressure has been considered to exist on the downstream face of the retaining wall as well, and a well-known expression approximating the effect of the inertia of the water due to the earthquake has been used for the estimation of this hydrodynamic pressure force. Simple expressions for the calculation of rotational displacement both during and after the earthquake have been proposed, and typical results have been obtained. It is observed that with an increase in the ratio of the water level to the total height of the wall from 0.50 to 1.00 the rotational displacement of the wall increases by about 110%. Similar trend of an increase in the value of the rotational displacement was observed for an increase in the values of the horizontal and vertical seismic acceleration coefficients. Also, the parametric study carried out in the analysis suggested that the rotational displacement is sensitive to other parameters such as the upstream water height, pore pressure ratio, soil, and wall friction angles. Due to nonavailability of the results in which rotational stability of the waterfront retaining wall under the seismic conditions has been studied, the results from the present analysis seem to bring out a unique approach.     

Kinematic Pile Response to Vertical P-wave Seismic Excitation

An analytical solution based on a rod-on-dynamic-Winkler-foundation model is developed for the response of piles in a soil layer subjected to vertical seismic excitation consisting of harmonic compressional waves. Closed-form solutions are derived for: (1) the motion of the pile head; (2) the peak normal strain in the pile, and (3) the group effect between neighboring piles. The solutions are expressed in terms of a dimensionless kinematic response factor Iv, relating pile-head motion and free-field soil surface motion, a dimensionless strain transmissibility factor Iε, relating pile and soil peak normal strains, and a pile-to-pile interaction factor α measuring group effects. It is shown that a pile foundation may significantly reduce the vertical seismic excitation transmitted to the base of a structure.     

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 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.     

Pseudostatic Approach for Seismic Analysis of Single Piles

This paper evaluates a simple approximate methodology for estimating the maximum internal forces of piles subjected to lateral seismic excitation. The method involves two main steps: computation of the free-field soil movements caused by the earthquake and the analysis of the response of the pile to the maximum free-field soil movements (considered as static movements) plus a static loading at the pile head, which depends on the computed spectral acceleration of the structure being supported. The applicability of this approach has been verified by an independent benchmark analysis developed by the writers. It is demonstrated that the proposed method yields reasonable estimates of the pile maximum moment and shear. The methodology is then used to obtain the response of the Ohba-Ohashi bridge in Japan to one of the earthquakes that occurred in the 1980s. Good agreement is found between the computed and measured pile moments.     

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 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.     

Rotating Block Method for Seismic Displacement of Gravity Walls

A rotating block method is developed to calculate the rotational displacements of gravity retaining walls based on rigid foundations under seismic loading. The method is similar to the pseudostatic sliding block method of Newmark. When a threshold acceleration for rotation is exceeded, a rigid wall will start to rotate until the angular velocity for rotation is reduced to zero. The influence of ground motion characteristics on computed wall deformation was evaluated. The procedure was validated by data from centrifuge tests. This method is also applicable for the most complex cases when the sliding and rotation of a gravity wall are coupled.     

Displacements of Multiblock Geotechnical Structures Subjected to Seismic Excitation

A method is presented for calculations of irreversible displacements of multiblock structures subjected to seismic excitation. Use is made of the kinematic approach of limit analysis. To make the analysis tractable a hodograph representing distribution of accelerations in the structure is introduced. Distinction is made between soils conforming to the associative and nonassociative flow rules, and the importance of this distinction is demonstrated. The yield acceleration calculated for slopes comprised of soils conforming to the nonassociative flow rule is lower than that for a soil with the same strength parameters, but its deformation governed by the associative flow rule. Consequently, the displacements predicted for the former are larger. An example of a slope is demonstrated, but the method presented is applicable to other structures, such as retaining walls and embankments.     

Active Earth Pressure on Retaining Wall for c-? Soil Backfill under Seismic Loading Condition

This technical note describes the derivation of an analytical expression for the total active force on the retaining wall for c-? soil backfill considering both the horizontal and vertical seismic coefficients. The results based on this expression are compared with those obtained from earlier analytical expressions for the active force for c-? soil backfill under seismic conditions, and found to have a similar trend of variation. The parametric study shows that the inclination of the critical failure plane with the horizontal plane decreases with the increase in values of seismic coefficients; the decrease being more for their higher values. The total active force increases with the increase in value of horizontal seismic coefficient; while it decreases with the increase in value of vertical seismic coefficient except for a very high value of horizontal seismic coefficient. Design charts are presented for various combinations of horizontal and vertical seismic coefficients (kh and kv), and values of cohesion and angle of shearing resistance for estimating the total active force on the retaining wall for c-? soil backfill for practical applications.     

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.     

挡土墙优化设计初探

挡土墙是应用比较广泛的构筑物,它的设计要考虑使用要求、周围环境、总图条件、地基情况、抗震设防、冻土深度及墙体总高度等因素,关键因素则是墙体总高度;由于挡土墙的计算是基于几个假定理论进行的近似计算,因此,合理选用材质、造型、构造等对于实现设计方案优化显得尤为重要.较大的挡土墙工程,经优化设计后可降低工程造价且能加快施工进...     

Behavior of Pile Groups Subject to Excavation-Induced Soil Movement in Very Soft Clay

A series of centrifuge model tests was conducted to investigate the behavior of pile groups of various sizes and configurations behind a retaining wall in very soft clay. With a 1.2-m excavation in front of the wall, which may simulate the initial stage of an excavation prior to strutting, the test results reveal that the induced bending moment on an individual pile in a free-head pile group is always smaller than that on a corresponding single pile located at the same distance behind the wall. This is attributed to the shadowing and reinforcing effects of other piles within the group. The degree of shadowing experienced by a pile depends on its relative position in the pile group. With a capped-head pile group, the individual piles are forced to interact in unison though subjected to different magnitudes of soil movement. Thus, despite being subjected to a larger soil movement, the induced bending moment on the front piles is moderated by the rear piles through the pile cap. A finite element program developed at the National University of Singapore is employed to back-analyze the centrifuge test data. The program gives a reasonably good prediction of the induced pile bending moments provided an appropriate modification factor is applied for the free-field soil movement and the amount of restraint provided by the pile cap is properly accounted for. The modification factor applied to the free-field soil movement accounts the reinforcing effect of the piles on the soil movement.     

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.     

矿山公路陡坡挡土墙设计实践

对矿山公路中陡坡挡土墙破坏原因，从设计、受力等方面进行分析，得出结论：从设计上根本解决挡土墙的工程隐患，不仅应综合考虑滑坡推力及主动土压力的作用，而且应充分考虑地形、地质及水文等实际影响，确定主动土压力或滑坡推力为其中设计推力进行控制设计。     

Combined Finite- and Boundary-Element Analysis of the Effects of Tunneling on Single Piles

An efficient and practical method of analysis to predict the effects of tunneling on existing single pile foundations is described. The method involves a combination of the finite- and boundary-element (FAB) methods, with free-field ground movements predicted by the finite-element method and the response of an embedded pile to these ground movements predicted by the boundary-element method. The method allows prediction of the full three-dimensional (3D) response of the pile as tunnel excavation proceeds towards the pile and away from it. Very good agreement is obtained between predictions of the pile response obtained by the FAB method and a 3D finite-element analysis which specifically includes the pile in the finite-element mesh. The vastly superior computational efficiency of the FAB method over the full 3D finite element approach is also illustrated.     

Predicting RC Frame Response to Excavation-Induced Settlement

In many tunneling and excavation projects, free-field vertical ground movements have been used to predict subsidence, and empirical limits have been employed to evaluate risk. Validity of such approaches is largely unknown given that ground movements are in fact not one-dimensional and that adjacent applied loads are known to have an impact. This paper employed analytical and large-scale experimental efforts to quantify these issues, in the case of excavation adjacent to a reinforced concrete frame with tieback anchors and a sheetpile wall in dry sand. With this flexible system, a disproportionate amount of the soil and building movements occurred prior to installation of the first tieback, even when conservative construction practices were applied. Furthermore, free-field data generated a trough as little as one-half the size of that recorded near the building frames. Empirically based relative gradient limits generally matched the extent and distribution of the damage, while the application of various structural limits did not fully identify local damage distribution but did generally reflect global response. The use of fully free-field data or a failure to include lateral soil displacements both underpredicted building displacements by as much as 50% for low-rise concrete frames without grade beams on sand.     

香炉山钨矿充填试验区挡墙力学特征分析

充填挡墙关系到充填工作的安全性和充填成本。挡墙设计时需根据所选定的位置,正确分析充填挡墙受力状况,合理计算其受力大小,以确定其结构参数。根据香炉山钨矿充填试验区充填料浆呈液态的特性、单次充填高度以及充填工艺等特点,较全面地分析了充填挡墙的受力特征,同时对该状态下的挡墙受力计算公式进行了推导和优化,总结了改善挡墙受力的措施。     

Observed Seismic Lateral Resistance of Liquefying Sand

This paper presents results from a study of the dynamic response of pile foundations in liquefying sand during seismic loading. The study included a series of dynamic centrifuge tests of pile-supported structures and the back-calculation of time histories for the lateral resistance p and relative displacement y between a pile and the free-field soil. Details of the centrifuge experiments and the procedures used to back-calculate p and y time histories are described. The back-calculated p-y time histories provide a concise representation of the experimental results and can be compared to the equivalent p-y behavior predicted by soil-pile interaction analysis methods. The observed p-y behavior provides insight into the mechanisms of soil-pile interaction in liquefying sand, showing characteristics that are consistent with the undrained cyclic loading behavior of saturated sand, including the effects of relative density, cyclic degradation, pore-pressure generation, prior displacement (strain) history, and phase transformation behavior.