Three-dimensional stability calculation method for high and large composite slopes formed by mining stope and inner dump in adjacent open pits

The 2D limit equilibrium method is widely used for slope stability analysis.However,with the advancement of dump engineering,composite slopes often exhibit significant 3D mechanical effects.Consequently,it is of significant importance to develop an effective 3D stability calculation method for composite slopes to enhance the design and stability control of open-pit slope engineering.Using the composite slope formed by the mining stope and inner dump in Baiyinhua No.1 and No.2 open-pit coal mine as a case study,this research investigates the failure mode of composite slopes and establishes spatial shape equations for the sliding mass.By integrating the shear resistance and sliding force of each row of microstrip columns onto the bottom surface of the strip corresponding to the main sliding surface,a novel 2D equivalent physical and mechanical parameters analysis method for the strips on the main sliding surface of 3D sliding masses is proposed.Subsequently,a comprehensive 3D stability calculation method for composite slopes is developed,and the quantitative relationship between the coordinated development distance and its 3D stability coefficients is examined.The analysis reveals that the failure mode of the composite slope is characterized by cutting-bedding sliding,with the arc serving as the side interface and the weak layer as the bottom interface,while the destabilization mechanism primarily involves shear failure.The spatial form equation of the sliding mass comprises an ellipsoid and weak plane equation.The analysis revealed that when the coordinated development distance is 1500 m,the error rate between the 3D stability calculation result and the 2D stability calculation result of the composite slope is less than 8%,thereby verifying the proposed analytical method of equivalent physical and mechanical parameters and the 3D stability calculation method for composite slopes.Furthermore,the3D stability coefficient of the composite slope exhibits an exponential correlation with the coordinated development distance,with the coefficient gradually decreasing as the coordinated development distance increases.These findings provide a theoretical guideline for designing similar slope shape parameters and conducting stability analysis.

Stability of Three-Dimensional Trunk Motion

Aim To analyse stability of the three-dimensional rotational movements of a human torso system under perturbations using anatomical data of muscles (McGill, 1992). Methods To use the linearized analysis methods and a special model in which the effect of ligamentous and passive resitance by discs and fibers is included. Results The model is capable of predicting the muscle forces,and joint reaction forces at the L5/Sl which are the biomechani- cal factors used to asses the risk of the discs and annulus fibers. Conclusions It can also be used to analyze and neural excitation levels for a diverse Set of trunk movement.

Effect of external and internal cues on core muscle activation during the Sahrmann five-level core stability test

BACKGROUND Pain in the back or pelvis or fear of back pain may affect the timing or cocontraction of the core muscles.In both static and dynamic movements,the Sahrmann core stability test provides an assessment of core muscle activation and a person's ability to stabilize the lumbopelvic complex.Preparatory cues and images can be used to increase the activation of these muscles.To attain optimal movement patterns,it will be necessary to determine what cueing will give the most effective results for core stability.AIM To investigate the effects of external and internal cues on core muscle activation during the Sahrmann five-level core stability test.METHODS Total 68 participants(21.83±3.47 years)were randomly allocated to an external(n=35)or internal cue group(n=33).Participants performed the Sahrmann fivelevel core stability test without a cue as baseline and the five-level stability exercises with an internal or external cue.External cue group received a pressure biofeedback unit(PBU),and the internal cue group received an audio cue.A Delsys Trigno^(TM)surface electromyography unit was used for muscle activation from the rectus abdominis,external oblique,and transverse abdominis/internal oblique muscles.RESULTS Linear mixed effects model analysis showed that cueing had a significant effect on core muscle activation(P=0.001);however,there was no significant difference between cue types(internal or external)(P=0.130).CONCLUSION Both external and internal cueing have significant effects on core muscle activation during the Sahrmann five-level core stability test and the PBU does not create higher muscle activation than internal cueing.

Criteria for the Nonlinear Stability of Three-Dimensional Quasi-Geostrophic Motions

Some more proper criteria for the nonlinear stability of three-dimensional quasi-geostrophic motions are given by combining variational principle with a prior estimates method. The criteria are suitable for perturbations of initial condition as well as parameters in the model. The basic flow can be steady or unsteady. Particularly the difficulty due to the nonlinear boundary condition is completely overcome by the use of our method.

On the Nonlinear Stability of Three-Dimensional Quasigeostrophic Motions in Spherical Geometry

Nonlinear stability criteria for the motions geoverned by three-dimensional quasigeostrophic model in spherical geometry are obtained by using Arnol＇d＇s variational principle and a priori estimate method. The results gained in this paper are parallel to Arnol＇d＇s second theorem and better than the known results. Especially, under the approximation of vertically integrated nondivergency, criteria corresponding to Arnol＇d＇s second theorem are first established by a detailed analysis.

Three-dimensional stability of landslides based on local safety factor

Unlike the limit equilibrium method(LEM), with which only the global safety factor of the landslide can be calculated, a local safety factor(LSF) method is proposed to evaluate the stability of different sections of a landslide in this paper. Based on three-dimensional(3D) numerical simulation results, the local safety factor is defined as the ratio of the shear strength of the soil at an element on the slip zone to the shear stress parallel to the sliding direction at that element. The global safety factor of the landslide is defined as the weighted average of all local safety factors based on the area of the slip surface. Some example analyses show that the results computed by the LSF method agree well with those calculated by the General Limit Equilibrium(GLE) method in two-dimensional(2D) models and the distribution of the LSF in the 3D slip zone is consistent with that indicated by the observed deformation pattern of an actual landslide in China.

Three-dimensional stability analysis of anisotropic and non-homogeneous slopes using limit analysis

A method of three-dimensional loaded slope stability for anisotropic and nonhomogeneous slopes was presented based on the upper-bound theorem of the limit analysis approach. The approach can be considered as a modification and extension of the solutions. The influences of friction angle, anisotropy factor, nonhomogeneous factor, slope angle, ratio of width to depth, and load on the slope crest were investigated. The results show that solutions are suitable to deal with the purely cohesive soils and frictional/cohesive soils, isotropic and anisotropic, homogeneous and nonhomogeneous, loaded and unloaded cases.

Limit analysis for the seismic stability of three-dimensional rock slopes using the generalized Hoek-Brown criterion

The parameters that influence slope stability and their criteria of failure are fairly understood but over-conservative design approaches are often preferred,which can result in excessive overburden removal that may jeopardize profitability in the context of open pit mining.Numerical methods such as finite element and discrete element modelling are instrumental to identify specific zones of stability,but they remain approximate and do not pinpoint the critical factors that influence stability without extensive parametric studies.A large number of degrees of freedom and input parameters may make the outcome of numerical modelling insufficient compared to analytical solutions.Existing analytical approaches have not tackled the stability of slopes using non-linear plasticity criteria and threedimensional failure mechanisms.This paper bridges this gap by using the yield design theory and the Hoek-Brown criterion.Moreover,the proposed model includes the effect of seismic forces,which are not always taken into account in slope stability analyses.The results are presented in the form of rigorous mathematical expressions and stability charts involving the loading conditions and the rock mass properties emanating from the plasticity criterion.

Probabilistic seismic stability of three-dimensional slopes by pseudo-dynamic approach

Probabilistic analysis is a rational approach for engineering design because it provides more insight than traditional deterministic analysis. Probabilistic evaluation on seismic stability of three dimensional (3D) slopes is studied in this paper. The slope safety factor is computed by combining the kinematic approach of limit analysis using a three-dimensional rotational failure mechanism with the pseudo-dynamic approach. The variability of input parameters, including six pseudo-dynamic parameters and two soil shear strength parameters, are taken into account by means of Monte-Carlo Simulations (MCS) method. The influences of pseudo-dynamic input variables on the computed failure probabilities are investigated and discussed. It is shown that the obtained failure probabilities increase with the pseudo-dynamic input variables and the pseudo-dynamic approach gives more conservative failure probability estimates compared with the pseudo-static approach.

Influence of fracture roughness on shear strength,slip stability and permeability:A mechanistic analysis by three-dimensional digital rock modeling

Subsurface fluid injections can disturb the effective stress regime by elevating pore pressure and potentially reactivate faults and fractures.Laboratory studies indicate that fracture rheology and permeability in such reactivation events are linked to the roughness of the fracture surfaces.In this study,we construct numerical models using discrete element method(DEM)to explore the influence of fracture surface roughness on the shear strength,slip stability,and permeability evolution during such slip events.For each simulation,a pair of analog rock coupons(three-dimensional bonded quartz particle analogs)representing a mated fracture is sheared under a velocity-stepping scheme.The roughness of the fracture is defined in terms of asperity height and asperity wavelength.Results show that(1)Samples with larger asperity heights(rougher),when sheared,exhibit a higher peak strength which quickly devolves to a residual strength after reaching a threshold shear displacement;(2)These rougher samples also exhibit greater slip stability due to a high degree of asperity wear and resultant production of wear products;(3)Long-term suppression of permeability is observed with rougher fractures,possibly due to the removal of asperities and redistribution of wear products,which locally reduces porosity in the dilating fracture;and(4)Increasing shear-parallel asperity wavelength reduces magnitudes of stress drops after peak strength and enhances fracture permeability,while increasing shear-perpendicular asperity wavelength results in sequential stress drops and a delay in permeability enhancement.This study provides insights into understanding of the mechanisms of frictional and rheological evolution of rough fractures anticipated during reactivation events.

Three-dimensional MHD flow over a shrinking sheet: Analytical solution and stability analysis

The magnetohydrodynamic（MHD） steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnetic field. The steady state problem results in a singular perturbation problem having an infinite domain singularity. The secular term appearing in the solution is removed and a two-term uniformly valid solution is derived using the Lindstedt–Poincaré technique. This asymptotic solution is validated by comparing it with the numerical solution. The solution for the unsteady problem is also presented analytically in the asymptotic limit of large magnetic field. The results of velocity profile and skin friction are shown graphically to explore the physical features of the flow field. The stability analysis of the unsteady flow is made to validate the asymptotic solution.

Influences of nonassociated flow rules on three-dimensional seismic stability of loaded slopes

The influences of soil dilatancy angle on three-dimensional （3D） seismic stability of locally-loaded slopes in nonassociated flow rule materials were investigated using a new rotational collapse mechanism and quasi-static coefficient concept. Extended Bishop method and Boussinesq theorem were employed to establish the stress distribution along the rupture surfaces that are required to obtain the rate of internal energy dissipation for the nonassociated flow rule materials in rotational collapse mechanisms. Good agreement was observed by comparing the current results with those obtained using the translational or rotational mechanisms and numerical finite difference method. The results indicate that the seismic stability of slopes reduces by decreasing the dilatancy angle for nonassociated flow rule materials. The amount of the mentioned decrease is more significant in the case of mild slopes in frictional soils. A nearly infinite slope under local loading, whether its critical failure surface is 2D or 3D, not only depends on the magnitude of the external load, but also depends on the dilataney angle of soil and the coefficient of seismic load.

Three-dimensional critical slip surface locating and slope stability assessment for lava lobe of Unzen volcano

Even Unzen volcano has been declared to be in a state of relative dormancy,the latest formed lava lobe No.11 now represents a potential slope failure mass based on the latest research.This paper concentrates on the stability of the lava lobe No.11 and its possible critical sliding mass.It proposes geographic information systems (GIS) based three-dimensional (3D) slope stability analysis models.It uses a 3D locating approach to identify the 3D critical slip surface and to analyze the 3D stability of the lava lobe No.11.At the same time,the new 3D approach shows the effectiveness in selecting the range of the Monte Carlo random variables and locating the critical slip surface in different parts of the lava lobe No.11.The results are very valuable for judging the stability of the lava lobe and assigning the monitoring equipments.

Stability analysis and modeling for the three-dimensional Darcy-Forchheimer stagnation point nanofluid flow towards a moving surface

In this research,the three-dimensional(3D)steady and incompressible laminar Homann stagnation point nanofluid flow over a porous moving surface is addressed.The disturbance in the porous medium has been characterized by the Darcy-Forchheimer relation.The slip for viscous fluid is considered.The energy equation is organized in view of radiative heat flux which plays an important role in the heat transfer rate.The governing flow expressions are first altered into first-order ordinary ones and then solved numerically by the shooting method.Dual solutions are obtained for the velocity,skin friction coefficient,temperature,and Nusselt number subject to sundry flow parameters,magnetic parameter,Darcy-Forchheimer number,thermal radiation parameter,suction parameter,and dimensionless slip parameter.In this research,the main consideration is given to the engineering interest like skin friction coefficient(velocity gradient or surface drag force)and Nusselt number(temperature gradient or heat transfer rate)and discussed numerically through tables.In conclusion,it is noticed from the stability results that the upper branch solution(UBS)is more reliable and physically stable than the lower branch solution(LBS).

Undrained Stability Analysis of Three-Dimensional Rectangular Trapdoor in Clay

A new collapse model of the trapdoors,three-dimensional rectangular trapdoor(3DRT),is presented for ground surface collapse.Undrained stability of 3DRT is examined with the upper bound method of plasticity limit analysis theory.The soil where the trapdoors are located is assumed to be a perfectly plastic model with a Tresca yield criterion.Block analysis technique is employed to investigate the collapse of 3DRT.The model is divided into five different block types and added up to ten rigid blocks.According to the law of conservation of energy,the critical stability ratios of 3DRT are obtained through a search proceeding.The results of upper bound solution for 3DRT are given,and three trapdoor models with depth various are discussed during the application in the stability analysis of square trapdoors.The critical stability ratios can be used in the design of underground excavation and support force.

Stability of an isothermal disc with three-dimensional magnetic fields and radial viscous force

The stability of an isothermal thin disk with three-dimensionalmagnetic fields and radial viscosity force is examined in this paper. We findthat the radial viscous force has no influence on stability of viscous modes. Butthere are more influence on the stability of magneto-acoustic modes, which isrelated to the perturbation wavelenth and different parts of disc .Finally, weuse our model to explain the long term variability of Quasar 3C345.

Stability of Three-Dimensional Interfacial Waves Under Subharmonic Disturbances

This study examines the stability regimes of three-dimensional interfacial gravity waves.The numerical results of the linear stability analysis extend the three-dimensional surface waves results of Ioualalen and Kharif(1994)to three-dimensional interfacial waves.An approach of the collocation type has been developed for this purpose.The equations of motion are reduced to an eigenvalue problem where the perturbations are spectrally decomposed into normal modes.The results obtained showed that the density ratio plays a stabilizing factor.In addition,the dominant instability is of three-dimensional structure,and it belongs to class I for all values of density ratio.

THREE-DIMENSIONAL SLOPE STABILITY ANALYSIS BASED ON NONLINEAR FAILURE ENVELOPE

The effects of nonlinearity of strength envelopes on 3D slope stability analysis are investigated.A power relation for the nonlinear envelope is employed to derive the 3D factor of safety equations of an extended Spencer method hich satisfies boty force equilibrium and moment equilibrium.Then,a search procedure is presented based on dynamic programming to determine the 3D critical slip surface for a general slope,Linear and nonlinear strength envelopes used for slope stability computations are obtained by fitting curves to the 103 strength data of consolidated-undrained(CU)triaxial compression tests for compacted Israeli clay.Results of a typical 3D problem show that a linear approximation of the nonlinear strength envelope may lead to a significant overestimation of calculated safety factors.

Evaluation of slope stability through rock mass classification and kinematic analysis of some major slopes along NH-1A from Ramban to Banihal, North Western Himalayas

The network of Himalayan roadways and highways connects some remote regions of valleys or hill slopes,which is vital for India’s socio-economic growth.Due to natural and artificial factors,frequency of slope instabilities along the networks has been increasing over last few decades.Assessment of stability of natural and artificial slopes due to construction of these connecting road networks is significant in safely executing these roads throughout the year.Several rock mass classification methods are generally used to assess the strength and deformability of rock mass.This study assesses slope stability along the NH-1A of Ramban district of North Western Himalayas.Various structurally and non-structurally controlled rock mass classification systems have been applied to assess the stability conditions of 14 slopes.For evaluating the stability of these slopes,kinematic analysis was performed along with geological strength index(GSI),rock mass rating(RMR),continuous slope mass rating(CoSMR),slope mass rating(SMR),and Q-slope in the present study.The SMR gives three slopes as completely unstable while CoSMR suggests four slopes as completely unstable.The stability of all slopes was also analyzed using a design chart under dynamic and static conditions by slope stability rating(SSR)for the factor of safety(FoS)of 1.2 and 1 respectively.Q-slope with probability of failure(PoF)1%gives two slopes as stable slopes.Stable slope angle has been determined based on the Q-slope safe angle equation and SSR design chart based on the FoS.The value ranges given by different empirical classifications were RMR(37-74),GSI(27.3-58.5),SMR(11-59),and CoSMR(3.39-74.56).Good relationship was found among RMR&SSR and RMR&GSI with correlation coefficient(R 2)value of 0.815 and 0.6866,respectively.Lastly,a comparative stability of all these slopes based on the above classification has been performed to identify the most critical slope along this road.

Gouge stability controlled by temperature elevation and obsidian addition in basaltic faults and implications for moonquakes

Basalt is a major component of the earth and moon crust.Mineral composition and temperature influence frictional instability and thus the potential for seismicity on basaltic faults.We performed velocitystepping shear experiments on basalt gouges at a confining pressure of 100 MPa,temperatures in the range of 100-400℃ and with varied obsidian mass fractions of 0-100%under wet/dry conditions to investigate the frictional strength and stability of basaltic faults.We observe a transition from velocity-neutral to velocity-weakening behaviors with increasing obsidian content.The frictional stability response of the mixed obsidian/basalt gouges is characterized by a transition from velocitystrengthening to velocity-weakening at 200℃ and another transition to velocity-strengthening at temperatures>300℃.Conversely,frictional strengths of the obsidian-bearing gouges are insensitive to temperature and wet/dry conditions.These results suggest that obsidian content dominates the potential seismic response of basaltic faults with the effect of temperature controlling the range of seismogenic depths.Thus,shallow moonquakes tend to occur in the lower lunar crust due to the corresponding anticipated higher glass content and a projected temperature range conducive to velocity-weakening behavior.These observations contribute to a better understanding of the nucleation mechanism of shallow seismicity in basaltic faults.