Three-dimensional upper bound limit analysis of underground cavities using nonlinear Baker failure criterion

A generalized nonlinear Baker failure criterion is employed with the upper bound limit analysis to study the surrounding rock stability of underground cavities. A three-dimensional(3D) failure mode is established by extending the two-dimensional(2D) failure mode, which offers an upper bound expression of the surrounding rock pressure. This method is validated with a series of examples before the influence of four parameters of scale parameter, curvature parameter, shift parameter and lateral pressure coefficient, on the surrounding rock pressure is analyzed. According to these results, failure ranges of the underground cavities are determined. The following conclusions are reached:(1) the proposed approach is more accurate to predict surrounding rock pressure than the Mohr-Coulomb failure criterion;(2) the surrounding rock with large scale parameter, curvature parameter, shift parameter, and lateral pressure coefficient can lead to a more stable underground cavity;(3) the failure range in 3D mode can be predicted according to the upper bound solutions.

Upper-bound limit analysis based on the natural element method

The natural element method （NEM） is a newly- developed numerical method based on Voronoi diagram and Delaunay triangulation of scattered points, which adopts natural neighbour interpolation to construct trial functions in the framework of Galerkin method. Owing to its distinctive advantages, the NEM is used widely in many problems of computational mechanics. Utilizing the NEM, this paper deals with numerical limit analysis of structures made up of perfectly rigid-plastic material. According to kinematic the- orem of plastic limit analysis, a mathematical programming natural element formulation is established for determining the upper bound multiplier of plane problems, and a direct iteration algorithm is proposed accordingly to solve it. In this algorithm, the plastic incompressibility condition is handled by two different treatments, and the nonlinearity and nons- moothness of the goal function are overcome by distinguishing the rigid zones from the plastic zones at each iteration. The procedure implementation of iterative process is quite simple and effective because each iteration is equivalent to solving an associated elastic problem. The obtained limit load multiplier is proved to monotonically converge to the upper bound of true solution. Several benchmark examples are investigated to validate the significant performance of the NEM in the application field of limit analysis.

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.

Upper bound limit analysis of roof collapse in shallow tunnels with arbitrary cross sections under condition of seepage force

The analytical solutions for predicting the exact shape of collapse mechanisms in shallow tunnels with arbitrary excavation profiles were obtained by virtue of the upper bound theorem of limit analysis and variation principle according to Hoek-Brown failure criterion. The seepage force was included in the upper bound limit analysis, and it was computed from the gradient of excess pore pressure distribution. The seepage was regarded as a work rate of external force. The numerical results of roof collapse in square and circular tunnels with different rock parameters were derived and discussed, which proves to be valid in comparison with the previous work. The influences of different parameters on the shape of collapsing blocks were also discussed.

Upper Bound Limit Analysis of Anisotropic Soils

In this paper,a novel discretization method inσ-τspace is developed to calculate the upper bound limit loads and failure modes of anisotropic Mohr-Coulomb materials.To achieve this objective,the Mohr-Coulomb yield criterion is linearized inσ-τspace,which allows for upper bound solution of soils whose cohesion and friction coefficient varying with direction.The finite element upper limit analysis formulation using the modified anisotropic yield criterion is then developed.Several examples are given to illustrate the capability and effectiveness of the proposed numerical procedure for computing rigorous upper bounds for anisotropic soils.

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.

A new failure mechanism for deep cavity and upper bound solution of supporting pressure

The investigation of supporting pressure is of great significance to the design of underground structures.Based on the kinematical approach of limit analysis,an improved failure mechanism is proposed,and the supporting pressure is investigated for deep buried cavity.Three failure mechanisms are first introduced according to the existing failure mechanisms of geotechnical structures of limit analysis.A comparison with respect to the optimal failure mechanisms and the upper bound solutions provided among these three mechanisms are then conducted in an attempt to obtain the improved failure mechanism.The results provided by the improved failure mechanism are in good agreement with those by the existing method,the numerical solution and field monitoring,which demonstrates that the proposed failure mechanism is effective for the upper bound analysis of supporting pressure.

Limit variation analysis of shallow rectangular tunnels collapsing with double-layer rock mass based on a three-dimensional failure mechanism

In the framework of upper bound theorem of limit analysis, the progressive collapse of shallow rectangular tunnels with double-layer rock mass has been theoretically analyzed based on the three-dimensional (3D) velocity discontinuity surfaces. According to the virtual work principle, the difference theorem and the variation method, the collapse surface of double-layer rock mass is determined based on the Hoek-Brown failure criterion. The formula can be degenerated to a single-layer rock collapsing problem when the rock mass is homogeneous. To estimate the validity of the result, the numerical simulation software PLAXIS 3D is used to simulate the collapse of shallow tunnels with double-layer rock mass, and the comparative analysis shows that numerical results are in good agreement with upper-bound solutions. According to the results of parametric analysis, the potential range of collapse of a double-layer rock mass above a shallow cavity decreases with a decrease in A1/A2,σci1/σci2 and σtm1/σtm2 and an increase in B1/B2,γ1/γ2. The range will decrease with a decrease in support pressure q and increase with a decrease in surface overload σs. Therefore, reinforced supporting is beneficial to improve the stability of the cavity during actual construction.

PLASTIC LIMIT ANALYSIS OF DISCONTINUOUS LINING UNDERGROUND PRESSURE

Discontinuous lining is a special form of support in underground excavation. Based on the method of plastic limit analysis, it is found the upper and the lower bound solution of the pressure of circular discontinuous lining and discussed support parameter of discontinuous lining and its applicable conditions , which provides theoretical basis for the design and calculation of discontinuous lining.

考虑水力效应的裂缝边坡稳定性非线性能耗分析

现有考虑水力效应的裂缝边坡稳定性分析大多基于线性破坏准则,而岩土体破坏往往呈现非线性特征,因此开展水力效应影响下的裂缝边坡稳定性非线性极限上限分析具有重要意义。基于极限分析上限定理及强度折减技术,结合“外切线法”非线性破坏准则,构建坡顶含竖直裂缝的边坡对数螺旋线破坏模式,根据虚功原理推导出裂缝边坡安全系数解析式,通过MATLAB优化计算,结合边坡工程实例探讨了典型因素对裂缝边坡稳定性、临界裂缝及滑动面位置的影响规律。研究结果表明:随着地下水位h的持续上升,边坡安全系数不断降低,临界裂缝深度逐渐增大且临界裂缝位置逐渐向坡顶缘偏移;非线性系数m明显影响边坡的稳定性,边坡安全系数随着非线性系数的增大显著减小,采用线性破坏准则会高估地下水位变化对边坡稳定性的影响;随着非线性系数的增大,临界裂缝深度随之增大,临界裂缝位置距离坡顶缘越来越远,滑坡体体积逐渐增大;裂缝与坡顶缘距离l m随着非线性系数m的增大而增大(当m增大0.2时,l m增大约1 m),且随着裂缝与坡顶缘距离的增大,边坡安全系数无明显变化,临界裂缝深度先逐渐减小后趋于稳定。

大截面矩形顶管施工对既有管线影响研究

顶管施工会扰动邻近建筑物,危及工程安全。该文以苏州市城北路综合管廊元和塘段顶管工程为背景,通过ABAQUS有限元分析软件建立三维模型,研究顶管下穿地下管线施工对管周土及既有管线影响,并基于极限分析方法探讨了管线失稳模式。结果表明:大直径矩形顶管顶进方向的影响范围约为2倍顶管宽度,两侧的影响范围约为1倍顶管宽度,地下管线到顶管轴线的水平距离为0.5倍~1倍顶管宽度时,应注意管线受到的水平方向附加荷载是否会导致管线破坏;管线与顶管相对位置对管线破坏影响较为显著,越靠近顶管的管线破坏越严重,滑移线由顶管两侧经由管线向地面发展,破坏部位由管线顶部两侧延伸至底部;除受与顶管相对位置影响外,管线破坏模式还受矩形顶管形状影响,管线顶部及靠近顶管顶角区域破坏风险最大。

开洞刚性墙后土体破坏模式运动单元上限分析

超载作用下开洞地下刚性连续墙后土体稳定性问题具有广泛的工程应用背景。考虑墙体矩形开洞宽度足够大,且刚性墙与土体完全光滑接触等条件,参考构造刚性多块体上限法思路,预设墙后土体极简破坏机构并转化为初始三角网格,提出交替循环式新增节点、单元缩减、对角互换及成层加密等网格更新措施,同步开展基于刚体平动运动单元上限方法的刚性墙后土体破坏分析,通过多层级非线性规划运算获得高精度临界超载系数σ_(s)/c上限解,界定墙后土体滑移线网破坏模式及其定量范围与扩展边界。进一步依前述流程计算获得多参数影响下的临界超载系数σ_(s)/c上限解图表,结果表明:1)刚性墙后土体典型破坏特征表现为土体上方和开洞处的整体下沉刚性区域,开洞前方核心区域以密集滑移线网区隔的刚性滑块群,以及外围主要滑动面;2)临界超载系数σ_(s)/c随土体内摩擦角ϕ增大而增大,且后续增幅显著增加;3)σ_(s)/c随开洞深度比C/D的增大呈现出近似线性增大的趋势;4)相较于ϕ和C/D,土体重度参数γD/c的变化对于σ_(s)/c的影响不甚明显,σ_(s)/c随γD/c增大呈现近似线性减小的趋势;5)σ_(s)/c受剪胀角参数ψ/ϕ的影响与ϕ的增大程度密切相关。本研究结果可为开洞地下刚性连续墙后土体失稳破坏模式定量分析、破坏机理研究及工程措施制定等工作提供有力的数据支持。

考虑底部塑性区的深埋隧洞围岩压力上限解

基于极限分析理论,提出一种适用于软弱围岩的深埋隧道围岩压力的计算方法。考虑隧道底部塑性变形区的影响,构建纺锤形的破坏模型。基于该破坏模型构建围岩速度场,引入侧压系数λ_(1)和底压系数λ_(2),推导围岩压力的理论计算公式。根据计算公式进行编程优化计算,分析不同非线性系数m下,侧压系数λ_(1)、底压系数λ_(2)对围岩压力的影响。研究结果表明:随着内摩擦角减小,“纺锤”上下两端塑性区不断向外延伸;非线性系数m对围岩压力有显著影响,当非线性系数一致时,提高侧压系数λ_(1)可以降低拱顶和隧道底部压力,提高底压系数λ_(2)可以降低拱顶和边墙压力;在岩土体非线性特征明显的地区,计算深埋隧洞围岩压力时应考虑底部塑性区。

考虑基质吸力影响的非饱和路堤三维稳定性上限分析

采用极限上限分析定理构建了路堤失稳的三维旋转破坏机构,继而根据Bishop非饱和土抗剪强度理论,考虑非饱路堤内部基质吸力的空间分布及其随地下水位的变化,建立了路堤破坏土体外力功率与内部能量耗散功率的能量守恒方程,并利用遗传算法编写了非饱和路堤最小上限解的高效搜索算法。通过将非饱和土路堤基底破坏模式退化为边坡破坏模式,并与现有非饱和土边坡稳定性计算结果对比,验证了所提上限解的正确性和遗传搜寻算法的准确性。进一步地,对路堤三维稳定性的关键影响因素展开了系统分析,研究了路堤填土孔径分布、基质吸力、进气值倒数、路堤倾角以及有效内摩擦角等因素对路堤三维稳定性的影响规律。研究表明,非饱和土质路堤的稳定性不仅取决于路堤填土性质,而且依赖于影响土体吸力大小与分布的填土孔径参数和进气值等因素。地下水位升降引起的基质吸力变化对路堤稳定性存在显著影响。研究结果为路堤稳定性精细化分析提供了重要的理论依据。

基于极限分析理论的复合地层中双模盾构开挖面稳定性研究

针对目前双模式盾构在复合地层土-岩交界面进行掘进模式转换过程中掘进面稳定性研究中存在的问题,采用空间离散技术构建双模式盾构在穿越土-岩交界面过程中开挖面前方岩土体的二维破坏机制,利用该破坏机制和极限分析上限定理推导得到极限状态下土舱压力的目标函数,通过优化计算得到盾构机在穿越土-岩交界面过程中维持开挖面稳定所需的土舱压力上限解,并讨论不同参数对土舱压力及开挖面前方岩土体破坏模式的影响。在此基础上,基于可靠度理论建立土舱压力的可靠度模型,并给出复合地层中容许可靠度下维持开挖面稳定性最小土舱压力的建议值。结果表明:盾构机在穿越土-岩交界面过程中维持开挖面稳定所需的土舱压力随着盾构机与土-岩交界面距离的减小而减小;开挖面前方岩土体的破坏范围随着界面倾角的增大而增大。

海啸作用下滨水挡土墙抗震滑动稳定性上限分析

针对沿海地区滨水挡土墙在海啸和地震联合作用下易发生被动破坏的问题,结合极限分析上限法和拟静力法确定地震荷载,研究了海啸作用下滨水挡土墙的抗震滑动稳定性。通过建立墙体滑动与破坏区土楔体整体滑动的墙-土系统及速度容许场,推导出水平地震加速度系数(kh)的表达式。分析了海啸、海平面与地下水高度及墙-地和墙-土摩擦角对地震屈服加速度系数的影响。结果表明,控制地下水位在适当高度并增大墙-土摩擦角可以有效提高滨水挡土墙的抗震滑动稳定性。与经典极限平衡理论相比,该方法考虑了土体的塑性流动及挡土墙的位移模式,且无需计算地震被动土压力的值。

地震作用下双层土质边坡稳定性上限分析

为探究地震作用对双层土质边坡稳定性的影响,基于极限分析上限理论,建立了地震作用下双层土质边坡旋转破坏机构。采用拟静力法简化地震荷载作用,推导了双层土质边坡安全系数表达式。分析土体黏聚力比、边坡坡角以及地震作用对双层土质边坡稳定性及其滑动面参数的影响。研究结果表明:在水平地震作用下,随着黏聚力比的增大,边坡安全系数呈非线性增大且潜在滑动面变浅;当水平地震作用增强时,边坡失稳破坏范围显著加大;随着竖向地震系数及黏聚力比的增大,边坡安全系数略微降低;水平地震作用增强时,竖向地震作用对边坡稳定性的影响逐渐增大,此时需要考虑竖向地震的影响。

含挖填界面边坡三维稳定性上限分析

针对工程实践中挖填交界面与边坡坡面走向线斜交的高边坡空间三维稳定分析问题,基于极限分析上限定理,构建拓展的三维牛角状破坏机构,通过引入机构参数挖填界面倾角α突出边坡特性,建立与之对应的功能平衡方程,采用序列二次规划优化算法求解强度折减后的边坡安全系数上限解。在此基础上,计算了宁夏黄土丘陵地区妙岭750kV变电站高边坡以及相关文献中极限状态下边坡稳定性系数γH/c工程案例,并将计算结果与有限元极限分析软件模拟值进行对比分析。结果表明:随着挖填界面倾角α的增大,边坡安全系数Fs上限解和模拟值均减小,两种方法的计算结果相对误差在5.9%以内,且拓展的破坏机构与数值模拟的剪切耗散变形模式基本一致;在极限状态下,拓展机构的上限解和数值模拟结果都十分接近于1.0,二者相对误差未超过8.3%。研究工作为此类高边坡空间稳定分析问题提供了一种简便实用的计算方法。

基于多对数螺旋曲线破坏机构的富水软岩隧道开挖面支护应力分析

为了避免对胡克-布朗准则进行任何线性化处理,将广义胡克-布朗(generalized Hoek-Brown, GHB)强度准则直接引入到开挖面稳定性分析中,基于极限分析理论构建了富水地层浅埋隧道开挖面多对数螺旋线破坏机构。在考虑孔隙水压力的作用下,推导出能量平衡方程,得到开挖面极限支护应力表达式,并且通过程序优化得到支护应力最优上限解。在此基础上,分析了GHB强度参数、孔隙水压力系数、岩土体重度以及隧道埋深比对开挖面稳定性的影响。最后通过归一化处理得到不同情况下的开挖面极限支护应力稳定性图表,通过该图表能够快速便捷地获得富水地层隧道开挖面维持稳定性所需的极限支护应力,为盾构隧道初步设计提供理论依据。

基于多块体上限法的层状珊瑚砂地基承载力分析

为研究层状珊瑚砂地基承载能力,基于极限分析上限理论,构建了适用于层状砂土的多块体破坏机构,推导了外力功率与内能耗散率的计算公式.采用序列二次规划优化算法,建立了层状珊瑚砂地基极限承载力的上限分析方法.通过与现有研究成果的对比分析,验证了所建立方法的有效性,所构建的破坏机构突破了现有分层地基破坏机构下层必须为黏土的局限.结果表明,当破坏机构穿过不同层状地层时,基于层状地基模型与均质地基模型计算得到的地基承载力和临界破坏机构有显著不同,因此有必要考虑不同分层性质.相比于地基载荷试验,所提出的上限分析方法通过调整不同地层土体参数,能够快速得到地基承载力上限值,为珊瑚砂地基设计提供参考.