Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Rock engineering is highly susceptible to cyclic loads resulting from earthquakes, quarrying or rockbursts. Acquiring the fatigue properties and failure mechanism of rocks is pivotal for long-term stability assessment of rock engineering structures. So far, significant progress has been gained on the mechanical characteristics of rocks subjected to cyclic loading. For providing a global insight of typical results and main features of rocks under cyclic loading conditions, this study comprehensively reviews the state-of-the-art of deformation and failure mechanism and fatigue constitutive relationship of rocks subjected to cyclic loading in the past 60 years. Firstly, cyclic tests on rocks are classified into different types based on loading paths, loading parameters, loading types and environment conditions. Secondly, representative results are summarized and highlighted in terms of the fatigue response of rocks, including the deformation degradation, energy dissipation, damage evolution and failure characteristics; both laboratory testing and numerical results are presented, and various measurement techniques such as X-ray micro-computed tomography (micro-CT) and digital image correlation (DIC) are considered. Thirdly, the influences of cyclic loads on the mechanical characteristics of rocks are discussed, including the cyclic stress, frequency, amplitude and waveform. Subsequently, constitutive relationships for rocks subjected to cyclic loading are outlined, in which typical fatigue constitutive models are compared and analyzed, regarding the elastoplastic model, the internal variable model, the energy-based damage model and the discrete element-based model. Finally, some ambiguous questions and prospective research are interpreted and discussed.

A review of experimental and theoretical research on the deformation and failure behavior of rocks subjected to cyclic loading

Change in mechanical properties of rocks under static loading has been widely studied and documented. However, the response of rocks to cyclic loads is still a much-debated topic. Fatigue is the phenomenon when rocks under cyclic loading fail at much lower strength as compared to those subjected to the monotonic loading conditions. A few selected cored granodiorite and sandstone specimens have been subjected to uniaxial cyclic compression tests to obtain the unconfined fatigue strength and life. This study seeks to examine the effects of cyclic loading conditions, loading amplitude and applied stress level on the fatigue life of sandstone, as a soft rock, and granodiorite, as a hard rock, under uniaxial compression test. One aim of this study is to determine which of the loading conditions has a stronger effect on rock fatigue response. The fatigue response of hard rocks and soft rocks is also compared. It is shown that the loading amplitude is the most important factor affecting the cyclic response of the tested rocks. The more the loading amplitude, the shorter the fatigue life, and the greater the strength degradation. The granodiorite specimens showed more strength degradation compared to the sandstone specimens when subjected to cyclic loading. It is shown that failure modes of specimens under cyclic loadings are different from those under static loadings. More local cracks were observed under cyclic loadings especially for granodiorite rock specimens.

Strength degradation of sandstone and granodiorite under uniaxial cyclic loading

/pdf/volumetric-deformation-and-damage-evolution-of-tibet-27pu2gmi.pdf

Volumetric deformation and damage evolution of Tibet interbedded skarn under multistage constant-amplitude-cyclic loading

Correlation between the rockburst proneness and friction characteristics of rock materials and a new method for rockburst proneness prediction: Field demonstration

The fatigue test for rock salt is conducted under different stress amplitudes, loading frequencies, confining pressures and loading rates, from which the evaluation rule of the dissipated energy is revealed and analysed. The evolution of energy dissipation under fatigue loading is divided into three stages: the initial stage, the second stage and the acceleration stage. In the second stage, the energy dissipation per cycle remains stable and shows an exponential relation with the stress amplitude; the failure dissipated energy only depends on the mechanical behaviour of the rock salt and confining pressure, but it is immune to the loading conditions. The energy dissipation of fatigued rock salt is discussed, and a novel model for fatigue life prediction is proposed on the basis of energy dissipation. A simple model for evolution of the accumulative dissipated energy is established. Its prediction results are compared with the test results, and the proposed model is validated.

Energy Dissipation-Based Method for Fatigue Life Prediction of Rock Salt

The constant mi is a fundamental parameter required in the Hoek–Brown (H–B) failure criterion for estimating rock strength. Triaxial tests for the calculation of this constant are time-consuming and expensive. In this paper, a new perspective is presented for the physical meaning of the parameter mi of the H–B model in consideration of the contact friction coefficient. A correlation between the contact friction coefficient and mi is established using published data. A practical approach is proposed to determine the value of the parameter mi. In addition, previously proposed methods of estimating the residual strength of rock are reviewed. A novel method based on the H–B failure criterion is established to predict the residual strength of rock. The single model parameter used in the new model controls the residual strength nonlinearity. The strengths predicted by the proposed method for limestone, granite, slate, and sandstone are in good agreement with those measured during laboratory tests. The corresponding errors are within a range of 15%. This method is applied to an actual rock mass around a tunnel in the Hanjiang to Weihe River Project of China.

A New Perspective on the Constant mi of the Hoek–Brown Failure Criterion and a New Model for Determining the Residual Strength of Rock

Rock strength parameters are substantially impacted by porosity. This paper proposes a new model for presenting the relationship between porosity and the ratio of the unconfined compressive strength to the tensile strength of rock. The correlation between porosity and the constant mi of the Hoek–Brown (H–B) criterion is studied. To consider the effect of porosity on the rock strength ratio, the H–B criterion is modified by incorporating porosity instead of the H–B constants mi and s. A series of uniaxial, triaxial and Brazilian tests are conducted on various types of rocks (sedimentary, metamorphic and magmatic rocks) to study the effect of porosity on rock strength characteristics. The modified H–B criterion provides a good representation of the effect of porosity on the failure envelopes of rock. The modified criterion can be used to estimate the porosity and strength parameters of rock.

Correlation Between the Constant mi of Hoek–Brown Criterion and Porosity of Intact Rock

The constant m i in the Hoek-Brown (H-B) criterion is a fundamental parameter required for determining the compressive strength of rock. In this paper, drilling parameters provide a new basis for determining the constant m i . An analytical relationship between the drilling parameters and constant m i is established in consideration of the contact response between the drilling bit and the cut rock in the crushed zone. New models are developed to predict the triaxial compressive strength ( TCS ), internal friction angle φ and cohesion c of rock. Drilling tests are carried out on 6 rock types to study the correlation between φ and m i . A comparison between the predicted values of rock mechanical properties and the measured values from the laboratory is performed to verify the accuracy of the proposed model (yielding an error less than 10%). The TCS s and constant m i values of fifteen rocks are cited to validate the accuracy of the proposed model. The result shows that the proposed model predicts the TCS and constant m i within a maximum error of 20%. The method can be conveniently applied to the rock mechanical properties. 

Determination of the constant m in the Hoek-Brown criterion of rock based on drilling parameters

Field evaluation of the strength properties of jointed rock masses is a challenging task in geotechnical engineering. Typically, laboratory tests using small jointed specimens have difficu...

Deep Convolutional Neural Network-Based Method for Strength Parameter Prediction of Jointed Rock Mass Using Drilling Logging Data

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