Seismic bearing capacity of strip footings on rock masses using the Hoeke Brown failure criterion

In this paper,the bearing capacity of strip footings on rock masses has been studied in the seismic case.The stress characteristics or slip line method was used for analysis.The problem was analyzed in the plane strain condition using the Hoeke Brown failure criterion.First,the equilibrium equations along the stress characteristics were obtained and the rock failure criterion was applied.Then,the equations were solved using the finite difference method.A computer code has been provided for analysis.Given the footing and rock parameters,the code can calculate the stress characteristics network and obtain the stress distribution under the footing.The seismic effects have been applied as the horizontal and vertical pseudo-static coefficients.The results of this paper are very close to those of the other studies.The seismic bearing capacity of weightless rock masses can be obtained using the proposed equations and graphs without calculating the whole stress characteristics network.

Numerical simulation study of the failure evolution process and failure mode of surrounding rock in deep soft rock roadways

Based on the safety coefficient method,which assigns rock failure criteria to calculate the rock mass unit,the safety coefficient contour of surrounding rock is plotted to judge the distribution form of the fractured zone in the roadway.This will provide the basis numerical simulation to calculate the surrounding rock fractured zone in a roadway.Using the single factor and multi-factor orthogonal test method,the evolution law of roadway surrounding rock displacements,plastic zone and stress distribution under different conditions is studied.It reveals the roadway surrounding rock burst evolution process,and obtains five kinds of failure modes in deep soft rock roadway.Using the fuzzy mathematics clustering analysis method,the deep soft surrounding rock failure model in Zhujixi mine can be classified and patterns recognized.Compared to the identification results and the results detected by geological radar of surrounding rock loose circle,the reliability of the results of the pattern recognition is verified and lays the foundations for the support design of deep soft rock roadways.

Elasto-plastic Analysis of Circular Tunnels in Jointed Rock Masses Satisfy the Hoek-Brown Failure Criterion

The relationship between the Hoek-Brown parameters and the mechanical response of circular tunnels is il-lustrated. Closed-form and approximate solutions are given for the extent of the plastic zone and the stress and dis-placement fields under axisymmetrical and asymmetric stress conditions. For the same rock masses and under axisym-metrical stress conditions,the radius of the plastic zone in terms of Hoek-Brown criterion is generally an approximation of the radius in terms of the Mohr-Coulomb criterion. The radius in terms of the Hoek-Brown criterion is larger under low stress conditions. For poor quality rock masses (GSI<25),measures (such as grouting,setting rock bolts,etc.) that improve the GSI of rock masses are effective in improving the stability of tunnels. It is not advisable to improve the sta-bility of the tunnels by providing a small support resistance p through shotcrete,except for very poor quality jointed rock masses. Without reference to the quality of the rock mass,the disturbance factor D should not less than 0.5. Meas-ures which disturb rock masses during tunnel construction should be taken carefully when the tunnel depth increases.

Retrospective and prospective review of the generalized nonlinear strength theory for geomaterials

Strength theory is the basic theory for calculating and designing the strength of engineering materials in civil,hydraulic,mechanical,aerospace,military,and other engineering disciplines.Therefore,the comprehensive study of the generalized nonlinear strength theory(GNST)of geomaterials has significance for the construction of engineering rock strength.This paper reviews the GNST of geomaterials to demonstrate the research status of nonlinear strength characteristics of geomaterials under complex stress paths.First,it systematically summarizes the research progress of GNST(classical and empirical criteria).Then,the latest research the authors conducted over the past five years on the GNST is introduced,and a generalized three-dimensional(3D)nonlinear Hoek‒Brown(HB)criterion(NGHB criterion)is proposed for practical applications.This criterion can be degenerated into the existing three modified HB criteria and has a better prediction performance.The strength prediction errors for six rocks and two in-situ rock masses are 2.0724%-3.5091%and 1.0144%-3.2321%,respectively.Finally,the development and outlook of the GNST are expounded,and a new topic about the building strength index of rock mass and determining the strength of in-situ engineering rock mass is proposed.The summarization of the GNST provides theoretical traceability and optimization for constructing in-situ engineering rock mass strength.

Real-time arrival picking of rock microfracture signals based on convolutional-recurrent neural network and its engineering application

Accurately picking P-and S-wave arrivals of microseismic(MS)signals in real-time directly influences the early warning of rock mass failure.A common contradiction between accuracy and computation exists in the current arrival picking methods.Thus,a real-time arrival picking method of MS signals is constructed based on a convolutional-recurrent neural network(CRNN).This method fully utilizes the advantages of convolutional layers and gated recurrent units(GRU)in extracting short-and long-term features,in order to create a precise and lightweight arrival picking structure.Then,the synthetic signals with field noises are used to evaluate the hyperparameters of the CRNN model and obtain an optimal CRNN model.The actual operation on various devices indicates that compared with the U-Net method,the CRNN method achieves faster arrival picking with less performance consumption.An application of large underground caverns in the Yebatan hydropower station(YBT)project shows that compared with the short-term average/long-term average(STA/LTA),Akaike information criterion(AIC)and U-Net methods,the CRNN method has the highest accuracy within four sampling points,which is 87.44%for P-wave and 91.29%for S-wave,respectively.The sum of mean absolute errors(MAESUM)of the CRNN method is 4.22 sampling points,which is lower than that of the other methods.Among the four methods,the MS sources location calculated based on the CRNN method shows the best consistency with the actual failure,which occurs at the junction of the shaft and the second gallery.Thus,the proposed method can pick up P-and S-arrival accurately and rapidly,providing a reference for rock failure analysis and evaluation in engineering applications.

Determination of geological strength index of jointed rock mass based on image processing

The geological strength index(GSI) system,widely used for the design and practice of mining process,is a unique rock mass classification system related to the rock mass strength and deformation parameters based on the generalized Hoek-Brown and Mohr-Coulomb failure criteria.The GSI can be estimated using standard chart and field observations of rock mass blockiness and discontinuity surface conditions.The GSI value gives a numerical representation of the overall geotechnical quality of the rock mass.In this study,we propose a method to determine the GSI quantitatively using photographic images of in situ jointed rock mass with image processing technology,fractal theory and artificial neural network(ANN).We employ the GSI system to characterize the jointed rock mass around the working in a coal mine.The relative error between the proposed value and the given value in the GSI chart is less than 3.6%.

Cracking process of rock mass models under uniaxial compression

Anisotropic strength and deformability of the rock mass with non-persistent joints are governed by cracking process of the rock bridges.The dependence of cracking process of jointed rock masses on the two important geometrical parameters,joint orientation and joint persistence,was studied systematically by carrying out a series of uniaxial compression tests on gypsum specimens with regularly arranged multiple parallel pre-existing joints.According to crack position,mechanism and temporal sequence,seven types of crack initiations and sixteen types of crack coalescences,were identified.It was observed that both tensile cracks and shear cracks can emanate from the pre-existing joints as well as the matrix.Vertical joints were included and coplanar tensile cracks initiation and coalescence were observed accordingly.For specimen with joint inclination angle β=75°,it was found that collinear joints can be linked not only by coplanar shear cracks but also by mixed tensile-shear cracks,and that a pair of them can form a small rotation block.Seven failure modes,including axial cleavage,crushing,crushing and rotation of new blocks,stepped failure,stepped failure and rotation of new blocks,shear failure along a single plane and shear failure along multiple planes,were observed.These modes shift gradually in accordance with the combined variation of joint orientation and joint persistence.It is concluded that cracking process and failure modes are more strongly affected by joint orientation than by joint persistence,especially when joint inclination angle is larger than 45°.Finally,variations of macroscopic mechanical behaviors with the two geometrical parameters,such as patterns of the complete axial stress-axial strain curves,peak strength and elastic modulus,are summarized and their mechanisms are successfully explained according to their different cracking process.

Numerical simulations of failure behavior around a circular opening in a non-persistently jointed rock mass under biaxial compression

Pre-existing discontinuities change the mechanical properties of rock masses,and further influence failure behavior around an underground opening.In present study,the failure behavior in both Inner and Outer zones around a circular opening in a non-persistently jointed rock mass under biaxial compression was investigated through numerical simulations.First,the micro parameters of the PFC^(3D) model were carefully calibrated using the macro mechanical properties determined in physical experiments implemented on jointed rock models.Then,a parametrical study was undertaken of the effect of stress condition,joint dip angle and joint persistency.Under low initial stress,the confining stress improves the mechanical behavior of the surrounding rock masses;while under high initial stress,the surrounding rock mass failed immediately following excavation.At small dip angles the cracks around the circular opening developed generally outwards in a step-path failure pattern;whereas,at high dip angles the surrounding rock mass failed in an instantaneous intact rock failure pattern.Moreover,the stability of the rock mass around the circular opening deteriorated significantly with increasing joint persistency.

Failure mode and strength anisotropic characteristic of stratified rock mass under uniaxial compressive situation

A stratified rock mass model was founded by FLAC3D. The failure mode and anisotropic characteristic of strength for stratified rock mass were analyzed. The analysis results show that the numerical simulation can visually reflect the failure modes of rock samples under different inclination angles β of structural plane. The stiffness of rock sample before peak strength changes in the compressive procedure. With the increase of β, the compressive strength σc of rock sample decreases firstly and then increases; when β is in the range of 20°-30° and 80°-90°, σc has the largest sensitivity to β; while β falls in the range of 30°-70°, σc varies little. When φ j<β<90°. (φj is friction angle of structure plane), the results obtained from numerical simulation and theoretical analysis are in almost the same values; while β≤φ j or β=90°, they are in great different values. The results obtained from theoretical analysis are obvious larger than those from numerical simulation; and the results from numerical simulation can reflect the difference of compressive strength of rock samples for the two situations of β≥φj and β=90°, which is in more accordance with the real situation.

Evolution process of rock mass engineering system using systems science

The rock mass engineering system （RMES） basically consists ofrock mass engineering （RME）, water system and surroundingecological environments, etc. The RMES is characterized by nonlinearity,occurrence of chaos and self-organization （Tazaka, 1998;Tsuda, 1998; Kishida, 2000）. From construction to abandonmentof RME, the RMES will experience four stages, i.e. initial phase,development phase, declining phase and failure phase. In thiscircumstance, the RMES boundary conditions, structural safetyand surrounding environments are varied at each phase, so arethe evolution characteristics and disasters （Wang et al., 2014）.

Dynamic Failure Model of Thin Coal and Rock Mass under Uniform Impact Load

During the excavation of deep coal and rock mass, the radial stress of the free face changes from three-dimensional compression state to two-dimensional stress, bearing the combined action of dynamic disturbance and static load at the same time. With that, many mines suffer from dynamic disasters, such as coal and gas outburst, rock burst and rock caving during deep mining excavation, which is often accompanied by plate crack, spalling and other disasters, seriously affecting the stability of stope and roadway. Taking thin rectangular coal and rock mass as the research object, the dual equation of the free vibration was derived and the exact solution model of the free vibration was established with the use of Hamilton dual system. Based on the action characteristics of the uniform impact load, the effective mode of the forced vibration was obtained by using the Duhamel integral principle and the orthogonality of the mode function. Based on the third strength theory and the numerical simulation results, the dynamic damage process and development trend of coal and rock mass were analyzed under uniform impact load. It was concluded that the starting position of dynamic damage can be judged by the first order main mode, and the development direction and trend of the damage can be judged by the fifth and sixth order main modes. It was concluded that the vibration mode functions of coal and rock mass with four side fixed (C-C-C-C), the two sides fixed and simply supported on the other (S-C-S-C) are mainly composed of three modes that are the first order (dominant frequency), the fifth order and the sixth order, from which the dynamic damage mechanism is preliminarily studied.

Mechanical response features and failure process of soft surrounding rock around deeply buried three-centered arch tunnel

Due to the extreme complexity of mechanical response of soft surrounding rock(SR) around a tunnel under high geostatic stress conditions, the integration of physical and numerical modeling techniques was adopted. Based on the similarity theory, new composite-similar material was developed, which showed good agreement with the similarity relation and successfully simulated physico-mechanical properties(PMP) of deep buried soft rock. And the 800 mm×800 mm×200 mm physical model(PM) was conducted, in which the endoscopic camera technique was adopted to track the entire process of failure of the model all the time. The experimental results indicate that the deformation of SR around a underground cavern possessed the characteristics of development by stages and in delay, and the initial damage of SR could induce rapid failure in the later stage, and the whole process could be divided into three stages, including the localized extension of crack(the horizontal load(HL) was in the range of 130 k N to 170 k N, the vertical load(VL) was in the range of 119 k N to 153.8 k N), rapid crack coalescence(the HL was in the range of 170 k N to 210 k N, the VL was in the range of 153.8 k N to 182.5 k N) and residual strength(the HL was greater than 210 k N, the VL was greater than 182.5 k N). Under the high stress conditions, the phenomenon of deformation localization in the SR became serious and different space positions show different deformation characteristics. In order to further explore the deformation localization and progressive failure phenomenon of soft SR around the deeply buried tunnel, applying the analysis software of FLAC3 D three-dimensional explicit finite-difference method, based on the composite strain-softening model of Mohr-Coulomb shear failure and tensile failure, the calculation method of large deformation was adopted. Then, the comparative analysis between the PM experiment and numerical simulation of the three centered arch tunnels was implemented and the relationship of deformation localization and progressive failure of SR around a tunnel under high stress conditions was discussed.

Particle flow study on strength and meso-mechanism of Brazilian splitting test for jointed rock mass

A discrete element method （DEM） called particle flow code （PFC2D） was used to construct a model for Brazilian disc splitting test in the present study. Based on the experimental results of intact Brazilian disc of rock-like material, a set of micro-parameters in PFC2D that reflected the macro-mechanical behavior of rock-like materials were obtained. And then PFC2D was used to simulate Brazilian splitting test for jointed rock mass specimens and specimen containing a central straight notch. The effect of joint angle and notch angle on the tensile strength and failure mode of jointed rock specimens was detailed analyzed. In order to reveal the meso-mechanical mechanism of crack coalescence, displacement trend lines were applied to analyze the displacement evolution during the crack initiation and propagation. The investigated conclusions can be described as follows. （1） The tensile strength of jointed rock mass disc specimen is dependent to the joint angle. As the joint angle increases, the tensile strength of jointed rock specimen takes on a nonlinear variance. （2） The tensile strength of jointed rock mass disc specimen containing a central straight notch distributes as a function of both joint angle and notch angle. （3） Three major failure modes, i.e., pure tensile failure, shear failure and mixed tension and shear failure mode are observed in jointed rock mass disc specimens under Brazilian test. （4） The notch angle roles on crack initiation and and joint angle play important propagation characteristics of jointed rock mass disc specimen containing a central straight notch under Brazilian test.

Advances in statistical mechanics of rock masses and its engineering applications

To efficiently link the continuum mechanics for rocks with the structural statistics of rock masses,a theoretical and methodological system called the statistical mechanics of rock masses(SMRM)was developed in the past three decades.In SMRM,equivalent continuum models of stressestrain relationship,strength and failure probability for jointed rock masses were established,which were based on the geometric probability models characterising the rock mass structure.This follows the statistical physics,the continuum mechanics,the fracture mechanics and the weakest link hypothesis.A general constitutive model and complete stressestrain models under compressive and shear conditions were also developed as the derivatives of the SMRM theory.An SMRM calculation system was then developed to provide fast and precise solutions for parameter estimations of rock masses,such as full-direction rock quality designation(RQD),elastic modulus,Coulomb compressive strength,rock mass quality rating,and Poisson’s ratio and shear strength.The constitutive equations involved in SMRM were integrated into a FLAC3D based numerical module to apply for engineering rock masses.It is also capable of analysing the complete deformation of rock masses and active reinforcement of engineering rock masses.Examples of engineering applications of SMRM were presented,including a rock mass at QBT hydropower station in northwestern China,a dam slope of Zongo II hydropower station in D.R.Congo,an open-pit mine in Dexing,China,an underground powerhouse of Jinping I hydropower station in southwestern China,and a typical circular tunnel in Lanzhou-Chongqing railway,China.These applications verified the reliability of the SMRM and demonstrated its applicability to broad engineering issues associated with jointed rock masses.

Damage smear method for rock failure process analysis

Damage smear method(DSM)is adopted to study trans-scale progressive rock failure process,based on statistical meso-damage model and finite element solver.The statistical approach is utilized to reflect the mesoscopic rock heterogeneity.The constitutive law of representative volume element(RVE)is established according to continuum damage mechanics in which double-damage criterion is considered.The damage evolution and accumulation of RVEs are used to reveal the macroscopic rock failure characteristics.Each single RVE will be represented by one unique element.The initiation,propagation and coalescence of meso-to macro-cracks are captured by smearing failed elements.The above ideas are formulated into the framework of the DSM and programed into self-developed rock failure process analysis(RFPA)software.Two laboratory-scale examples are conducted and the well-known engineering-scale tests,i.e.Atomic Energy of Canada Limited’s(AECL’s)Underground Research Laboratory(URL)tests,are used for verification.It shows that the simulation results match with other experimental results and field observations.

Mechanism of progressive failure of a slope with a steep joint under the action of freezing and thawing:model test

The stability of slope rock masses is influenced by freeze-thaw cycles in cold region,and the mechanism of stability deterioration is not clear.In order to understand the damage and progressive failure characteristics of rock masses under the action of freezing and thawing,a model test was conducted on slope with steep joint in this study.The temperature,frost heaving pressure and deformation of slope rock mass were monitored in real-time during the test and the progressive failure mode was studied.The experimental results show that the temperature variations of cracking and the rock mass of a slope are different.There are obvious latent heat stages in the temperature-change plot in the crack,but not in the slope rock masses.The frost heaving effect in the fracture is closely related to the constraint conditions,which change with the deformation of the fracture.The frost heaving pressure fluctuates periodically during freezing and continues to decrease during thawing.The surface deformation of the rock mass increases during freezing,and the deformation is restored when it thaws.Freeze-thaw cycling results in residual deformation of the rock mass which cannot be fully restored.Analysis shows that the rock mass at the free side of the steep-dip joint rotates slightly under the frost heaving effect,causing fracture propagation.The fracture propagation pattern is a circular arc at the beginning,then extends to the possible sliding direction of the rock mass.Frost heaving force and fracture water pressure are the key factors for the failure of the slope,which can cause the crack to penetrate the rock mass,and a landslide ensues when the overall anti-sliding resistance of the rock mass is overcome.

Rock mechanics for design of Brisbane tunnels and implications of recent thinking in relation to rock mass strength

This paper explores the potential implications of recent thinking in relation to rock mass strength for future tunnelling projects in Brisbane,Australia,particularly as they are constructed within deep horizons where the in situ stress magnitudes is larger.Rock mass failure mechanisms for the current tunnels in Brisbane are generally discontinuity controlled and the potential for stress-induced failure is relatively rare.For the road tunnels which have been constructed in Brisbane over the last 12 years,the strength of the more massive rock masses for continuum analysis has been estimated by the application of the Hoek-Brown(H-B)failure criterion using the geological strength index(GSI)to determine the H-B parameters mb,s and a.Over the last few years,alternative approaches to estimating rock mass strength for‘massive to moderately jointed hard rock masses’have been proposed by others,which are built on the work completed by E.Hoek and E.T.Brown in this area over their joint careers.This paper explores one of these alternative approaches to estimating rock mass strength for one of the geological units(the Brisbane Tuff),which is often encountered in tunnelling projects in Brisbane.The potential implications of these strength forecasts for future tunnelling projects are discussed along with the additional work which will need to be undertaken to confirm the applicability of such alternative strength criteria for this rock mass.

Failure behavior of highly stressed rocks under quasi-static and intensive unloading conditions

Unloading failure of rocks,especially highly stressed rocks,is one of the key issues in construction of underground structures.Based on this,analytical models for rocks under quasi-static and intensive unloading conditions are established to study the failure behavior of highly stressed rocks.In case of rock failure under quasi-static unloading,the rock mass ahead of working face is regarded as an elasto-brittle material,and the stress-displacement curves are used to characterize the tensile fracture of peak-stress area.It is observed that,when intensive unloading happens,there is an elastic unloading wave（perturbation wave） propagating in the rock mass.If the initial stress exceeds the critical stress,there will be a fracture wave,following the elastic unloading wave.To study the propagation feature of fracture wave,the conservation laws of mass,momentum and energy are employed.Results show that the post-peak deformation,strength and energy dissipation are essential to the failure process of highly stressed rocks.

Geotechnical investigations and remediation design for failure of tunnel portal section： a case study in northern Turkey

Mass movements are very common problems in the eastern Black Sea region of Turkey due to its climate conditions, geological, and geomorphological characteristics. High slope angle, weathering, dense rainfalls, and anthropogenic impacts are generally reported as the most important triggering factors in the region. Following the portal slope excavations in the entrance section of Cankurtaran tunnel, located in the region, where the highly weathered andesitic tuff crops out, a circular toe failure occurred. The main target of the present study is to investigate the causes and occurrence mechanism of this failure and to determine the feasible remedial measures against it using finite element method(FEM) in four stages. These stages are slope stability analyses for pre-and postexcavation cases, and remediation design assessments for slope and tunnel. The results of the FEM-SSR analyses indicated that the insufficient initial support design and weathering of the andesitic tuffs are the main factors that caused the portal failure. After installing a rock retaining wall with jet grout columns and reinforced slope benching applications, the factor of safety increased from 0.83 to 2.80. In addition toslope stability evaluation, the Rock Mass Rating(RMR), Rock Mass Quality(Q) and New Austrian Tunneling Method(NATM) systems were also utilized as empirical methods to characterize the tunnel ground and to determine the tunnel support design. The performance of the suggested empirical support design, induced stress distributions and deformations were analyzed by means of numerical modelling. Finally, it was concluded that the recommended stabilization technique was essential for the dynamic long-term stability and prevents the effects of failure. Additionally, the FEM method gives useful and reasonably reliable results in evaluating the stability of cut slopes and tunnels excavated both in continuous and discontinuous rock masses.

Fuzzy Random Reliability Analysis of Blocky Rock-Mass in Slopes

Slope stability assessment is a geotechnical problem characterized by many sources of uncertainty. In clas- sical reliability analysis, only the randomness of uncertainties is taken into account but the fuzziness of them is ignored. In this paper, a fuzzy probability approach and a fuzzy JC method are presented for the reliability analysis. The two methods have been applied to stability analysis of a certain slope of permanent ship lock in the Three-Gorges Project. The results obtained from these two methods are basically the same. However, compared with the fuzzy probability means, the fuzzy JC method can reflect the real situation better because it uses a fuzzy-based analysis applied to not only limit state equation but also mechanical parameters.