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Alternative TitleStudy on the Mechanism of Toppling Failure of Countertendency Slopes and Their Simulations By the Numerical Manifold Method
Thesis Advisor苏立君
Degree Grantor中国科学院大学
Place of Conferral北京
Degree Discipline岩土工程
Keyword反倾向层状边坡 弯曲倾倒 极限平衡 数值流形方法 串层锚杆
Abstract倾倒破坏是反倾向层状岩体边坡常见的一种破坏模式,在自然和工程边坡中均有发生。按破坏机制的不同,Goodman将倾倒破坏模式分为两类:弯曲倾倒和块体倾倒(块体-弯曲倾倒是两者的复合形式)。由于块体倾倒作用机制简单,破坏面是确定的直线或者双折线,因此,国内外学者在该方面的研究已取得了显著的成果,并建立了较为完善的理论分析方法。弯曲倾倒破坏相对较为复杂,由于反倾向边坡破坏面的位置、形状和破坏岩层的个数未知,使得学者无法从理论上定量分析岩层间的力学作用机制。因此,本文重点研究反倾向层状边坡弯曲倾倒破坏机制,主要工作包括以下几个方面:(1)提出了一种搜索弯曲倾倒破坏面的理论分析方法,该方法将反倾向层状边坡简化为叠合悬臂梁模型,并结合极限平衡方法和潘家铮最大最小原理,认为边坡破坏基准面(由各个岩层折断面组成)是使边坡发生整体破坏所需外力最小的破坏面。在破坏基准面搜索过程中,首先确定岩层破坏个数;然后,利用极限平衡方法,结合岩层的破坏模式,求出各组岩层发生整体破坏所需的最小外力F;最后,不断变化搜索角,得到一系列F,它们当中的最小值作为边坡发生整体破坏所需的最小外力,对应的破坏面作为边坡潜在破坏基准面,相对应的岩层组合为最危险的岩层组合。(2)对影响边坡稳定性的内部和外部因素作了参数敏感性分析。其中,内部因素是指岩土体物理力学参数,包括粘聚力、抗拉强度、内摩擦角、层间内摩擦角、岩体重度。外部因素重点研究了地震荷载、坡顶荷载和边坡开挖。(3)系统阐述了NMM的基本原理, 包括物理覆盖、数学覆盖、物理片、数学片、流形单元的基本概念以及它们之间的关系,接触理论及其实现过程。在NMM前处理方面,提出了矩形有限元网格覆盖系统的生成算法;在构造局部位移逼近函数过程中,提出了具有物理意义的泰勒展式升阶方法。(4)考虑到流形方法采用两套完全独立的覆盖系统,所以我们总可以用规则的数学网格来作为数学覆盖进行插值,这样就可以取得最佳的插值效果,单元收敛性便能得到保证。再结合适用于流形方法的变分提法,建立起流形方法处理含有任意物理边界的二阶、四阶偏微分问题的一般格式。以ACM薄板单元为例,与ANSYS、拟协调元法、广义协调元法进行了对比,证明本文提出的流形方法在处理具有曲线边界的薄板弯曲问题时具有收敛快和精度高等优势。此外,本文将流形方法拓展到其高阶形式,并成功解决了四阶偏微分问题。(5)根据反倾向层状边坡的变形破坏机制,建立了相应的破坏准则和弹塑性本构模型;在弹塑性应力修正过程中,给出了改进的切向预测径向返回的方法。最后采用5个算例验证了本文建立的弹塑性流形方法的有效性。(6)基于反倾向层状边坡的变形破坏机制,归纳出加固反倾向层状边坡的核心思想:增大岩层之间的摩擦阻力,减少岩层承受的弯矩或者提高边坡抗倾倒能力。重点介绍了串层锚杆的加固方法及其力学分析过程,并以皖南板岩边坡为工程实例,重点分析了锚杆长度、锚杆加固位置和使用锚杆数目对边坡加固效果的影响。最后,综合上述分析给出了皖南板岩边坡的串层锚杆最佳加固方案。
Other AbstractToppling failure is a common failure mode of countertendency layered rock slope, which happened in nature and practical engineering. Due to different failure mechanisms, toppling failure modes were mainly divided into two kinds by Goodman and Bray: flexural toppling and block toppling (block-flexural toppling can be treated as recombination form of the above two types). Considering failure plane of block toppling known as a linear type or bilinear type, the scholars had made significant results and established a relatively complete theoretical analysis method. Flexural toppling mechanism is relatively complex, because the position, shape of the slope failure plane and the number of failure stratum are unknown, which made scholars unable to quantitatively analyze rock mechanics in theory. As a result, this study focused on the mechanism of flexural toppling failure of countertendency layered slopes. The main researches of this paper included the follows:(1) An algorithm to search the basal failure surface for improving the computational reliability of flexural toppling was put forward. Based on the principle of Pan Jiazheng, the basal failure surface was considered as a surface which required the minimum external force to trigger overall failure of a slope. In the searching process for the basal failure surface, the number of stratum failure was obtained firstly. Then, the minimum external force F satisfied for overall failure in each groups was calculated through the limit equilibrium method and strata’ failure modes. Finally, after the searching angled changed constantly, a series of F could be achieved. Among which, the minimum one was taken as the final external force satisfied for overall failure to the slope; the failure surface corresponding to final external force was regarded as the basal failure surface of the slope; the corresponding strata group was considered as the most dangerous group.(2) The sensitivity analyses of the internal and external factors influencing the stability of a slope were made. In which, the internal factors indicate the mechanical parameters of rock mass, which include the tensile strength, cohesion, friction angle, internal friction angle and the unit weight of rock mass. The external factors contain seismic force, slope-top loading and slope excavation.(3) The basic principle of NMM was discussed, which include the basic concepts of mathematical cover, physical cover, mathematical patch, physical patch, manifold element and the relationship between them. Besides, the contact theory and its implementation were given in this paper. In the aspect of NMM pre-processing, the generation algorithm of rectangular finite element mesh covering system was proposed. In the process of constructing local displacement approximation function, the Taylor expansion method with physical meaning was developed. (4) Considering the two completely independent covering systems were used in the numerical manifold method (NMM), we could always use the best mesh as the mathematical cover for interpolation. In this way, the best interpolation precision could be achieved and the convergence was accordingly reached. With the variational formulation of second-order and fourth-order partial differential problems fitted to NMM, a unified scheme was proposed for NMM to deal with arbitrary boundaries of domains. By taking the ACM plate element as an example, finally, comparisons among the proposed scheme, ANSYS, thevquasi-conforming elements and the generalized conforming elements in the literature were made, indicating that the proposed scheme was advantageous in treating thin plate bending problems where the plate had a curve boundary. Furthermore, the manifold method was extended to its higher order case, and the fourth-order partial differential problem was solved successfully. (5) According to the deformation and toppling failure mechanism of the countertendency layered slopes, an appropriate failure criteria and an elastoplastic constitutive model were established. Finally, 5 numerical examples were given to verify the effectiveness of the proposed method.(6) Based on the toppling failure mechanism of the countertendency layered slopes, two core ideas of reinforcing those slopes were developed: increasing the frictional resistance between layers and reducing bending moment or increasing the ability to resist toppling. This paper mainly introduced the reinforcement method and the mechanical analysis process of the series anchor bolts. Taking the slate slope in South Anhui of China as an engineering example, the influence of the length, the position and the amount of anchor bolts on the reinforcement of the slope were discussed. Finally, based on the above analyses, the best reinforcement scheme of the series anchor bolts for the slate slope in South Anhui of China was obtained.
Document Type学位论文
Recommended Citation
GB/T 7714
屈新. 反倾向边坡倾倒破坏机制研究及其流形方法模拟[D]. 北京. 中国科学院大学,2017.
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