Stability analysis of intermittently jointed rock slopes based on the stepped failure mode

In practical engineering,due to the noncontinuity characteristics of joints in rock slopes,in addition to plane failure,stepped sliding failure may occur for intermittently jointed rock slopes.Especially for intermittently bedding jointed rock slopes,the correlation and difference in strength parameters between joints and rock bridges,along with the various failure modes and intermittency of rock bridges,contribute to the complexity of stepped failure modes and the unpredictability of failure regions.Based on the upper-bound limit analysis method and multi-sliders step-path failure mode,considering the shear and tensile failure of rock bridges and the weakened relationship between the strength parameters of rock bridges and jointed surfaces,by introducing the modified M-C failure criterion and the formula for calculating the energy consumption of tensile failure of rock bridges,two failure mechanisms are constructed to obtain the safety factor(F_(s))of intermittently jointed rock slopes.The sequential quadratic programming method is used to obtain the optimal upper-bound solution for F_(s).The influence of multiple key parameters(slope height H,horizontal distance L,Slope angleβ,shear strength parameters of the rock bridgeφr and cr,Dimensionless parameter u,weakening coefficients of the internal friction angle and cohesion between the rock bridges and joint surfaces Kφand Kc)on the stability analysis of intermittently jointed rock slopes under the shear failure mode of rock bridges as well as under the tensile failure mode is also explored.The reliability of the failure mechanisms is verified by comparative analysis with theoretical results,numerical results,and landslide cases,and the variation rules of F_(s)with each key parameter are obtained.The results show that F_(s) varies linearly withφr and cr of the rock bridge and with K_(φ)and K_(c),whereas F_(s)changes nonlinearly with H and L.In particular,with the increase in Kφand Kc,Fs increases by approximately 52.78%and 171.02%on average,respectively.For rock bridge tensile failure,F_(s) shows a nonlinearly positive correlation withφr,cr,Kφand Kc.In particular,with the increase in Kφand Kc,Fs increases by approximately 13%and 61.69%on average,respectively.Fs decreases rapidly with increasing slope gradientβand decreasing dimensionless parameterμ.When Kφand Kc are both less than 1.0,the stepped sliding surface occurs more easily than the plane failure surface,especially in the case of tensile failure of the rock bridge.In addition,rock slopes with higher strength parameters,taller heights,and greater weakening coefficients are prone to rock bridge tension failure with lower Fs,and more attention should be given to the occurrence of such accidents in actual engineering.

Impact of Earthquake Action on the Design and Sizing of Jointed Masonry Structures in South Kivu, DRC

This article deals with the investigation of the effects of seismic impacts on the design and dimensioning of structures in South Kivu. The starting point is the observation of an ambivalence that can be observed in the province, namely the non-consideration of seismic action in the study of structures by both professionals and researchers. The main objective of the study is to show the importance of dynamic analysis of structures in South Kivu. It adopts a meta-analytical approach referring to previous researches on South Kivu and proposes an efficient and optimal method. To arrive at the results, we use Eurocode 7 and 8. In addition, we conducted static analysis using the Coulomb method and dynamic analysis using the Mononobe-Okabe method and compared the results. At Nyabibwe, the results showed that we have a deviation of 24.47% for slip stability, 12.038% for overturning stability and 9.677% for stability against punching through a weight wall.

Shear mechanical properties and fracturing responses of layered rough jointed rock-like materials

This study aims to investigate mechanical properties and failure mechanisms of layered rock with rough joint surfaces under direct shear loading.Cubic layered samples with dimensions of 100 mm×100 mm×100 mm were casted using rock-like materials,with anisotropic angle(α)and joint roughness coefficient(JRC)ranging from 15°to 75°and 2-20,respectively.The direct shear tests were conducted under the application of initial normal stress(σ_(n)) ranging from 1-4 MPa.The test results indicate significant differences in mechanical properties,acoustic emission(AE)responses,maximum principal strain fields,and ultimate failure modes of layered samples under different test conditions.The peak stress increases with the increasingαand achieves a maximum value atα=60°or 75°.As σ_(n) increases,the peak stress shows an increasing trend,with correlation coefficients R² ranging from 0.918 to 0.995 for the linear least squares fitting.As JRC increases from 2-4 to 18-20,the cohesion increases by 86.32%whenα=15°,while the cohesion decreases by 27.93%whenα=75°.The differences in roughness characteristics of shear failure surface induced byαresult in anisotropic post-peak AE responses,which is characterized by active AE signals whenαis small and quiet AE signals for a largeα.For a given JRC=6-8 andσ_(n)=1 MPa,asαincreases,the accumulative AE counts increase by 224.31%(αincreased from 15°to 60°),and then decrease by 14.68%(αincreased from 60°to 75°).The shear failure surface is formed along the weak interlayer whenα=15°and penetrates the layered matrix whenα=60°.Whenα=15°,as σ_(n) increases,the adjacent weak interlayer induces a change in the direction of tensile cracks propagation,resulting in a stepped pattern of cracks distribution.The increase in JRC intensifies roughness characteristics of shear failure surface for a smallα,however,it is not pronounced for a largeα.The findings will contribute to a better understanding of the mechanical responses and failure mechanisms of the layered rocks subjected to shear loads.

Strength and deformation characteristics of irregular columnar jointed rock mass: A combined experimental and theoretical study

The irregularity of jointed network poses a challenge to the determination of field mechanical param-eters of columnar jointed rock mass(CJRM),and a reasonable prediction of deformation and strength characteristics of CJRM is important for engineering construction.The Voronoi diagram and three-dimensional printing technology were used to make an irregular columnar jointed mold,and the irregular CJRM(ICJRM)specimens with different dip directions and dip angles were prepared.Uniaxial compression tests were performed,and the anisotropic strength and deformation characteristics of ICJRM were described.The failure modes and mechanisms were revealed in accordance with the final appearances of the ICJRM specimens.Based on the model test results,the empirical correlations for determining the field deformation and strength parameters of CJRM were derived using the dip angle and modified joint factor.The proposed empirical equations were used in the Baihetan Project,and the calculated mechanical parameters were compared with the field test results and those obtained from the tunneling quality index method.Results showed that the deformation parameters determined by the two proposed methods are all consistent with the field test results,and these two methods can also estimate the strength parameters effectively.

A 3D microseismic data-driven damage model for jointed rock mass under hydro-mechanical coupling conditions and its application

Rock mass is a fractured porous medium usually subjected to complex geostress and fluid pressure simultaneously.Moreover,the properties of rock mass change in time and space due to mining-induced fractures.Therefore,it is always challenging to accurately measure rock mass properties.In this study,a three-dimensional(3D)microseismic(MS)data-driven damage model for jointed rock mass under hydro-mechanical coupling conditions is proposed.It is a 3D finite element model that takes seepage,damage and stress field effects into account jointly.Multiple factors(i.e.joints,water and microseismicity)are used to optimize the rock mass mechanical parameters at different scales.The model is applied in Shirengou iron mine to study the damage evolution of rock mass and assess the crown pillar stability during the transition from open-pit to underground mining.It is found that the damage pattern is mostly controlled by the structure,water and rock mass parameters.The damage pattern is evidently different from the two-dimensional result and is more consistent with the field observations.This difference is caused by the MS-derived damage acting on the rock mass.MS data are responsible for gradually correcting the damage zone,changing the direction in which it expands,and promoting it to evolve close to reality.For the crown pillar,the proposed model yields a more trustworthy safety factor.In order to guarantee the stability of the pillar,it is suggested to take waterproof and reinforcement measures in areas with a high degree of damage.

Numerical modelling of resonance mechanisms in jointed rocks using transfer functions

Resonance effects in parallel jointed rocks subject to stress waves are investigated using transfer functions,derived from signals generated through numerical modelling.Resonance is important for a range of engineering situations as it identifies the frequency of waves which will be favourably transmitted.Two different numerical methods are used for this study,adopting the finite difference method and the combined discrete element-finite difference method.The numerical models are validated by replicating results from previous studies.The two methods are found to behave similarly and show the same resonance effects;one operating at low frequency and the other operating at relatively high frequency.These resonance effects are interpreted in terms of simple physical systems and analytical equations are derived to predict the resonant frequencies of complex rock masses.Low frequency resonance is shown to be generated by a system synonymous with masses between springs,described as spring resonance,with an equal number of resonant frequencies as the number of blocks.High frequency resonance is generated through superposition of multiple reflected waves developing standing waves within intact blocks,described as superposition resonance.While resonance through superposition has previously been identified,resonance based on masses between springs has not been previously identified in jointed rocks.The findings of this study have implications for future analysis of multiple jointed rock masses,showing that a wave travelling through such materials can induce other modes of propagation of waves,i.e.spring resonance.

Fracture behaviors of columnar jointed rock mass using interface mechanics theorem

For a special geological structure of columnar jointed rock mass(CJRM),its mechanical properties are strongly affected by the columnar joints.To describe the fracture behaviors of CJRM using the basic theories of interface mechanics for composite materials,the interface stresses of the vertical and horizontal joints,which are the two primary joints in the CJRM under triaxial compression,are studied,and their mathematical expressions are derived based on the superposition principle.Based on the obtained interface stresses of the vertical and horizontal joints in the CJRM,the crack initiation of the joint interface in the CJRM is studied using the maximum circumferential stress theory in fracture mechanics.Moreover,based on this investigation,the fracture behaviors of CJRM are analyzed.According to the results of similar material physical model tests for the CJRM,the theoretical study is verified.Finally,the influence of the mechanical parameters of the CJRM on the joint interface stress is discussed comprehensively.

Assessment of cyclic deformation and critical stress amplitude of jointed rocks via cyclic triaxial testing

Jointed rock specimens with a natural replicated joint surface oriented at a mean dip angle of 60were prepared,and a series of cyclic triaxial tests was performed at different confining pressures and cyclic deviatoric stress amplitudes.The samples were subjected to 10,000 loading-unloading cycles with a frequency of 8 Hz.At each level of confining pressure,the applied cyclic deviatoric stress amplitude was increased incrementally until excessive deformation of the jointed rock specimen was observed.Analysis of the test results indicated that there existed a critical cyclic deviatoric stress amplitude(i.e.critical dynamic deviatoric stress)beyond which the jointed rock specimens yielded.The measured critical dynamic deviatoric stress was less than the corresponding static deviatoric stress.At cyclic deviatoric stress amplitudes less than the critical dynamic deviatoric stress,minor cumulative residual axial strains were observed,resulting in hysteretic damping.However,for cyclic deviatoric stresses beyond the critical dynamic deviatoric stress,the plastic strains increased promptly,and the resilient moduli degraded rapidly during the initial loading cycles.Cyclic triaxial test results showed that at higher confining pressures,the ultimate residual axial strain attained by the jointed rock specimen decreased,the steadystate dissipated energy density and steady-state damping ratio per load cycle decreased,while steadystate resilient moduli increased.

The law of strength damage and deterioration of jointed sandstone after dry-wet cycles

Under the periodic rise and fall of the water level in the Three Gorges Reservoir in China,the rock mass in the ebb and flow zone of the slope is always in a state of a dry-wet cycle.In order to explore the influence of dry-wet cycle on mechanical properties of jointed sandstone,the triaxial and uniaxial compression tests of dry-wet cycle of jointed sandstone were carried out.For the experiment,four groups of samples with different numbers of joints were set up,and the jointed rock samples were subjected to 20 dry-wet cycles.Using both the triaxial compression test and the Mohr-Coulomb(M-C)rock fracture criterion,the strength envelope of the sandstone samples was fitted,and their strength degradation was further analyzed and studied.The results show that:(1)The peak intensity and elastic modulus of the sandstone samples decrease with increased number of dry-wet cycles.(2)The total deterioration of mechanical properties of intact rock samples is bigger than that of jointed sandstone samples as the number of dry-wet cycles increases.(3)With the increase of confining pressure,the peak intensity of intact sandstone samples increases much more than that of jointed sandstone samples,which indicates that joints and their numbers have obvious influence.(4)Joints and their numbers play an important role in guiding the damage effects of sandstone samples,which weaken the damage caused by dry-wet cycles.Therefore,the envelope of the M-C strength criterion of intact sandstone samples moves more than that of jointed sandstone samples.

Analysis of the Elastic-Plastic Dynamic Finite Element on a Jointed Rock Mass

Aim To study the elastic plastic dynamical constitutive relations about a jointed rock mass under explosion load and its computer simulation. Methods\ Stress history is taken into account and stresses will follow changes in time during a period of explosion load. According to the principle of static force balance, the corresponding nodal concentrated force is calculated and the nodal displacement is counted. The elastic plastic dynamic finite element equations are thus obtained. Results\ A finite element method is given for a jointed rock mass under explosion load. Conclusion\ The problem of large plastic deformation for jointed rock mass on blasting was efficiently resolved through dynamic finite element analysis and the range of damages by blasting simulated, and this pushes forward the problem to engineering practice.

Energy evolution mechanism and failure criteria of jointed surrounding rock under uniaxial compression

The object of this article is to investigate the energy evolution mechanism and failure criteria of cross-jointed samples containing an opening during deformation and failure based on the uniaxial compression test and rock energy principle.The results show that the energy evolution characteristics of the samples correspond to a typical progressive damage mode.The peak total energy,peak elastic energy,and total input energy of the samples all first decrease and then increase with an increase of half of the included angle,reaching their minimum values when this angle is 45°,while the dissipated energy generally increases with this angle.The existence of the opening and cross joints can obviously weaken the energy storage capacity of the rock,and the change in the included angle of the cross joint has a great influence on the elastic energy ratio of the sample before the peak stress,which leads to some differences in the distribution laws of the input energy.The continuous change and the subsequent sharp change in the rate of change in the energy consumption ratio can be used as the criteria of the crack initiation and propagation and the unstable failure of the sample,respectively.

A Novel Pneumatic Soft Gripper with a Jointed Endoskeleton Structure

In current research on soft grippers,pneumatically actuated soft grippers are generally fabricated using fully soft materials,which have the advantage of flexibility as well as the disadvantages of a small gripping force and slow response speed.To improve these characteristics,a novel pneumatic soft gripper with a jointed endoskeleton structure(E-Gripper)is developed,in which the muscle actuating function has been separated from the force bearing function.The soft action of an E-Gripper finger is performed by some air chambers surrounded by multilayer rubber embedded in the restraining fiber.The gripping force is borne and transferred by the rigid endoskeleton within the E-Gripper finger Thus,the gripping force and action response speed can be increased while the flexibility is maintained.Through experiments,the bending angle of each finger segment,response time,and gripping force of the E-Gripper have been measured,which provides a basis for designing and controlling the soft gripper The test results have shown that the maximum gripping force of the E-Gripper can be 35 N,which is three times greater than that of a fully soft gripper(FS-Gripper)of the same size.At the maximum charging pressure of 150 kPa,the response time is1.123 s faster than that of the FS-Gripper.The research results indicate that the flexibility of a pneumatic soft gripper is not only maintained in the case of the E-Gripper,but its gripping force is also obviously increased,and the response time is reduced.The E-Gripper thus shows great potential for future development and applications.

Macro and meso analysis of jointed rock mass triaxial compression test by using equivalent rock mass(ERM) technique

Methods that can efficiently model the effects of rock joints on rock mass behavior can be beneficial in rock engineering. The suitability of equivalent rock mass(ERM) technique based upon particle methods is investigated. The ERM methodology is first validated by comparing calculated and experimental data of lab triaxial compression test on a set of cylindrical rock mass samples, each containing a single joint oriented in various dip angles. The simulated results are then used to study the stress-strain nonlinearity and failure mechanism as a function of the joint dip angle and confining stress. The anisotropy and size effects are also investigated by using multi-scale cubic ERM models subjected to triaxial compression test. The deformation and failure behavior are found to be influenced by joint degradation, the micro-crack formation in the intact rock, the interaction between two joints, and the interactions of micro-cracks and joints.

Crack initiation stress and strain of jointed rock containing multi-cracks under uniaxial compressive loading: A particle flow code approach

The ratio of crack initiation stress to the uniaxial compressive strength(SCI,B/SUC,B) and the ratio of axial strain at the crack initiation stress to the axial strain at the uniaxial compressive strength(B,UCB,CI,A,A/SSSS) were studied by performing numerical stress analysis on blocks having multi flaws at close spacing's under uniaxial loading using PFC3 D. The following findings are obtained: SCI,B/SUC,B has an average value of about 0.5 with a variability of ± 0.1. This range agrees quite well with the values obtained by former research. For joint inclination angle, β=90°,B,UCB,CI,A,A/SSSS is found to be around 0.48 irrespective of the value of joint continuity factor, k. No particular relation is found betweenB,UCB,CI,A,A/SSSS and β; however, the average B,UCB,CI,A,A/SSSS seems to slightly decrease with increasing k. The variability ofB,UCB,CI,A,A/SSSS is found to increase with k.Based on the cases studied in this work,B,UCB,CI,A,A/SSSS ranges between 0.3 and 0.5. This range is quite close to the range of 0.4to 0.6 obtained for SCI,B/SUC,B. The highest variability of ± 0.12 forB,UCB,CI,A,A/SSSS is obtained for k=0.8. For the remaining k values the variability ofB,UCB,CI,A,A/SSSS can be expressed within ± 0.05. This finding is very similar to the finding obtained for the variability of SCI,B/SUC,B.

Dynamic-static coupling analysis on rockburst mechanism in jointed rock mass

A numerical code called RFPA-Dynamics was used to study the rockburst mechanism under dynamic load based on coupled static-dynamic analysis.The results show that dynamic disturbance has a very distinct triggering effect on rockburst.Under the dynamic load,rockburst is motivated by tensile stress formed by the overlapping of dynamic waves in the form of instantaneous open and cutting through of cracks in weak planes and pre-damaged areas.Meanwhile,the orientation of joint sets has an obvious leading effect on rockburst locations.Finally,a higher initial static stress state before dynamic loading can cause more pre-damaged area,thus leading to a larger rockburst scope.

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.

Numerical investigation on the sensitivity of jointed rock mass strength to various factors

The mechanical properties of jointed rock masses, such as strength, deformation and the failure mechanism, can be understood only by studying the sensitivity of jointed rock mass strength (both the peak and residual strengths) to the factors that affect it. An orthogonal design of uniaxial compression tests was simulated on eighteen groups of jointed rock specimens having different geometric and mechanical properties using RFPA2D (Rock Failure Process Analysis) code. The results show that the peak strength is controlled by the geometric parameters of the joints, but that the residual strength is controlled by the mechanical prop- erties of the joint interfaces. The failure mode of jointed rock specimens is mainly shear failure. Joint quantity, or density, is the most important index that affects jointed rock mass strength and engineering quality.

Mechanical properties and reinforcement effect of jointed rock mass with pre-stressed bolt

Pre-stressed bolt anchorage is the key technology for jointed rock masses in rock tunnelling,slope treatment and mining engineering.To investigate the mechanical properties and reinforcement effect of jointed rock masses with pre-stressed bolts,in this study,uniaxial compression tests were conducted on specimens with different anchoring types and flaw inclination angles.ABAQUS software was used to verify and supplement the laboratory tests.The laws of the uniaxial compressive strength(UCS)obtained from the numerical simulations and laboratory tests were consistent.The results showed that under the same flaw angle,both the UCS and elastic modulus of the bolted specimens were improved compared with those of the specimens without bolts and the improvements increased with an increase in the bolt pre-stress.Under the same anchoring type,the UCS and elastic modulus of the jointed specimens increased with an increase in the flaw angle.The pre-stressed bolt could not only restrain the slip of the specimens along the flaw surface but also change the propagation mode of the secondary cracks and limit the initiation of cracks.In addition,the plot contours of the maximum principal strain and the Tresca stress of the numerical models were influenced by the anchoring type,flaw angle,anchoring angle and bolt position.

Simulation of failure process of jointed rock

A modified discontinuous deformation analysis (DDA) algorithm was proposed to simulate the failure behavior of jointed rock. In the proposed algorithm, by using the Monte-Carlo technique, random joint network was generated in the domain of interest. Based on the joint network, the triangular DDA block system was automatically generated by adopting the advanced front method. In the process of generating blocks, numerous artificial joints came into being, and once the stress states at some artificial joints satisfy the failure criterion given beforehand, artificial joints will turn into real joints. In this way, the whole fragmentation process of rock mass can be replicated. The algorithm logic was described in detail, and several numerical examples were carried out to obtain some insight into the failure behavior of rock mass containing random joints. From the numerical results, it can be found that the crack initiates from the crack tip, the growth direction of the crack depends upon the loading and constraint conditions, and the proposed method can reproduce some complicated phenomena in the whole process of rock failure.

Responses of jointed rock masses subjected to impact loading

Impact-induced damage to jointed rock masses has important consequences in various mining and civil engineering applications. This paper reports a numerical investigation to address the responses of jointed rock masses subjected to impact loading. It also focuses on the static and dynamic properties of an intact rock derived from a series of laboratory tests on meta-sandstone samples from a quarry in Nova Scotia, Canada. A distinct element code(PFC2D) was used to generate a bonded particle model(BPM) to simulate both the static and dynamic properties of the intact rock. The calibrated BPM was then used to construct large-scale jointed rock mass samples by incorporating discrete joint networks of multiple joint intensities into the intact rock matrix represented by the BPM. Finally, the impact-induced damage inflicted by a rigid projectile particle on the jointed rock mass samples was determined through the use of the numerical model. The simulation results show that joints play an important role in the impactinduced rock mass damage where higher joint intensity results in more damage to the rock mass. This is mainly attributed to variations of stress wave propagation in jointed rock masses as compared to intact rock devoid of joints.