临界滑动场法的改进与应用
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摘要
边坡临界滑动场将极限平衡法与最优性原理有机结合起来,能够快速、准确和方便地找出边坡任意形状的全局临界滑动面、局部临界滑动面和其对应的安全系数,全面评价边坡的整体和局部稳定性。经过十余年的发展,临界滑动场方法已初步成为计算边坡,土压力和地基承载力的岩土稳定分析新方法。本文在已有研究成果基础上,完善临界滑动场方法的理论基础,拓展其应用范围,并将改进和拓展后的方法成功应用于工程实例中,使其逐渐成为理论严密、适应性强、功能完善、通用性好的岩土稳定分析新方法。同时本文基于滑面正应力修正的三维边坡稳定性分析方法,提出了基于滑面正应力修正的计算浅埋矩形基础地基承载力的三维分析方法。本文主要研究工作如下：
1.针对岩体介质非线性破坏的特点,采取国际上广泛接受应用的建立在地质强度指标(GSI)法基础上的Hoek-Brown屈服准则,建立基于广义Hoek-Brown破坏准则的边坡临界滑动场新方法。首先,根据Hoek-Brown准则确定岩体强度参数；然后将Hoek-Brown准则不同法向应力水平上的剪切强度逐点等效到Mohr-Coulomb强度线上,用等效摩擦角和等效黏聚力的Mohr-Coulomb准则代替Hoek-Brown准则；最后将基于Mohr-Coulomb破坏准则的边坡临界滑动场计算方法进行改进,建立新的迭代方法,获得边坡在满足力与力矩平衡条件下的整体和局部临界滑动面和相对应的安全系数。将该方法应用于两个算例和铜陵新桥硫铁矿露天边坡的稳定性分析与比较,计算结果表明该方法既继承了临界滑动场方法快速、准确找到边坡整体局部临界滑动面的优点,又能考虑岩质边坡非线性破坏的特点,更加符合工程实际。
2.针对岩体介质不连续性的特点,充分考虑结构面存在对岩质边坡稳定性的影响,对结构面采取新的处理方法,并基于岩体介质具有抗拉性的特点,灵活设置张拉裂缝,建立考虑岩体不连续结构面的边坡临界滑动场。将此方法应用于五个算例和铜陵新桥硫铁矿露天边坡的稳定性分析与比较,结果表明该方法在岩质边坡稳定性分析中的准确性和合理性。
3.库水位升降过程中,边坡体内的孔隙水压力分布和坡外水位的变化,会对边坡的稳定性产生影响。对边坡临界滑动场进行改进,提出了可以考虑水位变化过程的边坡临界滑动场方法,该方法能够方便、快速的计算出边坡局部、整体安全系数和相对应的临界滑动面在水位变化程中的变化历程。通过对一个典型边坡和金坪子Ⅱ区蠕滑坡体在水位上升和下降过程中的稳定性分析与比较,结果表明水位变化过程中的临界滑动场方法能搜索任意形状的最危险滑面,计算得到的安全系数是合理的。
4.降雨入渗过程中,孔隙水压力升高与基质吸力降低引起边坡稳定性的下降,是导致边坡滑塌的主要诱导因素。利用饱和-非饱和渗流有限元计算得到的孔隙水压力场,基于Fredlund提出的非饱和土抗剪强度理论,对边坡临界滑动场进行改进,提出了可以考虑降雨过程的边坡临界滑动场方法,该方法能够方便、快速的计算出边坡局部、整体安全系数和相对应的临界滑动面在降雨过程中的变化历程。将该方法用于两个典型边坡算例和绩溪至黄山高速公路红砂岩路基边坡在降雨过程中的稳定性计算,分析了降雨持续时间、降雨强度和非饱和强度参数取值等因素对边坡稳定性的影响,并将计算结果与其他方法进行比较,结果表明降雨过程中的临界滑动场方法能搜索任意形状最危险滑面,计算得到的安全系数合理。
5.数值分析方法可以计算边坡应力、变形和破坏,但直接计算边坡安全系数比较困难；而极限平衡法需对边坡体内力做出假设,计算精度受到限制。利用数值分析方法计算得到的应力场,重新定义推力最大原理中推力的含义,将边坡临界滑动场方法作进一步的改进,提出了基于数值应力场的边坡临界滑动场方法。该方法可充分发挥两大方法的优势,能够准确、快速搜索出边坡临界滑动面位置,并给出更合理的边坡安全系数。通过两个算例的稳定性分析,并和其他方法进行比较,验证了该方法的准确性和合理性。
6.将改进和拓展后的临界滑动场计算方法应用到铜陵新桥硫铁矿下盘边坡、金坪子Ⅱ区蠕滑坡体和绩溪至黄山高速公路红砂岩路基边坡的稳定性分析与评价,并结合实际情况,给出了合理的治理建议,结果令人满意。结果表明改进和拓展后的方法完善了临界滑动场方法的理论基础,并拓展了其应用范围,大幅度得提高了计算结果的可靠性。
7.提出一种能够计算浅埋矩形基础地基承载力的三维分析方法。首先,假设滑动面为一组由沿基础长轴方向的具有不同初始半径的螺旋线构成的三维椭球滑面；然后,对基于滑面正应力修正的三维边坡极限平衡方法进行改进,建立基于滑面正应力修正的计算固定三维滑面极限承载力方法；最后,通过改变螺旋线极点位置,构造所有可能破坏的滑动面,试算不同滑面所对应的极限承载力,搜索出的最小值即为基础地基承载力,其对应的滑面即为破坏滑动面。为了使该方法能用传统的叠加法公式进行地基承载力计算,给出了三维条件下的各地基承载力系数值,并研究了基础长宽比和土的内摩擦角对各系数的影响。用该方法和给出的三维地基承载力系数分别对算例进行计算分析,并和其他方法进行比较,结果表明该方法合理可靠,能够方便、快速计算矩形基础地基承载力。
Combined with limit equilibrium method and optimality principle, critical slip field of slope method allows us to find critical slip surfaces quickly、exactly and conveniently as well as the corresponding safety factors. With decades of development, critical slip field method has preliminarily been developed as a new method used in calculation of slope stability, soil pressure and bearing capacity. Based on existing analysis results, in this paper, critical slip field gradually becomes a new geotechnical stability analysis method which is more rigorous、adaptable、functional and universal. The theory of the method is perfected and its application realm is extended,then the improved method has been applied to the stability analysis of engineering application. In addition, based on the modification of normal stresses over slip surface, a new method for the three-dimensional problem of bearing capacity of rectangular shallow footing is proposed.the main works and results are listed as follows:
1. According to nonlinear failure characteristic of rock mass, the new analysis method for critical slip field of slope based generalized Hoek-Brown failure criterion is proposed. The Hoek-Brown failure criterion based on the geology strength index (GSI) is one of the most useful criteria in forecasting and computing of rock mass strength. Firstly, the parameters of rock mass strength are obtained by Hoek-Brown failure criterion. Secondly, the shear strength of each point on the Hoek-Brown strength envelope is transferred equivalently to the Mohr-Coulomb linear relation which is tangent to the nonlinear envelope with relevant cohesive and frictional parameters. Finally, the new iterative method is established and the critical slip field of slope by Morgenster-Price method is improved. And then, the most dangerous sliding surfaces are traced according to the principle of maximum thrusts with satisfying both force and moment equilibriums and the corresponding safety factors are calculated quickly and exactly. This method is applied to the stability analysis of two slope examples and the slope in the Xinqiao open-cut pyrite mine. The results show that the present method absorbs the advantages of critical slip field and Hoek-Brown failure criterion and can further considers the nonlinear failure characteristic of slope. The calculation results are well agreed with the practical situation.
2. Improvement and extension of critical slip fields of rock slope is performed, in view of the discontinuity of rock. Considering the influence of structural surface on the stability of the slope, a new method is proposed for dealing with structural planes, and tensile cracks are readily introduced based on the tensile strength of rock. This method has been applied to the stability analysis of five example slopes and the slope in the Xinqiao open-cut pyrite mine, and the results prove its accuracy and high efficiency in rock slope stability analysis by compared with those obtained by other methods.
3. The process of reservoir water level fluctuation may cause the changes of the slope body in the pore water pressure distribution, which has influences on slope stability. Considering the process of water level changes, a improved numerical simulation method of critical slip field of slope was proposed. Thus, the local and global safety factor of the slope in the process of water changing are obtained conveniently and rapidly. By means of stability analysis of a typical slope in the process of rise and fall in water level and comparing with those by other methods, the results show that the critical slip field method could search for any shape of the most dangerous slip surface, and the safety factor is reasonable.
4. The rising of pore water pressure and decreasing of matric suction in the process of the infiltration of rainfall into slope is the main factor of slope failures.Numerical simulation method of critical slip field of slope considering rainfall process is proposed based on proposed unsaturated soil shear strength theory and water pressure field obtained by finite element method analysis of saturated-unsaturated seepage. Thus, slope local safety factor and slope safety factor of the whole as well as the corresponding critical slip surfaces during infiltration were calculated conveniently and rapidly. This method has been applied to the stability analysis of two slope cases and the effect study of rainfall intensity, duration and strength parameter on slope stability, the results show that the critical slip field method could search for any shape of the most dangerous slip surface, and the safety factor is reasonable.
5. Numerical methods can be used to calculate stress, strain and failure of slope; but it is difficult to calculate the safety factor of slope stability directly. Limit equilibrium methods can obtain the factor of safety, but they need to assume the interslice forces, which affects the calculation accuracy. Based on the stress field obtained by numerical methods, by defining the maximum thrust forces and improving numerical simulation method of conventional critical slip field of slope, the critical slip field method of slope based on numerical stress field is proposed. The results obtained by using this method for two examples have been compared with other methods. It is shown that the proposed method combines the advantages of numerical method and limit equilibrium method so as to find the critical slip surface of slope accurately and conveniently, and give more reasonable safety factor.
6. The improved and expanded calculation method of the critical slip field of slope theory is applied to the stability analysis and evaluation of the slope in the Xinqiao open-cut pyrite mine, the roadbeds of the expressway from Jixi to Huangshan and Jinpingzi Ⅱ section creep mass. Combining with practical situation, reasonable governance recommendations are provided, and the results are satisfactory. It demonstrates that the improved and expanded calculation method consummates the critical slip field of slope theory, expanding its applied range, and enhances the results' reliability by a wide margin.
7. A new method is proposed for three-dimensional analysis of bearing capacity of rectangular shallow footing based on the modification of normal stresses over slip surface. Firstly, the shape of the slip surface is assumed as ellipsoidal, which is composed of a set of log-spirals with different initial radii in the direction on the longer axis of the footing base. Secondly, establishing a method for analysis of bearing capacity of a fixed three-dimensional slip surface, by improving the limit equilibrium solution of3D slope stability based on the modification of normal stresses over slip surface. Finally, the bearing capacity of the footing is the minimum of selected fixed three-dimensional slip surfaces, by changing the position of the pole of log-spirals. Bearing capacity coefficients are then given for calculating the bearing capacity by using the method of the superposition involved in the conventional bearing capacity formula and investigating the effects of the angle of internal friction and the length-width ratio of footing. This method has been applied to calculate the bearing capacity of one example and compared with other methods; the results show its accuracy and reasonable and high effectiveness in three-dimensional bearing capacity analysis of rectangular shallow footing.
1.针对岩体介质非线性破坏的特点,采取国际上广泛接受应用的建立在地质强度指标(GSI)法基础上的Hoek-Brown屈服准则,建立基于广义Hoek-Brown破坏准则的边坡临界滑动场新方法。首先,根据Hoek-Brown准则确定岩体强度参数；然后将Hoek-Brown准则不同法向应力水平上的剪切强度逐点等效到Mohr-Coulomb强度线上,用等效摩擦角和等效黏聚力的Mohr-Coulomb准则代替Hoek-Brown准则；最后将基于Mohr-Coulomb破坏准则的边坡临界滑动场计算方法进行改进,建立新的迭代方法,获得边坡在满足力与力矩平衡条件下的整体和局部临界滑动面和相对应的安全系数。将该方法应用于两个算例和铜陵新桥硫铁矿露天边坡的稳定性分析与比较,计算结果表明该方法既继承了临界滑动场方法快速、准确找到边坡整体局部临界滑动面的优点,又能考虑岩质边坡非线性破坏的特点,更加符合工程实际。
2.针对岩体介质不连续性的特点,充分考虑结构面存在对岩质边坡稳定性的影响,对结构面采取新的处理方法,并基于岩体介质具有抗拉性的特点,灵活设置张拉裂缝,建立考虑岩体不连续结构面的边坡临界滑动场。将此方法应用于五个算例和铜陵新桥硫铁矿露天边坡的稳定性分析与比较,结果表明该方法在岩质边坡稳定性分析中的准确性和合理性。
3.库水位升降过程中,边坡体内的孔隙水压力分布和坡外水位的变化,会对边坡的稳定性产生影响。对边坡临界滑动场进行改进,提出了可以考虑水位变化过程的边坡临界滑动场方法,该方法能够方便、快速的计算出边坡局部、整体安全系数和相对应的临界滑动面在水位变化程中的变化历程。通过对一个典型边坡和金坪子Ⅱ区蠕滑坡体在水位上升和下降过程中的稳定性分析与比较,结果表明水位变化过程中的临界滑动场方法能搜索任意形状的最危险滑面,计算得到的安全系数是合理的。
4.降雨入渗过程中,孔隙水压力升高与基质吸力降低引起边坡稳定性的下降,是导致边坡滑塌的主要诱导因素。利用饱和-非饱和渗流有限元计算得到的孔隙水压力场,基于Fredlund提出的非饱和土抗剪强度理论,对边坡临界滑动场进行改进,提出了可以考虑降雨过程的边坡临界滑动场方法,该方法能够方便、快速的计算出边坡局部、整体安全系数和相对应的临界滑动面在降雨过程中的变化历程。将该方法用于两个典型边坡算例和绩溪至黄山高速公路红砂岩路基边坡在降雨过程中的稳定性计算,分析了降雨持续时间、降雨强度和非饱和强度参数取值等因素对边坡稳定性的影响,并将计算结果与其他方法进行比较,结果表明降雨过程中的临界滑动场方法能搜索任意形状最危险滑面,计算得到的安全系数合理。
5.数值分析方法可以计算边坡应力、变形和破坏,但直接计算边坡安全系数比较困难；而极限平衡法需对边坡体内力做出假设,计算精度受到限制。利用数值分析方法计算得到的应力场,重新定义推力最大原理中推力的含义,将边坡临界滑动场方法作进一步的改进,提出了基于数值应力场的边坡临界滑动场方法。该方法可充分发挥两大方法的优势,能够准确、快速搜索出边坡临界滑动面位置,并给出更合理的边坡安全系数。通过两个算例的稳定性分析,并和其他方法进行比较,验证了该方法的准确性和合理性。
6.将改进和拓展后的临界滑动场计算方法应用到铜陵新桥硫铁矿下盘边坡、金坪子Ⅱ区蠕滑坡体和绩溪至黄山高速公路红砂岩路基边坡的稳定性分析与评价,并结合实际情况,给出了合理的治理建议,结果令人满意。结果表明改进和拓展后的方法完善了临界滑动场方法的理论基础,并拓展了其应用范围,大幅度得提高了计算结果的可靠性。
7.提出一种能够计算浅埋矩形基础地基承载力的三维分析方法。首先,假设滑动面为一组由沿基础长轴方向的具有不同初始半径的螺旋线构成的三维椭球滑面；然后,对基于滑面正应力修正的三维边坡极限平衡方法进行改进,建立基于滑面正应力修正的计算固定三维滑面极限承载力方法；最后,通过改变螺旋线极点位置,构造所有可能破坏的滑动面,试算不同滑面所对应的极限承载力,搜索出的最小值即为基础地基承载力,其对应的滑面即为破坏滑动面。为了使该方法能用传统的叠加法公式进行地基承载力计算,给出了三维条件下的各地基承载力系数值,并研究了基础长宽比和土的内摩擦角对各系数的影响。用该方法和给出的三维地基承载力系数分别对算例进行计算分析,并和其他方法进行比较,结果表明该方法合理可靠,能够方便、快速计算矩形基础地基承载力。
Combined with limit equilibrium method and optimality principle, critical slip field of slope method allows us to find critical slip surfaces quickly、exactly and conveniently as well as the corresponding safety factors. With decades of development, critical slip field method has preliminarily been developed as a new method used in calculation of slope stability, soil pressure and bearing capacity. Based on existing analysis results, in this paper, critical slip field gradually becomes a new geotechnical stability analysis method which is more rigorous、adaptable、functional and universal. The theory of the method is perfected and its application realm is extended,then the improved method has been applied to the stability analysis of engineering application. In addition, based on the modification of normal stresses over slip surface, a new method for the three-dimensional problem of bearing capacity of rectangular shallow footing is proposed.the main works and results are listed as follows:
1. According to nonlinear failure characteristic of rock mass, the new analysis method for critical slip field of slope based generalized Hoek-Brown failure criterion is proposed. The Hoek-Brown failure criterion based on the geology strength index (GSI) is one of the most useful criteria in forecasting and computing of rock mass strength. Firstly, the parameters of rock mass strength are obtained by Hoek-Brown failure criterion. Secondly, the shear strength of each point on the Hoek-Brown strength envelope is transferred equivalently to the Mohr-Coulomb linear relation which is tangent to the nonlinear envelope with relevant cohesive and frictional parameters. Finally, the new iterative method is established and the critical slip field of slope by Morgenster-Price method is improved. And then, the most dangerous sliding surfaces are traced according to the principle of maximum thrusts with satisfying both force and moment equilibriums and the corresponding safety factors are calculated quickly and exactly. This method is applied to the stability analysis of two slope examples and the slope in the Xinqiao open-cut pyrite mine. The results show that the present method absorbs the advantages of critical slip field and Hoek-Brown failure criterion and can further considers the nonlinear failure characteristic of slope. The calculation results are well agreed with the practical situation.
2. Improvement and extension of critical slip fields of rock slope is performed, in view of the discontinuity of rock. Considering the influence of structural surface on the stability of the slope, a new method is proposed for dealing with structural planes, and tensile cracks are readily introduced based on the tensile strength of rock. This method has been applied to the stability analysis of five example slopes and the slope in the Xinqiao open-cut pyrite mine, and the results prove its accuracy and high efficiency in rock slope stability analysis by compared with those obtained by other methods.
3. The process of reservoir water level fluctuation may cause the changes of the slope body in the pore water pressure distribution, which has influences on slope stability. Considering the process of water level changes, a improved numerical simulation method of critical slip field of slope was proposed. Thus, the local and global safety factor of the slope in the process of water changing are obtained conveniently and rapidly. By means of stability analysis of a typical slope in the process of rise and fall in water level and comparing with those by other methods, the results show that the critical slip field method could search for any shape of the most dangerous slip surface, and the safety factor is reasonable.
4. The rising of pore water pressure and decreasing of matric suction in the process of the infiltration of rainfall into slope is the main factor of slope failures.Numerical simulation method of critical slip field of slope considering rainfall process is proposed based on proposed unsaturated soil shear strength theory and water pressure field obtained by finite element method analysis of saturated-unsaturated seepage. Thus, slope local safety factor and slope safety factor of the whole as well as the corresponding critical slip surfaces during infiltration were calculated conveniently and rapidly. This method has been applied to the stability analysis of two slope cases and the effect study of rainfall intensity, duration and strength parameter on slope stability, the results show that the critical slip field method could search for any shape of the most dangerous slip surface, and the safety factor is reasonable.
5. Numerical methods can be used to calculate stress, strain and failure of slope; but it is difficult to calculate the safety factor of slope stability directly. Limit equilibrium methods can obtain the factor of safety, but they need to assume the interslice forces, which affects the calculation accuracy. Based on the stress field obtained by numerical methods, by defining the maximum thrust forces and improving numerical simulation method of conventional critical slip field of slope, the critical slip field method of slope based on numerical stress field is proposed. The results obtained by using this method for two examples have been compared with other methods. It is shown that the proposed method combines the advantages of numerical method and limit equilibrium method so as to find the critical slip surface of slope accurately and conveniently, and give more reasonable safety factor.
6. The improved and expanded calculation method of the critical slip field of slope theory is applied to the stability analysis and evaluation of the slope in the Xinqiao open-cut pyrite mine, the roadbeds of the expressway from Jixi to Huangshan and Jinpingzi Ⅱ section creep mass. Combining with practical situation, reasonable governance recommendations are provided, and the results are satisfactory. It demonstrates that the improved and expanded calculation method consummates the critical slip field of slope theory, expanding its applied range, and enhances the results' reliability by a wide margin.
7. A new method is proposed for three-dimensional analysis of bearing capacity of rectangular shallow footing based on the modification of normal stresses over slip surface. Firstly, the shape of the slip surface is assumed as ellipsoidal, which is composed of a set of log-spirals with different initial radii in the direction on the longer axis of the footing base. Secondly, establishing a method for analysis of bearing capacity of a fixed three-dimensional slip surface, by improving the limit equilibrium solution of3D slope stability based on the modification of normal stresses over slip surface. Finally, the bearing capacity of the footing is the minimum of selected fixed three-dimensional slip surfaces, by changing the position of the pole of log-spirals. Bearing capacity coefficients are then given for calculating the bearing capacity by using the method of the superposition involved in the conventional bearing capacity formula and investigating the effects of the angle of internal friction and the length-width ratio of footing. This method has been applied to calculate the bearing capacity of one example and compared with other methods; the results show its accuracy and reasonable and high effectiveness in three-dimensional bearing capacity analysis of rectangular shallow footing.
引文
[1]Duncan, J.M. State-of-the-art:Limit equilibrium and finite-element analysis of slope. J. Geotech. Engrg.,ASCE.1996,122(7):577-596.
[2]Chowdhury, R.N. Slope Analysis. Elsevier, Amsterdam.,1978.
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