Three-dimensional non-cohesive earthen dam breach model. Part 2: Validation and applications

Our proposed three-dimensional dam breach model is tested using one field test from the European Community funded IMPACT project. Results show that this three-dimensional model accurately predicts the peak breach discharge and final breach width for this case. It is shown that the three-dimensional model is capable of simulating the breaches that develop in different locations along a hypothetical long non-cohesive dam while accounting for variations in the natural valley topography, including symmetrical and asymmetrical settings. Our results show that both the breach location and reservoir shape have a significant effect on the peak breach discharge and the outflow hydrograph shape. Different inflow hydrographs were found not to significantly change the peak breach discharge rate for the hypothetical reservoir and spillway. Comparisons with laboratory and field dam breach tests and one historically breached dam show that the real shape of the breach channel during the breach process is successfully modeled.     

Three-dimensional liquefaction potential analysis using geostatistical interpolation

We applied three-dimensional geostatistical interpolation to evaluate the extent of liquefiable materials at two sites that liquefied during the 1994 Northridge Earthquake. The sites were the Balboa Blvd site and the Wynne Ave. site located in the alluvial San Fernando Valley. The estimated peak ground accelerations at the sites are 0.84 g (Balboa Blvd) and 0.51 g (Wynne Ave.). These sites were chosen because surface effects due to liquefaction were not predicted using available techniques based on thickness and depth of liquefiable layers (Ishihara [Ishihara K. Stability of natural deposits during earthquakes. Proceedings of the 11th international conference on soil mechanics and foundation engineering, vol. 1. Rotterdam, The Netherlands: A.A. Balkema; 1985. p. 321–76.]) and the Liquefaction Potential Index (Iwasaki et al. [Iwasaki T, Tatsuoka F, Tokida K, Yasuda S. A practical method for assessing soil liquefaction potential based on case studies at various sites in Japan. In: Proceedings of the second international conference on microzonation, San Francisco; 1978. p. 885–96.]). During the earthquake, both sites experienced surface effects including ground cracking and extension as a result of liquefaction. Foundations and buried utilities were damaged at both sites. The sites were investigated after the event by researchers with the United States Geologic Survey using standard penetration tests (SPT) and cone penetration tests. In this paper, liquefaction potential was estimated for each soil sample using results from SPTs according to the updated Seed and Idriss simplified procedure. The probability of liquefaction was estimated by applying an indicator transform to the results of the liquefaction potential calculation. We compared our results to detailed geologic mapping of the sites performed by other researchers. Using geostatistical interpolation to estimate the probability of liquefaction is a useful supplement to geologic evaluation of liquefaction potential. The geostatistical analysis provides an estimate of the continuous volume of liquefiable soil along with an assessment of confidence in an interpolation. The probability of liquefaction volumes compare well with those predicted using geologic interpretations.     

Three-dimensional time-harmonic Green's functions of saturated soil under buried loading

Three-dimensional time-harmonic response of a poroelastic half space subjected to an arbitrary buried loading is investigated. The analysis starts with the field equations in cylindrical coordinates based on Biot's general theory of poroelasticity. General solutions for the displacements are first derived using the Fourier expansions and Hankel integral transform with respect to the circumferential and radial coordinates, respectively. The transformed-domain solutions are obtained in explicit form. The physical-domain displacements and stress components are then obtained numerically by inverse integral transform. Comparisons illustrating the accuracy of the developed approach are made with existing solutions for an elastic half space, which is reduced directly from the general solution developed in the paper. Numerical results are presented for the displacements of a saturated soil subjected to a horizontal internal excitation.     

Spatial and temporal mapping of water in soil by magnetic resonance imaging

Experiments on model and real soil blocks designed to assess the feasibility of using magnetic resonance imaging for three-dimensional mapping of the time-varying spatial distribution of water in structured soils are reported. The results show that, notwithstanding inherent problems in imaging natural soils with a significant iron content, experimental parameters can be identified which allow satisfactory images to be obtained. Magnetic resonance imaging may therefore provide important information on soil structure and water movement in dual porosity soils, with attendant benefits for the calibration of models of non-Darcian flow in such soils.     

Three-dimensional analysis of embankments on soft soils incorporating vertical drains by finite element method

Three-dimensional behaviour of an embankment on soft soils incorporating vertical drains is analysed by a numerical model based on the finite element method. The model, which incorporates the Biot’s consolidation theory (coupled formulation of the flow and equilibrium equations) and constitutive relations simulated by the p–q–θ critical state model, is applied on both the embankment with vertical drains (three-dimensional analysis) and the same problem but without vertical drains (two-dimensional analysis). Special emphasis is given to the analysis, during and after the construction period, of the excess pore pressures, settlements, horizontal displacements and stress levels.     

Soil–structure interaction in the time domain using halfspace Green's functions

A time-domain formulation is proposed for the transient response analysis of general, three-dimensional structures resting on a homogeneous, elastic halfspace subjected to either external loads or seismic motions. The formulation consists of two parts: (a) the time domain formulation of the soil behaviour and (b) the coupling of the corresponding soil algorithms to the Finite Element Code ANSYS. As far as the structure is concerned, this coupling opens the way for the analysis of non-linear soil–structure interaction. The approach is based on halfspace Green's functions for displacements elicited by Heaviside time-dependent surface point loads. Hence, the spatial discretisation can be confined to the contact area between the foundation and the soil, i.e. no auxiliary grid beyond the foundation as for conventional boundary element formulations is required. The method is applied to analyse the dynamic response of a railway track due to a moving wheel set by demonstrating the influence of ‘through-the-soil coupling’.     

Three-dimensional analysis of gravity anomalies of sedimentary basins by polygonal prismatic model with a quadratic density function

The decrease of density contrast in sedimentary strata may be approximated by a quadratic function. A sedimentary basin may be considered as a number of horizontal polygonal prisms of finite thickness placed one over the other. Equations for the gravity anomaly of ann-sided polygon prism have been derived using a quadratic density function. A method has been developed for inversion of the gravity anomalies using a polygonal prismatic model. An analytical method has been employed for evaluating the necessary derivatives as the computing time by this method is much slower than by a numerical method. Approximate equations have been derived for rapid calculation of the anomalies and derivatives. Efficient computer programs have been developed for calculation of the anomalies and derivatives by an appropriate use of the exact and approximate equations. The depths to the polygon prisms constituting the basin are iteratively adjusted by minimizing the sum of the squares of the differences between the observed and calculated anomalies. These methods have been applied to analyze the Bouguer anomaly map of the Los Angeles basin, California.     

三维脆性破裂的拉应力判据

用线弹性断裂力学对连续介质中三维裂纹(K_Ⅲ≠0)破裂的拉应力断裂准则提出了补充性假说和相应的计算方法（第一主微分面定点法）。对于给定应力强度因子K_i（i=Ⅰ,Ⅱ,Ⅲ）的裂纹问题,从理论上给出了初始破裂面完整形式的解析表示或数值计算结果。推导结果是,三维拉张破裂的初始破裂面是以破裂点为顶点的广角锥面,跨在原始裂纹面的前缘,它的外缘为螺旋线,锥面的每一条母线都与过该线的第一主微分面重合。大量的这样的初始破裂面叠错密接,互不相交。推算的结果与已有的三锥破裂实验结果基本符合。把补充后的拉应力判据和最大拉应力理论相比较,发现在应力分量只保留奇异项的情况下,这两种判据是等价的;但如果对应力分量作零阶项修正,则两种判据只在三维(K_Ⅲ≠0)问题中等价,在二维(K_Ⅲ=0)问题中不完全等价。     

The three-dimensional dynamic displacement discontinuity method: Theory and applications

A boundary element technique has been developed for solving three-dimensional elastodynamic problems in rock mechanics, such as joint slip and the sudden advance of excavations. Both implicit and explicit versions of the technique have been implemented. Comparisons of accuracy and computational efficiency are made for a simple verification problem. Examples in which the technique has been used to investigate the dynamic response of supported and unsupported excavations in tabular orebodies are presented.     

日本俯冲带应力产生与传播的数值模拟

用三维有限元模拟了日本地冲带，分析了板块推力、板块拉力、动态闭锁断层和解耦板间地震对上覆板块内部应力状态的贡献，表明大洋板块推力是海沟。岛弧地区挤压应力的主要来源，这种应力仅有小部分传播到上覆板块内部，软流圈的蠕变能促进这个应力传播过程使岛弧区的应力增大，由密度差异引起的板块拉力产生了分散的挤压应力和拉张应力。断层闭锁导致应力局部集中，板间地震的断层错动只对破裂附近小范围的应力状态产生影响