Rafael Jimenez

A Simplified Failure Criterion for Intact Rocks Based on Rock Type and Uniaxial Compressive Strength

The uniaxial compressive strength (UCS) of intact rock, which can be estimated using relatively straightforward and cost-effective techniques, is one of the most practical rock properties used in rock engineering. Thus, constitutive laws to represent the strength and behavior of (intact) rock frequently use it, along with additional intrinsic rock properties. Although triaxial tests can be employed to obtain best-fit failure criterion parameters that provide best strength predictions, they are more expensive and require time-consuming procedures; as a consequence, they are often not readily available at early stages of a project. Based on the analysis of an extensive triaxial test database for intact rocks, we propose a simplified empirical failure criterion in which rock strength at failure is expressed in terms of confining stress and UCS, with a new parameter which can be directly estimated from the UCS for a specified rock type in the absence of triaxial test data. Performance of the proposed failure criterion is then tested for validation against experimental data for eight rock types. The results show that strengths of intact rock estimated by the proposed failure criterion are in good agreement with experimental test data, with small discrepancies between estimated and measurements strengths. Therefore, the proposed criterion can be useful for preliminary (triaxial) strength estimation of intact rocks when triaxial tests data are not available.

Reliability Analysis of Circular Tunnel Face Stability Obeying Hoek–Brown Failure Criterion Considering Different Distribution Types and Correlation Structures

AbstractA reliability analysis is presented of a circular tunnel face driven by a pressurized shield in a highly fractured Hoek–Brown (HB) rock mass. A limit analysis approach is employed to define a limit state function (LSF) based on an advanced rotational mechanism. The objective is to analyze how different reliability methods, different assumptions about distribution types and correlation structures of the random variables, and different tunnel sizes and support pressures influence the computed reliability results. Results indicate that the reliability method has a limited influence on reliability results, hence suggesting that the LSF is not highly nonlinear and that a computationally efficient method can be employed; and that all random variables under consideration are resistance variables, with their assumed distribution types and correlation structures having a significant effect on the reliability results. This emphasizes the importance of an adequate characterization of geotechnical uncertainti...

A Simple Genetic Algorithm for Calibration of Stochastic Rock Discontinuity Networks

We present a novel approach for calibration of stochastic discontinuity network parameters based on genetic algorithms (GAs). To validate the approach, examples of application of the method to cases with known parameters of the original Poisson discontinuity network are presented. Parameters of the model are encoded as chromosomes using a binary representation, and such chromosomes evolve as successive generations of a randomly generated initial population, subjected to GA operations of selection, crossover and mutation. Such back-calculated parameters are employed to make assessments about the inference capabilities of the model using different objective functions with different probabilities of crossover and mutation. Results show that the predictive capabilities of GAs significantly depend on the type of objective function considered; and they also show that the calibration capabilities of the genetic algorithm can be acceptable for practical engineering applications, since in most cases they can be expected to provide parameter estimates with relatively small errors for those parameters of the network (such as intensity and mean size of discontinuities) that have the strongest influence on many engineering applications.

Statistical mechanics as guidance for particle‐based computational methods

Purpose – The purpose of this paper is to show that there are some underlying principles of granular media that can be derived from statistical mechanics and that could be useful when considered in the context of computer simulations.Design/methodology/approach – The fundamentals of statistical mechanics are presented and they are revised in order to set up a suitable approach for jammed static granular media. After a conceptual discussion about the entropy of granular matter, some specific statistical mechanics approaches that have been used for granular media are reviewed. Finally, a numerical simulation, conducted using an open source molecular dynamics code, is included as an illustrative example.Findings – It is shown qualitatively how statistical mechanics can be used to analytically compute the expected statistical distribution of some quantities in numerical simulations.Research limitations/implications – The computation of entropy from histograms and the establishment of the constraints of the en...

A genetic algorithm for slope stability analyses with concave slip surfaces using custom operators

Heuristic methods are popular tools to find critical slip surfaces in slope stability analyses. A new genetic algorithm (GA) is proposed in this work that has a standard structure but a novel encoding and generation of individuals with custom-designed operators for mutation and crossover that produce kinematically feasible slip surfaces with a high probability. In addition, new indices to assess the efficiency of operators in their search for the minimum factor of safety (FS) are proposed. The proposed GA is applied to traditional benchmark examples from the literature, as well as to a new practical example. Results show that the proposed GA is reliable, flexible and robust: it provides good minimum FS estimates that are not very sensitive to the number of nodes and that are very similar for different replications.

Analytical Bearing Capacity of Strip Footings in Weightless Materials with Power-Law Failure Criteria

AbstractSokolovskii’s method of characteristics is extended to provide analytical solutions for the ultimate load at the moment of plastic failure under plane-strain conditions of shallow strip foundations on weightless rigid-plastic media with a noncohesive power-law failure envelope. The formulation is made parametrically in terms of the instantaneous friction angle, and the key idea to obtain the bearing capacity is that information can be transmitted from the free surface (where external loads are known) to the contact plane of the foundation. The methodology can consider foundations adjacent to a slope, external surcharges at the free surface, and inclined loads (both on the slope and on the foundation). Sensitivity analyses illustrate the influence on bearing capacity of changes in the different geometrical parameters involved. An application example is presented and design plots are provided, and model predictions are compared with results of bearing capacity tests under low gravity.

Impact of the timestep in some molecular dynamics simulations on compression of granular systems

We conduct two-dimensional molecular dynamics simulations to study the statistical distribution of the force-moment (defined as stress multiplied by volume) of static granular packings under external isotropic compression. To that end, we generate packings by compressing initially ordered lattices using irregular, randomly generated, walls. Velocity-Verlet algorithm and linear spring-dashpot interactions are employed. With this specific method, the obtained statistical distributions of the force-moment are similar for different initial packings. However they depend on the timestep selection within a range of values. This shows that inadequate molecular dynamic simulations may provide different classes of solutions for the same physical process, and this could cause problems to validate theoretical approaches based on statistical mechanics.Graphical abstract

Extension of quasi-Newton approximation-based SORM for series system reliability analysis of geotechnical problems

The quasi-Newton approximation-based second-order reliability method is extended, through the incorporation of a linearization approach, to analyze the series system reliability of geotechnical problems. Two types of quasi-Newton approximations are applied to identify the design point and to compute the second-order probability of failure, respectively. The equivalent second-order reliability index is obtained using an approximation hyperplane for each limit state function. Then, the computed equivalent second order reliability indices can be employed, together with the corresponding unit direction vectors, to estimate the series system probability of failure using a linearization approach. Three geotechnical problems are employed to demonstrate the efficiency and accuracy of the suggested procedure, and advantages with respect to alternative computational tools are discussed.

Predicting the shear strength parameters of sandstone using genetic programming

The strength of intact rock is, together with the rock mass structure, probably the most important properties for rock engineering. To accurately estimate the Mohr–Coulomb (MC) strength parameters—cohesion c and angle of friction ϕ—of a rock, triaxial tests must be carried out at different stress levels so that a failure envelope can be obtained to be linearized. However, this involves a higher budget and time requirements that are often not available at the early stages of a project; thus faster and cheaper indirect methods have been developed as an alternative. In this paper, we use genetic programming (GP) to develop a predictive model to estimate the MC shear strength parameters of intact sandstone using other strength measures (the uniaxial compressive strength, UCS, and uniaxial tensile strength, UTS) under different stress conditions which shear failure takes place. The reliability of the proposed GP model is evaluated and compared with alternative linear regression models based on UCS or UTS only, and with the traditional triaxial-based approach. Results show that, although the triaxial method provides the better estimations, the proposed GP model has the best prediction performance in the absence of triaxial data, so that it can be used for practical strength estimations for intact sandstone at the early stage of projects or when triaxial test data are not available.

Bayesian Updating of Bearing Capacity Models for Individual Stone Columns

AbstractStone columns are often employed to increase the bearing capacity of soft clay. Many models—for instance based on plasticity theory or on statistical analysis of empirical data—have been pr...