Seismic earth pressures on rigid and flexible retaining walls

While limiting-equilibrium Mononobe–Okabe type solutions are still widely used in designing rigid gravity and flexible cantilever retaining walls against earthquakes, elasticity-based solutions have been given a new impetus following the analytical work of Veletsos and Younan [23]. The present paper develops a more general finite-element method of solution, the results of which are shown to be in agreement with the available analytical results for the distribution of dynamic earth pressures on rigid and flexible walls. The method is then employed to further investigate parametrically the effects of flexural wall rigidity and the rocking base compliance. Both homogeneous and inhomogeneous retained soil is considered, while a second soil layer is introduced as the foundation of the retaining system. The results confirm the approximate convergence between Mononobe–Okabe and elasticity-based solutions for structurally or rotationally flexible walls. At the same time they show the beneficial effect of soil inhomogeneity and that wave propagation in the underlying foundation layer may have an effect that cannot be simply accounted for with an appropriate rocking spring at the base.     

Static and dynamic response of massive caisson foundations with soil and interface nonlinearities—validation and results

The static, cyclic, and dynamic response of a massive caisson foundation embedded in nonlinear layered or inhomogeneous soil and loaded at its top is investigated. The caisson is supported against horizontal displacement and rotation by four types of inelastic springs and dashpots, described with the BWGG model that was developed in the preceding companion paper [Gerolymos N, Gazetas G. Development of winkler model for static and dynamic response of caisson foundations with soil and interface nonlinearities. Soil Dyn Earthq Eng, submitted companion paper]. The prediction of the model is satisfactorily compared with results from 3D-finite element analysis. Some experimental corroboration of the method is provided with the help of a 1/3-scale lateral load test that had been conducted in the field by EPRI. An illustrative example of a caisson embedded in linearly-inhomogeneous clay and subjected to static and dynamic loading is analysed. Characteristic results are presented highlighting the role of soil inelasticity and its interplay with the two dominant interface nonlinearities: separation (gapping) of the caisson shaft from the surrounding soil, and uplifting of the base from the underlying soil.     

Footings under seismic loading: Analysis and design issues with emphasis on bridge foundations

The paper provides state-of-the-art information on the following aspects of seismic analysis and design of spread footings supporting bridge piers: (1) obtaining the dynamic stiffness (“springs” and “dashpots”) of the foundation; (2) computing the kinematic response; (3) determining the conditions under which foundation–soil compliance must be incorporated in dynamic structural analysis; (4) assessing the importance of properly modeling the effect of embedment; (5) elucidating the conditions under which the effect of radiation damping is significant; (6) comparing the relative importance between kinematic and inertial response. The paper compiles an extensive set of graphs and tables for stiffness and damping in all modes of vibration (swaying, rocking, torsion), for a variety of soil conditions and foundation geometries. Simplified expressions for computing kinematic response (both in translation and rotation) are provided. Special issues such as presence of rock at shallow depths, the contribution of foundation sidewalls, soil inhomogeneity and inelasticity, are also discussed. The paper concludes with parametric studies on the seismic response of bridge bents on embedded footings in layered soil. Results are presented (in frequency and time domains) for accelerations and displacements of bridge and footing, while potential errors from some frequently employed simplifications are illustrated.     

Soil failure can be used for seismic protection of structures

A new seismic design philosophy is illuminated, taking advantage of soil “failure” to protect the superstructure. Instead of over-designing the foundation to ensure that the loading stemming from the structural inertia can be “safely” transmitted onto the soil (as with conventional capacity design), and then reinforce the superstructure to avoid collapse, why not do exactly the opposite by intentionally under-designing the foundation to act as a “safety valve” ? The need for this “reversal” stems from the uncertainty in predicting the actual earthquake motion, and the necessity of developing new more rational and economically efficient earthquake protection solutions. A simple but realistic bridge structure is used as an example to illustrate the effectiveness of the new approach. Two alternatives are compared : one complying with conventional capacity design, with over-designed foundation so that plastic “hinging” develops in the superstructure; the other following the new design philosophy, with under-designed foundation, “inviting” the plastic “hinge” into the soil. Static “pushover” analyses reveal that the ductility capacity of the new design concept is an order of magnitude larger than of the conventional design: the advantage of “utilising” progressive soil failure. The seismic performance of the two alternatives is investigated through nonlinear dynamic time history analyses, using an ensemble of 29 real accelerograms. It is shown that the performance of both alternatives is totally acceptable for moderate intensity earthquakes, not exceeding the design limits. For large intensity earthquakes, exceeding the design limits, the performance of the new design scheme is proven advantageous, not only avoiding collapse but hardly suffering any inelastic structural deformation. It may however experience increased residual settlement and rotation: a price to pay that must be properly assessed in design.     

Analysis of cut-and-cover tunnels against large tectonic deformation

Tunnels are believed to be rather “insensitive” to earthquakes. Although a number of case histories seem to favor such an argument, failures and collapses of underground structures in the earthquakes of Kobe (1995), Düzce–Bolu (1999), and Taiwan (1999) have shown that there are exceptions to this “rule”. Among them: the case of tunnels crossed by fault rupture. This paper presents the analysis and design of two highway cut-and-cover tunnels in Greece against large tectonic dislocation from a normal fault. The analysis, conducted with finite elements, places particular emphasis on realistically modeling the tunnel-soil interface. Soil behavior is modeled thorough an elastoplastic constitutive model with isotropic strain softening, which has been extensively validated through successful predictions of centrifuge model tests. A primary conclusion emerging from the paper is that the design of cut-and-cover structures against large tectonic deformation is quite feasible. It is shown that the rupture path is strongly affected by the presence of the tunnel, leading to development of beneficial stress-relieving phenomena such as diversion, bifurcation, and diffusion. The tunnel may be subjected either to hogging deformation when the rupture emerges close to its hanging-wall edge, or to sagging deformation when the rupture is near its footwall edge. Paradoxically, the maximum stressing is not always attained with the maximum imposed dislocation. Therefore, the design should be performed on the basis of design envelopes of the internal forces, with respect to the location of the fault rupture and the magnitude of dislocation. Although this study was prompted by the needs of a specific project, the method of analysis, the design concepts, and many of the conclusions are sufficiently general to merit wider application.     

Soil bentonite wall protects foundation from thrust faulting: analyses and experiment

When seismic thrust faults emerge on the ground surface,they are particularly damaging to buildings,bridges and lifelines that lie on the rupture path.To protect a structure founded on a rigid raft,a thick diaphragm-type soil bentonite wall(SBW) is installed in front of and near the foundation,at sufficient depth to intercept the propagating fault rupture.Extensive numerical analyses,verified against reduced–scale(1 g) split box physical model tests,reveal that such a wall,thanks to its high deformability and low shear resistance,"absorbs" the compressive thrust of the fault and forces the rupture to deviate upwards along its length.As a consequence,the foundation is left essentially intact.The effectiveness of SBW is demonstrated to depend on the exact location of the emerging fault and the magnitude of the fault offset.When the latter is large,the unprotected foundation experiences intolerable rigid-body rotation even if the foundation structural distress is not substantial.     

Behaviour of deep immersed tunnel under combined normal fault rupture deformation and subsequent seismic shaking

Immersed tunnels are particularly sensitive to tensile and compressive deformations such as those imposed by a normal seismogenic fault rupturing underneath, and those generated by the dynamic response due to seismic waves. The paper investigates the response of a future 70 m deep immersed tunnel to the consecutive action of a major normal fault rupturing in an earthquake occurring in the basement rock underneath the tunnel, and a subsequent strong excitation from a different large-magnitude seismic event that may occur years later. Non-linear finite elements model the quasi-static fault rupture propagation through the thick soil deposit overlying the bedrock and the ensuing interaction of the rupture with the immersed tunnel. It is shown that despite imposed bedrock offset of 2 m, net tension or excessive compression between tunnel segments could be avoided with a suitable design of the joint gaskets. Then, the already deformed (“injured”) structure is subjected to strong asynchronous seismic shaking. The thick-walled tunnel is modelled as a 3-D massive flexural beam connected to the soil through properly-calibrated nonlinear interaction springs and dashpots, the supports of which are subjected to the free-field acceleration time histories. The latter, obtained with 1-D wave propagation analysis, are then modified to account for wave passage effects. The joints between tunnel segments are modeled with special non-linear hyper-elastic elements, properly accounting for their 7-bar longitudinal hydrostatic pre-stressing. Sliding is captured with special gap elements. The effect of segment length and joint properties is explored parametrically. A fascinating conclusion emerges in all analysed cases for the joints between segments that were differentially deformed after the quasi-static fault rupture: upon subsequent very strong seismic shaking, overstressed joints de-compress and understressed joints re-compress—a “healing” process that leads to a more uniform deformation profile along the tunnel. This is particularly beneficial for the precariously de-compressed joint gaskets. Hence, the safety of the immersed tunnel improves with “subsequent” strong seismic shaking!     

Simplified approach for design of raft foundations against fault rupture. Part Ⅱ： soil-structure interaction

This is the second paper of two, which describe the results of an integrated research effort to develop a four-step simplified approach for design of raft foundations against dip-slip （normal and thrust） fault rupture. The first two steps dealing with fault rupture propagation in the free-field were presented in the companion paper. This paper develops an approximate analytical method to analyze soil-foundation-structure interaction （SFSI）, involving two additional phenomena： （i） fault rupture diversion （Step 3）; and （ii） modification of the vertical displacement profile （Step 4）. For the first phenomenon （Step 3）, an approximate energy-based approach is developed to estimate the diversion of a fault rupture due to presence of a raft foundation. The normalized critical load for complete diversion is shown to be a function of soil strength, coefficient of earth pressure at rest, bedrock depth, and the horizontal position of the foundation relative to the outcropping fault rupture. For the second phenomenon （Step 4）, a heuristic approach is proposed, which ＂scans＂ through possible equilibrium positions to detect the one that best satisfies force and moment equilibrium. Thus, we account for the strong geometric nonlinearities that govern this interaction, such as uplifting and second order （P-△） effects. Comparisons with centrifuge-validated finite element analyses demonstrate the efficacy of the method. Its simplicity makes possible its utilization for preliminary design.     

Simplified approach for design of raft foundations against fault rupture. Part Ⅰ: free-field

Over the past few decades, earthquake engineering research mainly focused on the effects of strong seismicshaking. After the 1999 earthquakes in Turkey and Taiwan, and thanks to numerous cases where fault rupture causedsubstantial damage to structures, the importance of faulting-induced deformation has re-emerged. This paper, along withits companion (Part Ⅱ), exploits parametric results of finite element analyses and centrifuge model testing in developing afour-step semi-analytical approach for analysis of dip-slip (normal and thrust) fault rupture propagation through sand, itsemergence on the ground surface, and its interaction with raft foundations. The present paper (Part Ⅰ) focuses on the effectsof faulting in the absence of a structure (i.e., in the free-field). The semi-analytical approach comprises two-steps: the firstdeals with the rupture path and the estimation of the location of fault outcropping, and the second with the tectonically-induced displacement profile at the ground surface. In both cases, simple mechanical analogues are used to derive simplifiedsemi-analytical expressions. Centrifuge model test data, in combination with parametric results from nonlinear finite elementanalyses, are utilized for model calibration. The derived semi-analytical expressions are shown to compare reasonably wellwith more rigorous experimental and theoretical data, thus providing a useful tool for a first estimation of near-fault seismichazard.