基于再生核质点法的地基承载力及边坡稳定性分析
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摘要
地基承载力和边坡稳定性问题是土力学的两个重要分支,本文将无网格之再生核质点法引入到这两个问题中,通过对多种影响因素的分析,及模拟土体的破坏性状,以期对地基承载力和边坡工程的设计有所借鉴。具体开展了以下工作:
1.阐述了无网格法与有限元法的本质区别,通过实例得到再生核质点法的核函数及数值积分时背景网格的选取原则。构造了采用增量分析的再生核质点法计算格式,并推导了采用广义von Mises屈服条件的实现过程。
2.条形基础情况下,详细讨论了流动法则及基底粗糙程度对承载力系数的影响,结果显示对三个承载力系数的影响明显不同,流动法则对N_c和N_q的影响很大,而基底粗糙程度对N_r的影响更大。分析了不同的流动法则及基底粗糙程度与地基破坏模式之间的关系。在同时考虑粘聚力、超载和自重三项因素情况下,将本文的结果与经典的地基承载力公式的结果进行了对比,其中考虑流动法则和基底粗糙程度不同的情况。
3.讨论了几种不同的边坡失稳判据,并基于实例提出了本文观点。对计算区域离散质点密度、屈服准则和流动法则对稳定性结果的影响进行了分析,并给出工程应用上的合理值。
4.利用再生核质点法分析结果,探讨了基于应变分析的确定临界滑裂面的方法,比利用有限元法分析结果更容易实现,并根据搜索所得临界滑移面,提出一种计算边坡安全系数的新方法,算例表明该方法是可行的。
5.研究了双层土质边坡随着土体强度变化的稳定性状,其安全系数和破坏形态随着上下两层土体强度比值的变化表现出一定的规律。对带软弱夹层的土质边坡,边坡的安全系数和破坏形态与软弱夹层土体的强度密切相关,软弱夹层土体强度相对其他土体强度的变化,使边坡的失稳破坏存在两种典型的机制。
6.讨论了潜水一维非稳态运动Boussinesq方程的对称性,并采用Lie群变换,就某些边界条件得到其解析解。在此基础上,分析了对Boussinesq方程线性化所引起的误差问题,并得到了特定条件下严格的零误差线性化方法。最后,通过算例的分析对比,提出了在线性化时应该遵循的一些原则。
7.滑坡是深圳地区主要地质灾害类型,具有数量多、规模小、分布广、群发性、危害大等特点。通过大量实例,总结了其滑坡发育的一般规律,对滑坡的治理及平时特别是汛期的预防具有一定的参考价值。
Based on the Reproducing Kernel Particle Method (RKPM), the study of bearing capacity of strip footings and slope stability is performed. The major works are as follows:
1. The literature review RKPM theory is given and major differences between meshfree method and finite element method are illuminated. Then, two examples of RKPM analyses of cantilever beam and plate with a central hole are performed to show how to select kernel function and background mesh for numerical integration. The RKPM algorithm based on incremental analysis is also formulated and the procedures with von Mises yield rule are deduced.
2. In case of strip footings, effects of associated and non-associated flow rules and baseroughness on bearing capacity coefficients are studied. It is proven that flow rules affect N_c and N_q greatly, while N_r depends on roughness of base other than flow rules. Therelationship between failure mechanism and base roughness or flow rules is established. Also, considering effects of cohesion, overloading and self-weight, the comparison of results of this study and classical numerical solutions is carried out.
3. Several criteria of slope failure are discussed. The influences of discrete particle density, yield rule and flow rule on slope stability are analyzed and the sound values of above-mentioned factors are given for engineering practice.
4. Based on numerical analyses of RKPM, a kind of strain analysis method used to seek critical failure surface and calculate factor of safety is proposed, which is simpler than finite element method. The result of a numerical example shows its feasibility.
5. The stability analyses of slope with weak foundation and thin weak layer are studied. The factor of safety and failure moods vary correlated to variation of strength ratio. There are two failure mechanisms for a slope with thin weak layer.
6. The symmetry of the 1-D Boussinseq equation for transient phreatic flows is discussed in this paper, and its analytical solution under such conditions as initial and boundary conditions is obtained by the method of the Lie group transformation. The errors between the non-linear Boussinesq equation and that of its linearization are compared. Based on the analytical solution, a new method for null error linearization of the Boussinesq equation is proposed, and some principles in the linearization are analyzed.
7. Landslide is main type of geological disasters in Shen Zhen area, which has characteristics of small scale, many amount, long span, high loss, etc. Based on some case study, inherent law of landslide development is concluded. It has practical values for the renovation of landslide, particularly for precaution in flood season.
1.阐述了无网格法与有限元法的本质区别,通过实例得到再生核质点法的核函数及数值积分时背景网格的选取原则。构造了采用增量分析的再生核质点法计算格式,并推导了采用广义von Mises屈服条件的实现过程。
2.条形基础情况下,详细讨论了流动法则及基底粗糙程度对承载力系数的影响,结果显示对三个承载力系数的影响明显不同,流动法则对N_c和N_q的影响很大,而基底粗糙程度对N_r的影响更大。分析了不同的流动法则及基底粗糙程度与地基破坏模式之间的关系。在同时考虑粘聚力、超载和自重三项因素情况下,将本文的结果与经典的地基承载力公式的结果进行了对比,其中考虑流动法则和基底粗糙程度不同的情况。
3.讨论了几种不同的边坡失稳判据,并基于实例提出了本文观点。对计算区域离散质点密度、屈服准则和流动法则对稳定性结果的影响进行了分析,并给出工程应用上的合理值。
4.利用再生核质点法分析结果,探讨了基于应变分析的确定临界滑裂面的方法,比利用有限元法分析结果更容易实现,并根据搜索所得临界滑移面,提出一种计算边坡安全系数的新方法,算例表明该方法是可行的。
5.研究了双层土质边坡随着土体强度变化的稳定性状,其安全系数和破坏形态随着上下两层土体强度比值的变化表现出一定的规律。对带软弱夹层的土质边坡,边坡的安全系数和破坏形态与软弱夹层土体的强度密切相关,软弱夹层土体强度相对其他土体强度的变化,使边坡的失稳破坏存在两种典型的机制。
6.讨论了潜水一维非稳态运动Boussinesq方程的对称性,并采用Lie群变换,就某些边界条件得到其解析解。在此基础上,分析了对Boussinesq方程线性化所引起的误差问题,并得到了特定条件下严格的零误差线性化方法。最后,通过算例的分析对比,提出了在线性化时应该遵循的一些原则。
7.滑坡是深圳地区主要地质灾害类型,具有数量多、规模小、分布广、群发性、危害大等特点。通过大量实例,总结了其滑坡发育的一般规律,对滑坡的治理及平时特别是汛期的预防具有一定的参考价值。
Based on the Reproducing Kernel Particle Method (RKPM), the study of bearing capacity of strip footings and slope stability is performed. The major works are as follows:
1. The literature review RKPM theory is given and major differences between meshfree method and finite element method are illuminated. Then, two examples of RKPM analyses of cantilever beam and plate with a central hole are performed to show how to select kernel function and background mesh for numerical integration. The RKPM algorithm based on incremental analysis is also formulated and the procedures with von Mises yield rule are deduced.
2. In case of strip footings, effects of associated and non-associated flow rules and baseroughness on bearing capacity coefficients are studied. It is proven that flow rules affect N_c and N_q greatly, while N_r depends on roughness of base other than flow rules. Therelationship between failure mechanism and base roughness or flow rules is established. Also, considering effects of cohesion, overloading and self-weight, the comparison of results of this study and classical numerical solutions is carried out.
3. Several criteria of slope failure are discussed. The influences of discrete particle density, yield rule and flow rule on slope stability are analyzed and the sound values of above-mentioned factors are given for engineering practice.
4. Based on numerical analyses of RKPM, a kind of strain analysis method used to seek critical failure surface and calculate factor of safety is proposed, which is simpler than finite element method. The result of a numerical example shows its feasibility.
5. The stability analyses of slope with weak foundation and thin weak layer are studied. The factor of safety and failure moods vary correlated to variation of strength ratio. There are two failure mechanisms for a slope with thin weak layer.
6. The symmetry of the 1-D Boussinseq equation for transient phreatic flows is discussed in this paper, and its analytical solution under such conditions as initial and boundary conditions is obtained by the method of the Lie group transformation. The errors between the non-linear Boussinesq equation and that of its linearization are compared. Based on the analytical solution, a new method for null error linearization of the Boussinesq equation is proposed, and some principles in the linearization are analyzed.
7. Landslide is main type of geological disasters in Shen Zhen area, which has characteristics of small scale, many amount, long span, high loss, etc. Based on some case study, inherent law of landslide development is concluded. It has practical values for the renovation of landslide, particularly for precaution in flood season.
引文
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