Force analysis of pile foundation in rock slope based on upper-bound theorem of limit

Based on the characteristic that the potential sliding surfaces of rock slope are commonly in the shape of either line or fold line,analysis thought of conventional pile foundation in the flat ground under complex load condition was applied and the upper-bound theorem of limit analysis was used to compute thrust of rock layers with all possible distribution shapes. The interaction of slope and pile was considered design load in terms of slope thrust,and the finite difference method was derived to calculate inner-force and displacement of bridge pile foundation in rock slope under complex load condition. The result of example shows that the distribution model of slope thrust has certain impact on displacement and inner-force of bridge pile foundation. The maximum displacement growth rate reaches 54% and the maximum moment and shear growth rates reach only 15% and 20%,respectively,but the trends of inner-force and displacement of bridge pile foundation are basically the same as those of the conventional pile foundation in the flat ground. When the piles bear the same level lateral thrust,the distribution shapes of slope thrust have different influence on inner-force of pile foundation,especially the rectangle distribution,and the triangle thrust has the smallest displacement and inner-force of pile foundation.

Upper Bound Solution of the Resisting Moment Bearing Capacity of A Composite Bucket Shallow Foundation of An Offshore Wind Turbine in Sand

Bearing the large moment that is generated by the wind load that acts on the upper structure of offshore wind turbines is an important feature of their foundations that is different from other offshore structures.A composite bucket shallow foundation(CBSF)has been proposed by Tianjin University to address the soft geological conditions in the offshore regions of China for wind turbines.The CBSF is a new type of foundation and is effective against large moments.The soil deformation test of a CBSF and the numerical simulation study under the same working conditions are carried out to determine the failure mechanism of a CBSF under moment loading.The resisting soil compression rateηm is defined as a new empirical parameter that indicates the ability of the soil inside the bucket to resist moment loading.The upper limit of the resisting moment bearing capacity of the bucket foundation is derived through the upper bound theorem of classical plasticity theory based on the failure mechanism.The calculation method is validated by tests of bucket models with different height-diameter ratios in sand under moment loading.

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 m,slope foot gradient β,height of slope H,slope top gradient α and soil bulk density γ have significant effects on the safety factor of the slope.

Upper bound solution for supporting pressure acting on shallow tunnel based on modified tangential technique

Based on the nonlinear failure criterion and the upper bound theorem, the modified tangential technique method was proposed to derive the expression of supporting pressure acting on shallow tunnel. Instead of the same stress state, different normal stresses on element boundaries were used. In order to investigate the influence of different factors on supporting pressures, the failure mechanism was established. The solution of supporting pressure, with different parameters, was obtained by optimization theory. The corresponding failure mechanism and numerical results were presented. In comparison with the results using the single tangential technique method, it is found that the proposed method is effective, and the good agreement shows that the present solution of supporting pressure is reliable.

Upper bound solutions of stability factor of shallow tunnels in saturated soil based on strength reduction technique

Based on the upper bound theorem of limit analysis,the factor of safety for shallow tunnel in saturated soil is calculated in conjunction with the strength reduction technique.To analyze the influence of the pore pressure on the factor of safety for shallow tunnel,the power of pore pressure is regarded as a power of external force in the energy calculation.Using the rigid multiple-block failure mechanism,the objective function for the factor of safety is constructed and the optimal solutions are derived by employing the sequential quadratic programming.According to the results of optimization calculation,the factor of safety of shallow tunnel for different pore pressure coefficients and variational groundwater tables are obtained.The parameter analysis shows that the pore pressure coefficient and the location of the groundwater table have significant influence on the factor of safety for shallow tunnel.

UPPER-BOUND APPROACH ANALYSIS OF DRIVING POWER OF WHEEL FOR CASTEX

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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.

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。

基于极限分析上限法的地震作用下分层地基盾构隧道开挖面稳定性研究

目前针对盾构隧道开挖面稳定性的研究还较少考虑土体分层特性和地震作用的耦合影响,因此构建了一种在分层土体中考虑地震作用的开挖面三维对数螺旋破坏模型进行研究。首先,将地震引起的动态响应通过拟静力法简化为水平和竖直两个方向上的惯性力作用;其次,在均质土体中的三维对数螺旋破坏机制的基础上,将其改进为适用于分层土体的三维对数螺旋破坏机制;再次,根据上限定理,在虚功率方程中引入地震惯性力所做功率,得到考虑土体分层特性和地震作用条件下的盾构隧道开挖面支护力的上限解;最后,将上限理论解与三维数值模拟结果和既有模型试验结果进行对比,得到了较好的一致性。此外,针对水平地震加速度系数和地层厚度对关键物理特征进行了影响因素分析。结果表明,当比例系数ζ>0时,极限支护力随水平地震加速度系数的增大显著增大;当ζ<0时,极限支护力随水平地震加速度系数增大而增大的趋势减弱。当水平地震加速度系数kh=0时,即在无地震作用情况下,归一化极限支护力不随ζ的变化而变化;在上硬下软土层中,下部土层厚度比的增大会引起极限支护力的增大,在上软下硬土层中,下部土层厚度比的增大会引起极限支护力的减小。

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。

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。

地震荷载下边坡抗滑桩有效加固区与最优加固位置理论

假设边坡滑裂面为对数螺旋曲线,应用极限分析上限定理,根据典型均质边坡的局部失稳模式,分别计算桩前和桩后坡体的局部稳定性,提出抗滑桩有效加固区理论.采用Ito理论考虑桩-土相互作用,分别计算抗滑桩加固边坡的地震安全系数、已知设计安全系数所需的最小桩径或桩间净距及其对应的所需抗力、抗力合力作用点位置和滑面以上桩长.根据计算结果结合工程的安全性、经济性和施工难度可确定合理的设计桩位,通过算例分析地震荷载和岩土物理力学参数对抗滑桩加固边坡的有效加固区的影响.

L型加筋土挡墙地震动力响应理论分析

将L型挡墙与加筋土2种柔性支挡结构相结合,充分利用其良好的抗震性能,可用于地震多发区和高烈度区的支挡工程中。研究地震荷载作用下L型加筋土挡墙的破坏机制与动力响应问题。根据第二、第三滑裂面产生条件,提出踵板长度临界系数λ_(cr),以界定长踵板式和短踵板式2种破坏模式。假设填土滑裂面为直线,应用极限分析上限定理,采用Mohr-Coulomb破坏准则,分别建立2种破坏模式下L型加筋土挡墙临界状态方程,推导其地震屈服加速度系数。根据极值原理给出最优解,得到临界屈服加速度系数及其对应的填土滑裂面倾角,分析破坏模式与临界屈服加速度系数受几何参数、物理力学参数和加筋作用的影响。通过算例分析可知:加筋作用可有效地提高L型挡墙的抗震能力,改变其破坏模式;当设计筋材拉伸强度较大时,L型加筋土挡墙只发生长踵板式破坏。

单排桩工况下软弱地基刚性桩支承路堤稳定性计算

刚性桩支承路堤的稳定性评价是近年来研究的热点和难点问题。从刚性桩桩间软弱土是否发生绕流滑动破坏的角度出发,基于Ito T塑性变形理论率先推导了路堤荷载下单排刚性桩桩身被动荷载的分布模式;以极限分析的上限定理为框架,基于单排桩支承路堤旋转破坏机构的内外功能平衡关系构建了以安全系数为目标函数的约束方程,提出了软弱地基单排刚性桩支承路堤的稳定性计算方法,并借助数值模拟验证了该方法的合理性。计算结果表明:当路堤潜在滑裂面经过单排桩时,单排桩加固位置由路堤坡趾向路堤中心移动,其安全系数总体上呈现出先增大后减小的趋势;单排桩的最大加固比受路堤堆载高度影响不大,但随着软弱地基抗剪强度的降低而增大,亦随着路堤坡率的降低而降低;单排桩的最优加固位置则受路堤堆载高度、路堤坡率以及地基内摩擦角等的影响显著,受地基土黏聚力的影响较小。研究结果为刚性桩支承路堤的稳定性计算提供了一种新的思路和理论支撑。

强降雨影响下盾构隧道开挖面稳定性的三维对数螺旋模型上限解

目前针对盾构隧道开挖面稳定性的既有成果,还较少考虑降雨环境和地下水位的影响,尤其是强降雨入渗带来的土工影响。首先,基于分层假定Green-Ampt模型来模拟强降雨入渗过程;其次,在土体抗剪强度理论和有效应力理论的基础上,将修正后的Mohr-Coulomb准则和Darcy定律结合,推导出与降雨强度和降雨历时相关的分段形式表观黏聚力表达式;然后,基于极限分析上限理论构建三维对数螺旋破坏机制,将表观黏聚力做功引入上限定理的虚功率方程,通过优化计算,得到考虑强降雨入渗和地下水位条件下盾构隧道开挖面支护力的上限解。最后,将上限解析解与三维数值模拟结果及既有试验结果进行对比,得到了较好的一致性。此外,针对降雨强度和地下水位深度等关键参数进行了影响因素分析。结果表明:当降雨强度较小时(F/ks≤1,F为平均降雨强度,ks为饱和渗透系数),隧道开挖面极限支护力随降雨强度的增大而加速增大,随降雨历时的变化不明显,当降雨强度较大时(F/ks>1),极限支护力随降雨强度的增大而缓慢增大,随降雨历时的增加而显著增大;当地下水位深度较小时(Z_(w)/D≤3,Z_(w)为地下水位深度,D为开挖直径),极限支护力随地下水位深度的增加线性减小,当地下水位深度较大时(Z_(w)/D>3),其变化速率逐渐减小,最后趋于平稳。

刚性桩复合地基稳定性计算及其图解法

刚性桩复合地基支承路堤的稳定性评价是近年来研究的热点和难点问题。本文首先从刚性桩复合地基的承载特性出发,仅考虑其竖向支承作用对路堤的稳定性贡献,通过计算桩和桩间土的荷载分担比,进而基于路堤折减荷载原理将刚性桩复合地基支承路堤的稳定性问题转化为折减路堤荷载下天然地基的稳定性问题;其次,将折减荷载后的路堤边坡视为双层土质边坡,以极限分析上限定理为框架,推导双层土质路堤边坡两段对数螺旋线滑面破坏机制下的外力功率及内部耗散功率的解析表达式,结合最优化方法与强度折减技术,藉此提出了基于折减荷载原理的刚性桩复合地基支撑路堤稳定性的快速计算方法,并基于某一具体算例将其与其他方法进行对比,验证该方法的合理性;最后,提出一种适用于路堤稳定性分析的图解法,并依托不同路堤填土工况介绍了该图解法的使用步骤与方法。研究成果为刚性桩支承路堤的稳定性计算提供了一种新的思路和理论支撑。

Weyl定理与(R)性质的判定

利用半Fredholm算子的扰动不变性,研究有界线性算子与上三角算子矩阵的Weyl型定理。首先,给出有界线性算子同时满足Browder定理和(R_(1))性质,或者同时满足Weyl定理和(R)性质的充要条件;然后,讨论上三角算子矩阵同时满足Weyl定理和(R)性质的条件。

双层土质边坡稳定性评价的解析上限法

极限分析上限法在边坡稳定性分析中广泛应用。基于极限分析上限定理,针对一般几何形状的双层土质边坡,通过建立两段对数螺旋线滑面和引入土层分界变量,推导得到该破坏机制下外力功率及内部能量耗散功率的解析式;在求解过程中构建了关于土层分界变量的函数,结合最优化方法与强度折减技术,建立了以安全系数为求解目标的且含多元变量的非线性隐式方程,借助对土层分界参数与安全系数双变量的迭代求解方法,实现了体系内外功率的精确求解,进而得到适用于双层土质边坡的简便且易于实现的上限解答。依托若干典型算例,将所得结果与其它上限法、极限平衡法以及有限元强度折减法进行了对比分析,结果表明该方法合理可行。

基于非线性Mohr–Coulomb破坏准则的浅埋倾斜条形锚板抗拔承载力预测

针对浅埋倾斜布置条形锚板抗拔承载力预测问题,本文采用非线性Mohr–Coulomb破坏准则,提出了极限上拔荷载作用下锚板上方土体的非对称曲线型破坏机制,并利用极限分析上限法与虚功率原理,导出了浅埋倾斜条形锚板极限抗拔力和土体破裂曲线的理论解析解。在此基础上,分析得到了埋深比、布设倾角、非线性系数、初始黏聚力、土体重度和地面超载等参数对锚板极限抗拔力和土体破裂范围的影响规律。研究结果显示:锚板极限抗拔力随布设倾角、埋深比、土体初始黏聚力、重度与地面超载增加而增大,但随非线性系数增加而减小;土体破裂范围随非线性系数和土体重度增加而减小,随初始黏聚力和地面超载增加而增大;锚板倾角、埋深比、土体黏聚力与非线性系数对倾斜条形锚板极限抗拔力和土体破裂范围影响较为显著,在工程设计及施工中应予以重视。将本文结果和现有研究工作进行对比分析,本文方法计算求得的锚板极限抗拔力及土体破裂范围与已有研究方法成果具有较好的吻合特性,进一步验证了本文方法的有效性。本文研究工作可为条形锚板设计及施工提供一定理论参考。

暴雨条件下含软弱夹层岩质滑坡启动的上限法研究

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