Upper bound analysis of ultimate pullout capacity of shallow 3-D circular plate anchors based on nonlinear Mohr-Coulomb failure criterion

Based on the nonlinear Mohr-Coulomb failure criterion and the associated flow rules,the three-dimensional(3-D)axisymmetric failure mechanism of shallow horizontal circular plate anchors that are subjected to the ultimate pullout capacity(UPC)is determined.A derivative function of the projection function for projecting the 3-D axisymmetric failure surface on plane is deduced using the variation theory.By using difference principle,the primitive function of failure surface satisfying boundary condition and numerical solution to its corresponding ultimate pullout capacity function are obtained.The influences of nonlinear Mohr-Coulomb parameters on UPC and failure mechanism are studied.The result shows that UPC decreases with dimensionless parameter m and uniaxial tensile strength increases but increases when depth and radius of plate anchor,surface overload,initial cohesion,geomaterial density and friction angle increase.The failure surface is similar to a symmetrical spatial funnel,and its shape is mainly determined by dimensionless parameter m;the surface damage range expands with the increase of radius and depth of the plate anchor as well as initial cohesion but decreases with the increase of dimensionless parameter m and uniaxial tensile strength as well as geomaterial density.As the dimensionless parameter m=2.0,the numerical solution of UPC based on the difference principle is proved to be feasible and effective through the comparison with the exact solution.In addition,the comparison between solutions of UPC computed by variation method and those computed by upper bound method indicate that variation method outperforms upper bound method.

Upper bound solutions for supporting pressures of shallow tunnels with nonlinear failure criterion

Linear failure criterion is widely used in calculation of earth pressure acting on shallow tunnels. However, experimental evidence shows that nonlinear failure criterion is able to represent fairly well the failure of almost all types of rocks, A nonlinear Hock-Brown failure criterion is employed to estimate the supporting pressures of shallow tunnels in limit analysis framework. Two failure mechanisms are proposed for calculating the work rate of extemal force and the internal energy dissipation. A tangential line to the nonlinear failure criterion is used to formulate the supporting pressure problem as a nonlinear programming problem. The objective function formulated in this way is minimized with respect to the failure mechanism and the location of tangency point. In order to assess the validity, the supporting pressures for the proposed failure mechanisms are calculated and compared with each other, and the present results are compared with previously published solutions when the nonlinear criterion is reduced to linear criterion. The agreement supports the validity of the proposed failure mechanisms. An experiment is conducted to investigate the influences of the nonlinear criterion on collapse shape and supporting pressures of shallow tunnels.

Upper bound analysis of slope stability with nonlinear failure criterion based on strength reduction technique

Based on the upper bound limit analysis theorem and the shear strength reduction technique, the equation for expressing critical limit-equilibrium state was employed to define the safety factor of a given slope and its corresponding critical failure mechanism by means of the kinematical approach of limit analysis theory. The nonlinear shear strength parameters were treated as variable parameters and a kinematically admissible failure mechanism was considered for calculation schemes. The iterative optimization method was adopted to obtain the safety factors. Case study and comparative analysis show that solutions presented here agree with available predictions when nonlinear criterion reduces to linear criterion, and the validity of present method could be illuminated. From the numerical results, it can also be seen that nonlinear parameter rn, slope foot gradient ,β, height of slope H, slope top gradient a and soil bulk density γ have significant effects on the safety factor of the slope.

Energy analysis of rock plug thickness in karst tunnels based on non-associated flow rule and nonlinear failure criterion

The geological hazards, such as water inrush and mud outburst, are easily induced by the high water pressure caverns ahead of a karst tunnel face. Therefore, it is a pivotal issue to determine the reserved thickness of rock plug during the construction of tunnels. The limit analysis principle is employed to analyze the safe thickness from the point of energy dissipation, and the nonlinear and non-associated characteristics of geotechnical materials are both considered. On the basis of a plane failure pattern of rock plug, the expressions of detaching curve and rock plug thickness are derived. The effect of each parameter on the safe thickness of rock plug is discussed in detail, which interprets the corresponding failure scope of rock plug. The obtained results indicate that the thickness of rock plug is highly influenced by the nonlinear dilatancy coefficient and the nonlinear coefficient. The proposed method is validated by a comparison of the calculated results with those of the engineering project of the "526 karst cavern" of Yunwushan tunnel. This proposed method can provide reference basis for the design and excavation of karst tunnels in the future.

Kinematical analysis of highway tunnel collapse using nonlinear failure criterion

For different kinds of rocks,the collapse range of tunnel was studied in the previously published literature.However,some tunnels were buried in soils,and test data showed that the strength envelopes of the soils followed power-law failure criterion.In this work,deep buried highway tunnel with large section was taken as objective,and the basic expressions of collapse shape and region were deduced for the highway tunnels in soils,based on kinematical approach and power-law failure criterion.In order to see the effectiveness of the proposed expressions,the solutions presented in this work agree well with previous results if the nonlinear failure criterion is reduced to a linear Mohr-Coulomb failure criterion.The present results are compared with practical projects and tunnel design code.The numerical results show that the height and width of tunnel collapse are greatly affected by the nonlinear criterion for the tunnel in soil.

Safe retaining pressures for pressurized tunnel face using nonlinear failure criterion and reliability theory

Based on the active failure mechanism and passive failure mechanism for a pressurized tunnel face, the analytical solutions of the minimum collapse pressure and maximum blowout pressure that could maintain the stability of pressurized tunnel faces were deduced using limit analysis in conjunction with nonlinear failure criterion under the condition of pore water pressure. Due to the objective existence of the parameter randomness of soil, the statistical properties of random variables were determined by the maximum entropy principle, and the Monte Carlo method was employed to calculate the failure probability of a pressurized tunnel. The results show that the randomness of soil parameters exerts great influence on the stability of a pressurized tunnel, which indicates that the research should be done on the topic of determination of statistical distribution for geotechnical parameters and the level of variability. For the failure probability of a pressurized tunnel under multiple failure modes, the corresponding safe retaining pressures and optimal range of safe retaining pressures are calculated by introducing allowable failure probability and minimum allowable failure probability. The results can provide practical use in the pressurized tunnel engineering.

Upper bound solution of surrounding rock pressure of shallow tunnel under nonlinear failure criterion

The nonlinear Baker failure criterion is introduced into the upper-bound limit analysis to examine the face stability of a shallow tunnel. The tunnel face under the ultimate limit state is analyzed from the perspective of energy balance. The work rates of external forces and internal energy dissipation are calculated. An analytical solution of necessary face pressures is derived. The optimal upper-bound solution of the face pressures is obtained by optimization. The results show that the three dimensionless parameters A, T, n of nonlinear Baker failure criterion have different effects on the necessary face pressures and the pattern failure mechanisms ahead of tunnel face. A is the most important one;n takes the second place, and T is the least one. The computed necessary face pressures are nonlinearly increasing when A is reduced. Combined with the actual monitoring data of Taxia tunnel, the calculation results in this paper is verified. It is suggested that the tunnel face supports should be strengthened timely in soft rocks to prevent the occurrence of face collapse.

Variation analysis of ultimate pullout capacity of shallow horizontal strip anchor plate with 2-layer overlying soil based on nonlinear M-C failure criterion

Based on the nonlinear Mohr-Coulomb failure criterion and an associated flow rule,a kinematic admissible velocity field of failure mechanism of the 2-layer soil above a shallow horizontal strip anchor plate is constructed.The ultimate pull-out force and its corresponding failure mechanism through the upper bound limit analysis according to a variation principle are deduced.When the 2-layer overlying soil is degraded into single-layer soil,the model of ultimate pullout force could also be degraded into the model of single-layer soil.And the comparison between results of single-layer soil variation method and those calculated by rigid limit analysis method proves the correctness of our method.Based on that,the influence of changes of geotechnical parameters on ultimate pullout forces and failure mechanism of a shallow horizontal strip anchor with the 2-layer soil above are analyzed.The results show that the ultimate pull-out force and failure mechanism of a shallow horizontal strip anchor with the 2-layer soil above are affected by the nonlinear geotechnical parameters greatly.Thus,it is very important to obtain the accurate geotechnical parameters of 2-layer soil for the evaluation of the ultimate pullout capacity of the anchor plate.

Energy analysis of stability of twin shallow tunnels based on nonlinear failure criterion

Based on nonlinear Mohr-Coulomb failure criterion, the analytical solutions of stability number and supporting force on twin shallow tunnels were derived using upper bound theorem of limit analysis. The optimized solutions were obtained by the technique of sequential quadratic programming. When nonlinear coefficient equals 1 and internal friction angle equals 0, the nonlinear Mohr-Coulomb failure criterion degenerates into linear failure criterion. The calculated results of stability number in this work were compared with previous results, and the agreement verifies the effectiveness of the present method. Under the condition of nonlinear Mohr-Coulomb failure criterion, the results show that the supporting force on twin shallow tunnels obviously increases when the nonlinear coefficient, burial depth, ground load or pore water pressure coefficients increase. When the clear distance is 0.5to 1.0 times the diameter of tunnel, the supporting force of twin shallow tunnels reaches its maximum value, which means that the tunnels are the easiest to collapse. While the clear distance increases to 3.5 times the diameter of tunnel, the calculation for twin shallow tunnels can be carried out by the method for independent single shallow tunnel. Therefore, 3.5 times the diameter of tunnel serves as a critical value to determine whether twin shallow tunnels influence each other. In designing twin shallow tunnels,appropriate clear distance value must be selected according to its change rules and actual topographic conditions, meanwhile, the influences of nonlinear failure criterion of soil materials and pore water must be completely considered. During the excavation process, supporting system should be intensified at the positions of larger burial depth or ground load to avoid collapses.

Validation of Hoek-Brown failure criterion charts for rock slopes

Although stability charts suggested by Hoek and Bray on the basis of Mohr-Coulomb criterion are used for rock slopes,but complete and precise recognition is required for distinguishing cohesive strength and Mohr-Coulomb equivalent internal friction angle for rock mass.The paper by Lia et al.[6]is the only one that introduced rock slope charts according to Hoek-Brown failure criterion.In this paper,at first,this type of charts is introduced.Then,Mohr-Coulomb failure criterion charts[2]are compared and validated with Hoek-Brown failure criterion ones[6].Next,Bishop method utilizing Slide software is compared with Hoek-Brown failure criterion stability charts.Average standard deviation(ASD),root mean square error(RMSE)and variance account for(VAF)were used for the comparison.According to the results,because of high distribution and very low correlation among the comparisons,Hoek-Brown failure criterion charts are not efficient.

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.

Modified Mohr-Coulomb strength criterion considering rock mass intrinsic material strength factorization

With the increase of mining depth of mineral resources,the rock mass stress state is being more and more complex.The rock mass show different features,namely,with the increase of hydrostatic pressure,rock mass failure mode turns from brittle tension failure to structure ductile failure and its limit strength also increases.The restriction of minimal principal stress on the initiation and development of microcrack and the change of micro-unit stress state by the intermediate principal stress play a decisive role in the increase of rock mass limit strength.Based on the rock mass failure behavior law under complex stress state and the σ2-dependence on the rock mass strength,we proposed a Modified Mohr-Coulomb(M-MC) strength criterion which is smooth and convex.Finally,the M-MC criterion is validated by multiaxial test data of eight kinds of rock mass.We also compared the fitting results with Mohr-Coulomb criterion(MC).It shows that the new criterion fits the test data better than the Mohr-Coulomb criterion.So the M-MC strength criterion well reveals the rock mass bearing behavior and can be widely used in the rock mass strength analysis.The results can provide theoretical foundations for stability analysis and reinforcement design of complex underground engineering.

System reliability analysis of seismic pseudo-static stability of rock wedge based on nonlinear Barton–Bandis criterion

Based on the nonlinear Barton–Bandis(B–B)failure criterion,this study considers the system reliability of rock wedge stability under the pseudo-static seismic load.The failure probability(Pf)of the system is calculated based on the Monte−Carlo method when considering parameter correlation and variability.Parameter analysis and sensitivity analysis are carried out to explore the influence of parameters on reliability.The relationships among the failure probability,safety factor(Fs),and variation coefficient are explored,and then stability probability curves of the rock wedge under the pseudo-static seismic load are drawn.The results show that the parameter correlation of the B–B failure criterion has a significant influence on the failure probability,but correlation increases system reliability or decreases system reliability affected by other parameters.Under the pseudo-static seismic action,sliding on both planes is the main failure mode of wedge system.In addition,the parameters with relatively high sensitivity are two angles related to the joint dip.When the coefficient of variation is consistent,the probability of system failure is a function of the safety factor.

Establishment of tensile failure induced sanding onset prediction model for cased-perforated gas wells

Sand production is a challenging issue in upstream oil and gas industry,causing operational and safety problems.Therefore,before drilling the wells,it is essential to predict and evaluate sanding onset of the wells.In this paper,new poroelastoplastic stress solutions around the perforation tunnel and tip based on the Mohr-Coulomb criterion are presented firstly.Based on the stress models,a tensile failure induced sanding onset prediction model for cased-perforated gas wells is derived.Then the analytical model is applied to field data to verify its applicability.The results from the perforation tip tensile failure induced sanding model are very close to field data.Therefore,this model is recommended for forecasting the critical conditions of sand production analysis.Such predictions are necessary for providing technical support for sand control decision-making and predicting the production condition at which sanding onset occurs.

基于非线性Mohr-Coulomb强度准则下锚索极限抗拔力研究

根据预应力锚索破裂面的形状参数方程、非线性Mohr-Coulomb强度准则和极限平衡原理,推导出一个能够考虑锚索破裂面形状、岩土体种类、抗拉强度以及围岩压力和灌浆压力等因素的预应力锚索极限抗拔承载力计算公式。理论计算结果和算例分析表明了该理论及其求解方法的有效性和可靠性。

考虑孔隙水压力及非线性Mohr-Coulomb破坏准则下浅埋土质隧道三维塌落机制的上限分析

浅埋土质隧道的稳定性研究一直是隧道工程的关键问题,而孔隙水压力的存在影响着浅埋土质隧道的安全。构建了隧道顶部为圆弧形的浅埋土质隧道的三维塌落机制,基于非线性Mohr-Coulomb破坏准则和极限分析上限法,并考虑孔隙水压力的作用,推导出浅埋土质隧道的塌落范围及支护力的最优上限解计算公式。通过与既有研究进行对比,验证了所提方法的合理性。分析了不同参数对塌落范围、塌落土体的重力及支护力的影响,结果表明:孔隙水压力对浅埋土质隧道的塌落范围、塌落土体的重力及支护力有着显著的影响;孔隙水压力对塌落范围、塌落土体重力的影响比较复杂,而支护力都随着孔隙水压力系数的增大而增大;不同参数对浅埋土质隧道的塌落范围、塌落土体的重力及支护力的影响规律不同。新方法可为浅埋土质隧道的设计优化提供理论支撑。

基于非线性Mohr-Coulomb准则的刚性条形基础下伏孔洞承载特性变分分析

基于非线性Mohr-Coulomb(MC)破坏准则以及相关流动法则,构建刚性条形基础下伏孔洞冲切破坏机制;结合变分原理,推导出刚性条形基础下伏孔洞冲切破坏曲线的表达式,进而得到冲切破坏时的极限承载力。分析刚性基础随岩土体参数变化时,冲切破坏极限承载力的变化情况和破坏模式。研究结果表明:非线性系数m的大小对刚性基础极限承载力的影响较为显著。随着非线性系数m的增大,刚性基础极限承载力不断减小;极限承载力随岩土体初始黏聚力C0的增大而增大,随岩土体重度以及抗拉强度的增大而减小。岩溶顶板冲切破坏宽度随初始黏聚力C0的增大、重度的减小以及抗拉强度的减小而增大。

运用非线性Mohr-Coulomb破坏准则分析尾矿坝稳定性

为了获得尾矿坝上限安全系数,采用切线法将非线性Mohr-Coulomb破坏准则与极限分析上限法相结合,基于尾矿坝对数螺旋破坏模式,建立了基于极限分析上限定理的尾矿坝非线性安全系数上限分析模型。以某尾矿坝为工程背景,求解得到了不同非线性系数和抗拉强度下的安全系数。结果表明,尾矿坝的安全系数随着非线性系数和抗拉强度的增大,呈递减趋势。在满足尾矿坝设计安全的前提下,运用尾矿坝上限非线性安全系数数学模型,反演设计参数,根据反演结果可优化设计方案。

Combined influence of nonlinearity and dilation on slope stability evaluated by upper-bound limit analysis

The combined influence of nonlinearity and dilation on slope stability was evaluated using the upper-bound limit analysis theorem.The mechanism of slope collapse was analyzed by dividing it into arbitrary discrete soil blocks with the nonlinear Mohr–Coulomb failure criterion and nonassociated flow rule.The multipoint tangent(multi-tangent) technique was used to analyze the slope stability by linearizing the nonlinear failure criterion.A general expression for the slope safety factor was derived based on the virtual work principle and the strength reduction technique,and the global slope safety factor can be obtained by the optimization method of nonlinear sequential quadratic programming.The results show better agreement with previous research result when the nonlinear failure criterion reduces to a linear failure criterion or the non-associated flow rule reduces to an associated flow rule,which demonstrates the rationality of the presented method.Slope safety factors calculated by the multi-tangent inclined-slices technique were smaller than those obtained by the traditional single-tangent inclined-slices technique.The results show that the multi-tangent inclined-slices technique is a safe and effective method of slope stability limit analysis.The combined effect of nonlinearity and dilation on slope stability was analyzed,and the parameter analysis indicates that nonlinearity and dilation have significant influence on the result of slope stability analysis.

Slope stability analysis considering joined influences of nonlinearity and dilation

The soil masses of slopes were assumed to follow a nonlinear failure criterion and a nonassociated flow rule.The stability factors of slopes were calculated using vertical slice method based on limit analysis.The potential sliding mass was divided into a series of vertical slices as well as the traditional slice technique.Equating the external work rate to the internal energy dissipation,the optimum solutions to stability factors were determined by the nonlinear programming algorithm.From the numerical results,it is found that the present solutions agree well with previous results when the nonlinear criterion reduces to the linear criterion,and the nonassociated flow rule reduces to the associated flow rule.The stability factors decrease by 39.7%with nonlinear parameter varying from 1.0 to 3.0.Dilation and nonlinearity have significant effects on the slope stability factors.