下限原理在岩土工程中的应用

采用极限分析下限原理求解了岩土工程中基础的极限载力和边坡的安全系数。求解过程中把有限元法和非线性规划相结合,把整个结构离散化,设定每个结点的应力,把原问题变成一个以边坡的稳定安全系数或基础的极限承载力为目标函数,以结点应力为优化变量,以对可静应力场的各种制约为约束条件的非线性规划问题。采用序列二次规划法求解该非线性规划问题,得到了人为构造的严格满足应力边界条件、平衡微分方程、不违反Mohr-Coulomb或Drucker-Prager屈服准则的应力场,解决了三维可静应力场的构造问题。算例分析表明,本文的方法是正确、可行的。     

岩土中的剪切带局部化问题研究:回顾与展望

回顾了圆弧滑动面理论的产生及其在土坡抗滑动稳定分析和极限承载力计算中的应用，并指出了圆弧滑动面理论和刚塑性理论及极限平衡条件的关系及其局限性。介绍了剪切带局部化问题的研究现状，包括一些热点研究领域和最新研究成果。着重介绍了用子负荷面模型模拟超固结黏性土剪切带局部化和用动态剪切带单元模拟摩尔一库仑材料剪切带局部化的最新研究成果。对剪切带局部化问题研究提出了几个主要发展方向。     

Bearing capacity analysis using the method of characteristics

Using the method of characteristics,the bearing capacity for a strip footing is analyzed.The method of characteristics leads to an exact true limit load when the calculations of the three terms in the bearing capacity formula are consistent with one collapse mechanism and the soil satisfies the associated flow rule.At the same time,the method of characteristics avoids the assumption of arbitrary slip surfaces,and produces zones within which equilibrium and plastic yield are simultaneously satisfied for given boundary stresses.The exact solution without superposition approximation can still be expressed by Terzaghi's equation of bearing capacity,in which the bearing capacity factor N γλ is dependent on the dimensionless parameter λ and the friction angle φ.The influence of groundwater on the bearing capacity of the shallow strip footing is considered,which indicates that when the groundwater effect is taken into account,the error induced by the superposition approximation can be reduced as compared with dry soil condition.The results are presented in the form of charts which give the modified value(Nwγλc /Nγλc) of bearing capacity factor.Finally,an approximated analytical expression,which provides results in close agreement with those obtained by numerical analysis in this paper,has been suggested for practical application purposes.     

Confining effect on the bearing capacity of circular footings on a purely cohesive soilEffet du confinement sur la capacité portante d'une fondation circulaire sur un sol purement cohérent

The bearing capacity of axially symmetrical footings acting on a purely cohesive soil foundation contained by a rigid wall at a finite distance is investigated within the framework of the Yield design theory. Following the same tracks as in a preceding paper devoted to strip footings, the analysis is performed by referring to already existing results concerning the bearing capacity of a circular footing on a soil layer with limited thickness. It comes out that the bearing capacity factor determined by Eason and Shield for a rough circular footing on an unlimited soil foundation is increased by a correction factor that increases when the diameter of the container decreases. Comparison with the results obtained for strip footings acting on a purely cohesive soil in the same conditions shows that the confining effect is significantly lower for a circular footing than for a strip footing. To cite this article: J. Salençon, C. R. Mecanique 330 (2002) 521–525.     

The influence of confinement on the bearing capacity of strip footingsEffet du confinement sur la capacité portante d'une fondation superficielle

The bearing capacity for a strip footing acting on a soil foundation with rigid boundaries at a finite distance is investigated within the framework of the Yield design theory both for a purely cohesive soil and for a frictional soil. It is shown that the analysis can be performed simply by referring to already existing results concerning the bearing capacity of a strip footing on a soil layer with limited thickness. Each bearing capacity factor in Terzaghi formula is increased by a factor that increases when the distance of the rigid boundary to the edge of the footing decreases. The bearing capacity is proved to be the more sensitive to this confining effect as the friction angle of the soil increases. From a physical point of view this theoretical analysis would show that, when effective, confinement reduces the depth of the soil layer involved in the collapse mechanism. To cite this article: J. Salençon, C. R. Mecanique 330 (2002) 319–326.     

复杂条件下地基承载力系数N_γ的上限解

由地基土重量引起的地基承载力系数N_γ的真实解答至今尚未获取．本文根据极限分析法与极限平衡法的等效性,构造出最危险的运动许可滑动机构,得出N_γ尽可能小的上限解．分别定量分析了在荷载倾斜、基底倾斜、地表倾斜对N_γ的影响,提出了近似影响系数公式,并与现有研究结果进行比较．     

混凝土分段曲线损伤模型

在对比分析国内外现有的混凝土受拉损伤模型基础上，结合素混凝土受拉应力应变曲线的试验结果，提出了一个新的混凝土分段曲线损伤模型，并利用应力连续条件确定了损伤模型中各系数的值。运用该模型到力学分析中，推导了矩形截面的混凝土梁在纯弯矩作用下，在损伤较小和损伤较大时的力学方程，算出了梁的最大承载能力，并与材料力学计算的梁承载能力进行了对比。详细分析了损伤区域及损伤应力在横截面上的变化过程，确定了极限状态下含损伤混凝土梁的应力分布和相应的承载能力，画出了损伤状态梁截面的应力分布图。     

Compression analysis of rectangular elastic layers bonded between rigid plates

An elastic layer bonded between two rigid plates has higher compression stiffness than the elastic layer without bonding. While the finite element method can be applied to calculate the stiffness, the compression stiffness of bonded rectangular layers derived through a theoretical approach in this paper provides a convenient way for parametric study. Based on two kinematics assumptions, the governing equation for the mean pressure is derived from the equilibrium equations. Using the approximate shear boundary condition, the mean pressure is solved and the compression stiffness of the bonded rectangular layer is then established in an explicit single-series form. Through the solved pressure, the horizontal displacements are derived from the corresponding equilibrium equations, from which the shear stress on the bonding surface can be found. It is found that the effect of the rectangular aspect on the compression stiffness is significant only when Poisson’s ratio is near 0.5. For the smaller Poisson’s ratio, the compression stiffness of the rectangular layer can be approximated by the formula for the infinite-strip layer of the same shape factor.     

A direct approach to fiber and membrane reinforced bodies. Part II. Membrane reinforced bodies

The paper deals with membrane reinforced bodies with the membrane treated as a two-dimensional surface with concentrated material properties. The bulk response of the matrix is treated separately in two cases: (a) as a coercive nonlinear material with convex stored energy function expressed in the small strain tensor, and (b) as a no-tension material (where the coercivity assumption is not satisfied). The membrane response is assumed to be nonlinear in the surface strain tensor. For the nonlinear bulk response in Case (a), the existence of states of minimum energy is proved. Under suitable growth conditions, the equilibrium states are proved to be exactly states of minimum energy. Then, under appropriate invertibility condition of the stress function, the principle of minimum complementary energy is proved for equilibrium states. For the no-tension material in Case (b), the principle of minimum complementary energy (in the absence of the invertibility assumption) is proved. Also, a theorem is proved stating that the total energy of the system is bounded from below if and only if the loads can be equilibrated by a stress field that is statically admissible and the bulk stress is negative semidefinite. Two examples are given. In the first, we consider the elastic semi-infinite plate with attached stiffener on the boundary (Melan’s problem). In the second example, we present a stress solution for a rectangular panel with membrane occupying the main diagonal plane.     

Slip-line field solution for ultimate bearing capacity of a pipeline on clay soils

A slip-line field solution is presented for the ultimate bearing capacity of the pipeline on a purely-cohesive clay soil, taking into account of circular configuration of the pipe, the pipe embedment, and the pipe-soil interfacial cohesion. The derived bearing capacity factors for a smooth rigid pipe may degenerate into those for the conventional rectangular-shaped strip footing while the pipe embedment approaches zero. Parametric studies indicate that, the pipe-soil interfacial properties have much influence on the bearing capacity for the pipe foundation on clayedy soils.     

锈蚀钢筋混凝土双筋矩形梁抗弯承载力分析

钢筋锈蚀是钢筋混凝土桥梁的主要病害之一。在锈蚀钢筋混凝土双筋矩形截面梁中,钢筋锈蚀易造成结构性能退化,并引起钢筋和混凝土相对滑移,导致结构的承载力降低,受拉区的钢筋与混凝土变形不协调。通过构造新的几何条件,推导了锈蚀钢筋混凝土双筋矩形梁正截面极限抗弯承载力计算公式。对室内快速锈蚀双筋矩形梁进行正截面抗弯承载力实验,结果表明推导的锈后双筋矩形梁正截面抗弯承载力公式的计算值与实验值吻合较好。上述工作为进一步进行工程实践奠定了基础。     

Bearing capacity of strip footings with horizontal confinementLa capacité portante des fondations superficielles en présence de parois rigides

For a strip footing under axial loading, the bearing capacity is influenced by the presence of rigid walls confining the foundation soil. This problem is investigated within the framework of the theory of yield design, considering both a perfectly rough and a frictionless contact condition at the interfaces with the walls in the case of a purely cohesive soil. Upper bounds for the correction factor to be applied to the classical value of the bearing capacity are determined, as functions of the non-dimensional geometric parameter of the problem, through the kinematic approach, implementing virtual velocity fields inspired from the solution to the problem of inverted extrusion. In the perfectly rough case, it appears that the new upper bound is a significant improvement of those already available. A very simple relationship is established, which derives the upper bound for the frictionless walls from the upper bound for the rough walls. A general conclusion of the analysis is that, for the values of the geometric parameter that are likely to be encountered in practice, the increase in the bearing capacity due to the presence of the rigid walls remains very small. To cite this article: J. Salençon, C. R. Mecanique 331 (2003).     

带裂纹矩形板自由振动解析解

选取带有补充项的双重正弦傅里叶级数作为振型函数通解,来解析研究带裂纹矩形板的自由振动特性。先将带裂纹矩形板分割成若干小矩形板,利用各小矩形板的边界条件,并结合振型函数中待定常数的物理意义,简化得到各小矩形板的振型函数,再结合各板的控制方程、未使用的边界条件、公共边协调条件及本文提出公共自由角点的协调条件,建立求解频率的代数方程组,然后将其转化为广义特征值问题来求解带裂纹矩形板的无量纲频率;最后选取具体参数进行计算并与文献结果对比,吻合良好,证明了本文采用的研究方法以及所提出公共角点协调条件的正确性和合理性。由于该振型函数能满足矩形板的任意边界约束,且其中的待定常数具有明确的物理意义,所以可使矩形板问题的求解统一化、简单化和规律化。     

粗糙表面滑动轴承非牛顿介质润滑的计算

分析了轴承润滑中非牛顿介质的流变特性以及轴承表面形貌对润滑效果的影响,推导出了修正的雷诺方程,在方程中用差分粘度和第一正应力差函数表征非牛顿介质的流变特性,采用流量因子表征表面形貌的作用.结果表明:差分粘度的变化是影响润滑结果的主要因素,它取决于不同介质的动态参数和剪切频率范围,非牛顿介质润滑的承载力并非总高于或低于牛顿介质;在动载荷条件下,第一正应力差效应使油膜压力明显增大;影响流量因子的2个因素为表面形貌的粗糙度和纹理,但其作用远小于非牛顿介质流变特性的影响.     

刚塑性矩形板在冲击载荷作用下的一个新的界限

通过加权残数法，给出了考虑有限变形时刚塑性板在冲击载荷下的能量守恒方程。广义屈服条件由Mij和Nij表示，通过将非光滑屈服函数用其内切和外接光滑函数代替，从而得到板位移的上、下界限解。采用此方法对一矩形板受横向冲击载荷进行了分析，计算结果与有关文献符合较好。     

钢管初应力对钢管砼拱桥承载力影响非线性分析

基于非线性问题的平衡方程和空间梁单元非线性几何方程,推导了一般线弹性关系下计入初应力影响的空间梁单元显式切线刚度矩阵。针对钢管混凝土哑铃型截面的构造特点,提出了组合空间梁单元法,较好解决了哑铃型截面钢管初应力的计算与存储问题,并给出了承载力分析时单元划分的具体方法,编制了专用计算程序,计算结果与试验吻合良好。开展了不同钢管初应力系数、不同截面含钢率和不同跨径对钢管混凝土拱桥承载力的影响分析。结果表明,钢管初应力将使钢管混凝土拱桥的承载力降低,降低幅度与拱肋截面型式有关,承载力最大降低值可超过30%。最后给出了三种考虑钢管初应力影响的常用拱肋截面型式拱桥承载力影响系数实用计算公式。     

Numerical simulation of sedimentation of rectangular particle in Newtonian fluid

The sedimentation of a rectangular particle falling in a two-dimensional channel filled with Newtonian fluid was simulated with finite element arbitrary Lagrangian–Eulerian domain method. The numerical procedure was validated by comparison of the simulation results with existing numerical work. Moreover, good agreement was obtained between the simulation results and experimental measurements performed in the current study. The equilibrium position, stable orientation and drag coefficient of a rectangular particle for different particle Reynolds numbers (Re_p) were studied. The results show that there is a critical particle Reynolds number for the preferred orientation of a rectangular particle falling in a Newtonian fluid. When Re_p is smaller than the critical value, the particle falls with its long side parallel to gravity; otherwise the particle falls with its long side perpendicular to gravity. The critical particle Reynolds number is a decreasing function of the blockage ratio and aspect ratio. The distributions of pressure and shear stress on rectangular particle surface were analyzed. Moreover, the drag coefficient of the rectangular particle decreases as Re_p or the blockage ratio increases; however, it appears to be independent of aspect ratio.     

A bipotential approach for plastic limit loads of strip footings with non-associated materials

This paper is concerned with a bipotential approach for estimating the plastic collapse loads of a half-space made with a non-associated Mohr–Coulomb material and indented by a rigid punch. In geotechnics, this problem is called the bearing capacity of shallow strip footing for which the analytical solution is derived by Prandtl (1920) [46] and Hill (1950) [35] in the context of associated plasticity. However, when the plastic model is not associated, no analytical methods have yet been developed. Here we explore this issue in a rigorous mathematical framework coupling the bipotential concept and limit analysis. First, the method proposed makes use of the method of characteristics to build a statically and plastically admissible stress field that enables a lower estimate of the plastic limit loads. Next, the extended kinematic theorem of limit analysis to non-standard plasticity is applied to derive an upper quasi-bound of the collapse loads. For this aim, the internal rate of plastic dissipation is obtained thanks to the bipotential functional depending on both a trial stress field and a Prandtl-like collapse mechanism. The analytic estimates are compared to the formulae and numerical results provided in literature.     

A variational formulation for plate buckling problems by the hybrid finite element method

A functional is derived for development of stress hybrid finite elements for plate buckling problems. The equilibrium equations inside the element are identically satisfied in terms of Southwell stress functionsand the transverse displacement. Along the boundary of the element further displacement and normal slope functions are employed. These functions are so chosen as to satisfy the interelement compatibility requirements when the elements are connected. The boundary and internal displacements are selected entirely independently and comments are made on the choice of interpolation functions for the internal displacement.The stationarity of the functional is shown to lead to satisfaction of the equilibrium conditions along interelement boundaries, and the compatibility conditions inside the elements. The paper includes the details of a simple rectangular element and the results of a number of plate buckling problems analysed by the developed element.