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The objective of this study was to investigate the liquefaction response of soil using the spatial variability of the shear modulus by considering different values of the coefficient of variation (COV) and the horizontal scale of fluctuation (SOF). For this purpose, a Monte Carlo simulation, combining the digital generation of a non-Gaussian random field with finite difference analyses, was utilized. Parametric studies were performed from the perspectives of the liquefaction area, excess pore water pressure (EPWP), and displacement at the ground surface. We found that a larger COV of the soil shear modulus was correlated with a slower reduction of liquefaction area and a lower EPWP ratio. To explain the influence from the perspective of the spatial distribution characteristics of the shear modulus, a deterministic model test was carried out. Additionally, it was found that the displacement history and the differential settlement at the end of shaking were regularly affected by the COV and the horizontal SOF, especially for large COV and horizontal SOF.

To improve the understanding of the near-field soil and topographic amplification effects, an analytical solution by the authors for the scattering of plane SH waves by a radially inhomogeneous semi-cylindrical valley is extended to the case of a line source of cylindrical SH waves. Upon confirmation of its accuracy with past exact solutions for a homogeneous and an inhomogeneous semi-cylindrical valley under far-field plane SH waves, the extended solution is used to calculate the ground motion amplification factors for both the homogeneous and inhomogeneous valleys subjected to near-field waves. A comprehensive parametric study is conducted with respect to the location of the wave source, the dimensionless frequency of the incident waves, and the inhomogeneity degree of the covering soil layer. It is found that more amplifications and reductions of ground motions will occur within a certain range in and around the valley as the sources are located further. Consistent with the far-field case, it is confirmed that an increase of the degree of inhomogeneity of the covering soil layer generally amplifies the ground motions significantly.

The kinematic approach of limit analysis is explored in three-dimensional face stability of large-diameter tunnels in soils with linearly increasing undrained strength with depth. Due to the slurry density by a shield machine, the support pressure is not uniformly distributed on the face. Such a non-uniform distribution cannot be ignored, especially for the large-diameter shield tunnels. This paper includes it into the stability analysis of the tunnel face subjected to local and global failures. The failure mechanism with a spherical cap is adopted to obtain the least upper-bound solutions of local stability of the tunnel face. To evaluate its global stability, a continuous velocity field with a toric envelope is employed and yields the critical pressures on tunnel face against collapse and blow-out. The calculated results are compared with the solutions derived from other well-established methods for verification of the presented approach. An approximation formula based on the derived upper-bound solutions, is given to directly calculate the necessary collapse and blow-out pressures, which can be used for preliminary design in practice. An example is given to illustrate its convenient use.

The aim of this paper is to determine the critical supporting pressure on the circular face of an advancing tunnel in undrained clay in which undrained strength increases linearly with depth. Based on the kinematic approach of limit analysis, a continuous velocity field with a toric envelope is adopted to yield upper bounds of the face pressure for both collapse and blow-out. Combining with a closed-form expression describing the overall velocity field, an optimisation procedure is carried out to find the lowest upper-bound solutions. The calculated results are presented in terms of a dimensionless coefficient N (called the stability number) and then stability charts for use are produced. Alternatively, an approximation formula is given to estimate easily the collapse and blow-out pressure in practice.

The conventional pseudo-static approach often neglects the effect of the vertical seismic acceleration on the stability of a slope, but some analyses under plane-strain (2D) conditions show a significant effect on the slope stability. The purpose of this study is to investigate the effect of the vertical acceleration on the safety of three-dimensional (3D) slopes. In the strict framework of limit analysis, a 3D kinematically admissible rotational failure mechanism is adopted here for 3D homogeneous slopes in frictional/cohesive soils. A set of stability charts is presented in a wide range of parameters for 3D slopes under combined horizontal and vertical seismic loading conditions. Accounting for the effects of the vertical seismic acceleration, the difference in safety factors for 3D slopes can exceed 10%, which will significantly overestimate the safety of the 3D slopes.

A method of simulating spatially varying ground motions in V-shaped symmetric canyon is presented. The topographic amplification effect is taken into account by considering a 2-dimension wave propagation model. Two approaches are developed to simulate spatially varying ground motions. First, the spatially varying ground motions are simulated by using the power spectral density and an empirical coherency loss function. Second, the spatially varying ground motions are simulated by using given ground motions and an empirical coherency loss function. These two proposed methods are validated by comparing statistical characteristics of the synthetic motions with target theoretical models.

In dynamic analyses of important structures, seismic input may be defined in the form of time series. It is required that the response spectrum of this input time series be compatible with a specified target response spectrum. Time domain spectral matching, which is used to generate spectrum compatible acceleration time series, is investigated in some detail. First, a new, improved wavelet is presented, and the new adjustment wavelet can prevent drifts in the resulting velocity and displacement time series without applying a baseline correction. Next, the analytical solution of the matrix accounting for the cross correlation of each wavelet is given in order to ensure the speed of the matching procedure. Finally, some aspects, such as the reduction factors and the matching order, are discussed to ensure the stability and efficiency of the matching procedure. Accordingly, the characteristics of the matching procedure are illustrated by numerical examples.

Pullout resistance is one of the most important factors governing seismic stability of reinforced soil walls. The previous studies on the seismic stability of reinforced soil walls have focused on the axial resistance of the reinforcement against the pullout. However, the kinematics of failure causes the reinforcement to be subjected to the oblique pullout force and bending deformation. Considering the kinematics of failure and bending deformation of the reinforcement, this paper presents a pseudo-static seismic analysis for evaluating the pullout resistance of reinforcements in soil wall subjected to oblique pullout forces. A modified horizontal slice method (HSM) and Pasternak model are used to calculate the required force to maintain the stability of the reinforced soil wall and shear resistance mobilized in the reinforcements, respectively. In addition, this paper studies the effect of various parameters on the pullout resistance of the reinforcements in soil wall subjected to seismic loads. Results of this study are compared with the published data and their differences are analyzed in detail.

The spectral representation method (SRM) is widely used when simulating spatially variable ground motions. It has mainly two formulas, i.e., the random amplitudes and the random phases formulas. There exist three methods for decomposing the cross spectral density matrix: Cholesky decomposition, eigen decomposition, and root decomposition. Therefore, there are six forms with respect to the different combinations of the simulation formulas and the decomposition methods. To provide researchers and engineers with the guidance on choosing simulation method, the six forms are systematically investigated from five aspects: the power intensity, response spectra, and stochastic error of auto/cross spectral density, Fourier spectra, and difference indexes for Fourier amplitudes and phases. Finally, we give the following advice: the characteristics of the ground motions simulated by the random amplitudes formula are independent of the decomposition method, while the characteristics of the ground motions simulated by...

A three-dimensional (3D) kinematically admissible rotational failure mechanism is extended from toe failure to include face failure and base failure for homogeneous slopes in both purely cohesive and frictional/cohesive soils. In the strict framework of limit analysis, an analytical approach is derived to obtain the upper bounds on slope stability and the corresponding type of the critical failure mechanism. Compared with the available results from the finite-element limit-analysis method, the 3D rotational failure mechanisms give the best estimate on the upper bound. A set of stability charts is presented in a wide range of parameters for 3D homogeneous slopes under both static and pseudostatic seismic loading conditions. This set is useful in assessing the safety of the 3D homogeneous slopes in practical applications.

This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetrical V-shaped canyon is divided into two sub-regions by using a circular-arc auxiliary boundary. The two sub-regions are represented by global and local cylindrical coordinate systems, respectively. In each coordinate system, the wave field satisfying the Helmholtz equation is represented by the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then, the two wave fields are described in the local coordinate system using the Graf addition theorem. Finally, the unknown coefficients are sought by satisfying the continuity conditions of the auxiliary boundary. To consider the phase characteristics of the wave scattering, a parametric analysis is carried out in the time domain by assuming an incident signal of the Ricker type. Surface and subsurface transient responses demonstrate the characteristics and mechanisms of wave propagating and scattering.

A new model to simulate spatially correlated earthquake ground motions is developed. In the model, the main factors that characterize three distinct effects of spatial variability, namely, the incoherency effect, the wave-passage effect and the site-response effect, are taken into account, and corresponding terms/parameters are incorporated into the well known model of uniform ground motions. Some of these terms/parameters can be determined by the root operation, and others can be calculated directly. The proposed model is first verified theoretically, and examples of ground motion simulations are provided as a further illustration. It is proven that the ensemble expected value and the ensemble auto-/cross-spectral density functions of the simulated ground motions are identical to the target spectral density functions. The proposed model can also be used to simulate other correlated stochastic processes, such as wave and wind loads.

An analytical solution for diffraction of both plane and cylindrical SH waves induced by a horseshoe shaped cavity with an inverted arch is presented in this paper. The geometry of the cavity is assumed to be composed of two circular arcs. By introducing an auxiliary boundary, the whole physical region is divided into two computational regions. The scattered wavefield in the open region and the standing wavefield in the enclosed region are presented by means of the wave function expansion method. Both of the wavefields are given in terms of the wave function series with unknown coefficients. By applying the Graf’s addition formula, two systems of equations for seeking the unknowns are derived by taking advantage of the boundary conditions based on the region-matching strategy. The problem of wave scattering is finally solved after seeking the solutions of the two systems of equations through standard matrix techniques. Then the effects of the excitation frequency, the cavity embedment depth and cavity geometry are discussed. The differences in terms of ground motions under different excitations and the influence of source location under cylindrical waves are also examined.