D. V. Griffiths

Influence of Spatial Variability on Slope Reliability Using 2-D Random Fields

The paper investigates the probability of failure of slopes using both traditional and more advanced probabilistic analysis tools. The advanced method, called the random finite-element method, uses elastoplasticity in a finite-element model combined with random field theory in a Monte-Carlo framework. The traditional method, called the first-order reliability method, computes a reliability index which is the shortest distance (in units of directional equivalent standard deviations) from the equivalent mean-value point to the limit state surface and estimates the probability of failure from the reliability index. Numerical results show that simplified probabilistic analyses in which spatial variability of soil properties is not properly accounted for, can lead to unconservative estimates of the probability of failure if the coefficient of variation of the shear strength parameters exceeds a critical value. The influences of slope inclination, factor of safety (based on mean strength values), and cross correlation between strength parameters on this critical value have been investigated by parametric studies in this paper. The results indicate when probabilistic approaches, which do not model spatial variation, may lead to unconservative estimates of slope failure probability and when more advanced probabilistic methods are warranted.

Probabilistic Settlement Analysis by Stochastic and Random Finite-Element Methods

The paper discusses finite element models for predicting the elastic settlement of a strip footing on a variable soil. The paper then goes on to compare results obtained in a probabilistic settlement analysis using a stochastic finite element method based on first order second moment approximations, with the random finite element method based on generation of random fields combined with Monte Carlo simulations. The paper highlights the deficiencies of probabilistic methods that are unable to properly account for spatial correlation.

Statistics of block conductivity through a simple bounded stochastic medium

A Monte Carlo approach is employed to estimate the distribution of an equivalent conductivity measure, the block conductivity, which characterizes the total flow rate through a two-dimensional bounded domain and which is itself a random variable. Chi-square goodness-of-fit tests indicate that the lognormal distribution is an appropriate choice for the block conductivity distribution. For square domains, the mean and variance of the block conductivity are seen to be closely approximated using the statistics of local averages of log conductivity.

Load and resistance factor design of shallow foundations against bearing failure

Shallow foundation designs are typically governed either by settlement, a serviceability limit state, or by bearing capacity, an ultimate limit state. While geotechnical engineers have been designing against these limit states for over half a century, it is only recently that they have begun to migrate towards reliability-based designs. At the moment, reliability-based design codes are generally derived through calibration with traditional working stress designs. To take advantage of the full potential of reliability-based design the profession must go beyond calibration and take geotechnical uncertainties into account in a rational fashion. This paper proposes a load and resistance factor design (LRFD) approach for the bearing capacity design of a strip footing, using load factors as specified by structural codes. The resistance factors required to achieve an acceptable failure probability are estimated as a function of the spatial variability of the soil and by the level of “understanding” of the soil p...

Reliability›Based Deep Foundation Design

Modern geotechnical design codes are migrating towards Load and Resistance Factor Design (LRFD) methodologies. The Danish geotechnical code has been based on LRFD for several decades, but more recently the Eurocode and the Australian Standards have turned in this direction. Where the geotechnical system supports a structure, the load factors are generally determined by the structural codes. The geotechnical resistance factors, typically determined by calibration with traditional working stress (or allowable stress) design, have yet to be clearly dened in geotechnical design codes. Research into the reliability of geotechnical systems is needed in order for resistance factors to be determined. This paper presents the results of a preliminary study into the effect of a soil’s spatial variability on the settlement and ultimate load statistics of a pile. The results are used to provide recommendations on approaches to reliability›based deep foundation design at the serviceability and ultimate limit states.

On the reliability of earth slopes in three dimensions

The paper investigates the probability of failure of two-dimensional and three-dimensional slopes using the random finite-element method (RFEM). In this context, RFEM combines elastoplastic finite-element algorithms with random field theory in a Monte Carlo framework. Full account is taken of local averaging and variance reduction over each element, and an exponentially decaying (Markov) spatial correlation function is incorporated. It is found that two-dimensional probabilistic analysis, which implicitly assumes perfect spatial correlation in the out-of-plane direction, may underestimate the probability of failure of slopes.

Influence of viscous damping in the dynamic analysis of an earth dam using simple constitutive models

Abstract The results of dynamic non-linear two-dimensional finite element analyses of the Long Valley Dam in the Mammoth Lake area of California subjected to a real measured earthquake are presented. A simple elastic-perfectly plastic constitutive soil model is used to describe the stress-strain response of the soil and Rayleigh damping (i.e. viscous damping) is applied to account for the lack of hysteretic damping. The effect of the initial stress condition and the Rayleigh damping ratio are discussed, and the results of the analysis are compared to the measured response of the dam and to results presented by previous researchers. Good agreement is obtained in the up/downstream direction, but as experienced by previous researchers, the correct vertical frequency range is not achieved. The limitations of using viscous damping combined with simple constitutive models when studying the dynamic behaviour of real earth dams are shown.

Numerical Modeling of Pore Pressure Influence on Fracture Evolution in Brittle Heterogeneous Rocks

Rock is a heterogeneous geological material. When rock is subjected to internal hydraulic pressure and external mechanical loading, the fluid flow properties will be altered by closing, opening, or other interaction of pre-existing weaknesses or by induced new fractures. Meanwhile, the pore pressure can influence the fracture behavior on both a local and global scale. A finite element model that can consider the coupled effects of seepage, damage and stress field in heterogeneous rock is described. First, two series of numerical tests in relatively homogeneous and heterogeneous rocks were performed to investigate the influence of pore pressure magnitude and gradient on initiation and propagation of tensile fractures. Second, to examine the initiation of hydraulic fractures and their subsequent propagation, a series of numerical simulations of the behavior of two injection holes inside a saturated rock mass are carried out. The rock is subjected to different initial in situ stress ratios and to an internal injection (pore) pressure at the two injection holes. Numerically, simulated results indicate that tensile fracture is strongly influenced by both pore pressure magnitude and pore pressure gradient. In addition, the heterogeneity of rock, the initial in situ stress ratio (K), the distance between two injection holes, and the difference of the pore pressure in the two injection holes all play important roles in the initiation and propagation of hydraulic fractures. At relatively close spacing and when the two principal stresses are of similar magnitude, the proximity of adjacent injection holes can cause fracturing to occur in a direction perpendicular to the maximum principal stress.

Enhanced visualization of failure mechanisms by finite elements

Abstract The finite element method, in conjunction with elasto-plastic constitutive laws, is able to give accurate estimates of collapse loads in geotechnical problems. The mechanisms of failure produced by these analyses, however, are often diffuse and poorly defined, as compared with those assumed in classical limit analysis techniques. This paper describes two methods for improving their visualization. It is shown that by introducing a small degree of post-peak material softening into the constitutive law, a considerably more localized mechanism is achieved. In contrast to previous attempts to “trigger” mechanisms whereby select elements were weakened, all elements are given the same constitutive law in the present approach. A second method involves a re-gridding approach, together with the use of incremental displacements. In this approach, the displacement field is enhanced by interpolating between the nodal values.

Some theoretical observations on conical failure criteria in principal stress space

Abstract The properties of the conical failure criteria that lie just inside and just outside the Mohr-Coulomb surface are discussed. Expressions are developed for the maximum stress ratio predicted by these surfaces as a function of the angular stress invariant. For plane strain problems, assuming elastoplastic behaviour, the effect of Poissons ratio and the dilation angle on the stress paths and failure loads have been expressed in a closed-form solution. Finally, the expressions are confirmed using finite element analysis of a simple boundary value problem.