基于线性与非线性破坏准则的边坡强度折减法研究
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摘要
稳定性分析是边坡工程最基本最重要的问题,也是边坡设计与施工中最难和最迫切需要解决的问题之一。近年来随着计算机技术的不断发展,采用强度折减法进行边坡稳定性分析成为新的趋势；与传统的极限平衡法相比,强度折减法不但满足力的平衡条件,而且考虑了材料的应力应变关系,计算时不需任何假定,能自动地求得任意形状的临界滑动面及相应的最小安全系数,同时还可反映坡体失稳及塑性区的开展过程,使分析研究的理论基础更为严密。目前,强度折减法计算边坡安全系数方面的研究,虽然取得了不少成果,但还远未达到完善的程度。本文针对目前强度折减法的一些细节进行研究,主要内容和结论如下：
(1)讨论了强度折减法安全系数的定义,推导了其与极限平衡法安全系数定义的关系,从理论上阐述两者的一致性;
(2)分析了在不同坡角情况下,粘结力c和内摩擦角φ对于稳定性的影响程度,从岩土体微观抗剪机理阐述了边坡稳定性的影响因素；提出了等效影响角θe的概念；当坡角β=θe时,c和φ对稳定性的影响程度相同；当坡角β<θe时,摩擦角φ发挥的作用大于粘结力c发挥的作用；当β>θe时,c对稳定性的影响程度大于φ；该等效影响角适用于所有均质边坡,具有普遍性,其值为θe=34.1°；
(3)对同一边坡算例建立三种临界失稳判据,采用拉格朗日元法对边坡进行弹塑性稳定分析,将三种判据得到的安全系数进行对比,探讨各个判据的合理性及实用性,得到：塑性区贯通判据在判断塑性区是否贯通时需人为进行观察,“自动化”程度不高；计算不收敛判据原理简单,得到的安全系数与位移突变判据的结果差别十分微小,并且便于程序编制；位移突变判据物理意义明确；
(4)为了确定位移突变判据中的监测点和监测方式,在边坡面和内部布设若干监测点进行对比分析,并采用曲线方程对位移-折减系数的关系进行拟合,得到：a、双曲线方程S=(b+cK)/(1+aK)的拟合效果较好；拟合结果能够得到边坡的安全系数；b、监测点须在临界滑移线以内选取；在未知滑移线位置的情况下,选取坡脚作为监测点是不合适的；同一点在不同位移方式下,得到的安全系数相等；
(5)采用边坡的位移等值线对滑动面进行判断,并利用自编FISH程序将该曲线和边坡线数据取出,从而量化滑动面上各点的位置,实现了滑动面直接确定方法；设置不同弹性区高度,得到多滑动面的确定方法；
(6)分析影响因素粘结力,内摩擦角,抗拉强度,剪胀角和弹性模量对边坡安全系数和滑动面的影响,得到：内摩擦角和粘结力对安全系数和滑动面位置的影响最大;定义了新的参数λcφ=ccr/(γhtanφcr),统一了滑动面随粘结力和内摩擦角的变化趋势；安全系数随着抗拉强度的增大而呈现递增的规律；探讨了不同工况下,剪胀角和弹性模量对安全系数的影响,完善了以往稳定性分析对这些参数的处理方法；
(7)采用双弹簧锚杆单元,模拟了边坡开挖过程中,锚杆的加固效应,讨论了强度折减法在考虑锚杆加固情况下的实施过程以及锚杆参数对稳定性的影响,得到一些新的见解对科学研究和工程应用都有一定参考价值；
(8)为了在Hoek-Brown准则中实施强度折减法,并使其得到的结果与Mohr-Coulomb准则中强度折减法得到的结果等效,通过理论推导得到Hoek-Brown准则与Mohr-Coulomb准则参数之间的关系；采用等效粘结力和内摩擦角,计算边坡的安全系数,从而间接得到Hoek-Brown准则下边坡的安全系数,该方法方便可行,具有实用价值；
(9)将强度折减法与描述层状岩体的Ubiquitous-Joint准则相结合,通过数值计算,分析了层状岩质边坡稳定性的影响因素,扩展了强度折减法的应用范围；
(10)进一步探讨Hoek-Brown准则强度折减法在三维边坡稳定性分析中的应用,以某露天矿边坡为工程背景,利用快速拉格朗日差分法(FLAC3D),建立三维数值分析模型,计算边坡的安全系数和破坏模式,从宏观角度揭示出边坡开挖后,不同区域的位移变形响应,为工程实践提供指导；
(11)采用FLAC3D对层状边坡的破坏模式进行模拟,利用低强度弹塑性单元模拟软弱结构面的变形；通过数值分析得到的结果与试验相符,推广了FLAC3D强度折减法在工程中的应用。
Slope stability analysis is the most basic and important stage in slope engineering, which is also the most difficult and emergent problem need to be solved. In the recent year, with the development of compute technology, the strength reduction method (SRM) is becoming a new trend in the area of slope stability analysis. When compared to the traditional limit equilibrium method (LEM), SRM not only meets the mechanical equilibrium condition, but also takes into consideration of the stress-strain relationship; During calculation, SRM does not have to make any assumption, it can search for the critical slip plane and find out the minimum safety factor for the slope in the automatic way, while the failure of slope and development of plastic zone can be reflected in the result of SRM, as well, which indicates that SRM has more advantages than LEM for it is based on the more precisely theories. Although many people have done much work on SRM, and get many achievements. The SRM is still far away from the perfect state. So the present paper has done the studies on some details for SRM which needs to be renovated. The main contents and conclusions are:
(1) The different definitions of safety factor for strength reduction method are discussed, and the relationship of safe factor for SRM and LEM is obtained, which shows the consistency of definitions for SRM and LEM;
(2) The impact of cohesion c and internal friction angleφto the stability of slope are analyzed, which studied the influential factors for stability of slope in the microscopic mechanism of shear strength; the equivalent influential angleθe is proposed; whenβ=θe, the c andφhave the same impact on the stability of slope; whenβ<θe,φhas the larger impact on the stability of slope than that of c; whenβ>θe, c has larger impact on the stability of slope than that ofφ; the equivalent influential angleθe is suitable in different homogenous slopes, whose value isθe=34.1°;
(3) Three critical failure criterions, the connectivity of plastic zone criterion, the convergence of numerical computations criterion and the mutation of displacement criterion, are founded in the same homogenous slope; The elasto-plastic analysis is done to the stability of slope by the method of fast lagrangian analysis of continua three dimensions (FLAC3D). Safety factors obtained from the three criterions are compared with that from Janbu's procedure of limit equilibrium. The analysis results show that, the automatic characteristic for the connectivity of plastic zone criterion is not obvious, it need observation and judgment from people; The calculation theory of the numerical computations convergence criterion is easy to understand, and convenient to be programmed, with great precision for its result is in small differences with that from LEM; the physical meaning of displacement mutation criterion is clear;
(4) In order to analyze the rationality of the chosen point's location and the displacement mode, numerical calculation models are founded for isotropic soil slope and joint rock slope, separately. Some monitoring points are located in slope while some in the internal of slope. The relationships between displacement and reduction factor are analyzed. According to the displacement mutation characteristic of displacement-reduction factor curves, hyperbola fitting equations are founded. The fitting results show that (a) fitting data are in good correlation with the monitoring data; (b) the points on and below the critical slip line can be chosen as the monitoring points of displacement mutation criterion; the top of slope is recommended to be chosen as the monitoring point in the universal slope with the consideration that the top of slope is sure to be below the critical slip line and its location is easy to obtained; If the location of slip plane is not certain, it is not proper to choose the toe of slope as the monitoring point; All the three displacement modes can lead to the same safety factor for the same monitoring point;
(5) A numerical model was founded in plane strain mode by FLAC3D for homogeneous soil slope, whose parameters were reduced until slope reached the critical state. Then FISH program was used to get the location data of slip plane from displacement contour lines, which are used to determine the critical slip plane. Furthermore, method to determine multiple slip planes is also proposed by setting different height of elastic areas;
(6) The influences of cohesion, internal friction angle, tensile strength, dilation angle and elastic modulus to the safety factor and slip plane of slope are obtained, which show that, cohesion and friction angle have the largest impact on the safety and slip plane; the parameter ofλcφ= ccr/(γhtanφcr) is defined, and the variation trends of slip plane with cohesion and internal friction angle are unified; The safety factor increases with the increase of tensile strength; The influences of dilation angle and elastic modulus to the safety factor are obtained for different practical situation, which prefect the past dealing method for influence of these parameters to the stability of slope;
(7) The dual-spring element is adopted to simulate the characteristic of cable. A numerical calculation model for slope reinforced by cable is founded by FLAC3D. The excavation procedure of slope is simulated during the calculation. The procedure of SRM and parameters of cable to the stability of slope are discussed, the analysis results can give some guidance for both science research and engineering project;
(8) In order to apply the SRM in Hoek-Brown criterion, and make the result the same with that from Mohr-Coulomb criterion, the relationship between parameters of Hoek-Brown criterion and Mohr-Coulomb criterion is analyzed; the equivalent cohesion and friction angle are adopted to calculated the safety factor of slope, which explores a new way to indirectly calculate the safety factor of slope based on the Hoek-Criterion; The new is convenient and practical to be processed;
(9) The SRM is combined with the ubiquitous-joint criterion; the influential factors of the stratified rock slope are analyzed according to the numerical calculation, which expands the application of SRM;
(10) The SRM in Hoek-Brown criterion is further expanded in the three dimensional stability analysis; Rock slope in one surface mine is chosen as the analysis object. Three dimensional numerical analysis model is founded by FLAC3D, the safety factor and failure mode of slope are calculated, the deformation responses of different areas in slope are recorded in the macroscopic way, which can give guidance for engineering practices;
(11) The failure modes of stratified rock slope are simulated by FLAC3D, during simulation, the elastic-plastic elements are adopted to simulate the deformation of weakness plane; the results from the numerical simulation are in accordance with that from laboratory tests, which extends the application area of SRM with FLAC3D.
(1)讨论了强度折减法安全系数的定义,推导了其与极限平衡法安全系数定义的关系,从理论上阐述两者的一致性;
(2)分析了在不同坡角情况下,粘结力c和内摩擦角φ对于稳定性的影响程度,从岩土体微观抗剪机理阐述了边坡稳定性的影响因素；提出了等效影响角θe的概念；当坡角β=θe时,c和φ对稳定性的影响程度相同；当坡角β<θe时,摩擦角φ发挥的作用大于粘结力c发挥的作用；当β>θe时,c对稳定性的影响程度大于φ；该等效影响角适用于所有均质边坡,具有普遍性,其值为θe=34.1°；
(3)对同一边坡算例建立三种临界失稳判据,采用拉格朗日元法对边坡进行弹塑性稳定分析,将三种判据得到的安全系数进行对比,探讨各个判据的合理性及实用性,得到：塑性区贯通判据在判断塑性区是否贯通时需人为进行观察,“自动化”程度不高；计算不收敛判据原理简单,得到的安全系数与位移突变判据的结果差别十分微小,并且便于程序编制；位移突变判据物理意义明确；
(4)为了确定位移突变判据中的监测点和监测方式,在边坡面和内部布设若干监测点进行对比分析,并采用曲线方程对位移-折减系数的关系进行拟合,得到：a、双曲线方程S=(b+cK)/(1+aK)的拟合效果较好；拟合结果能够得到边坡的安全系数；b、监测点须在临界滑移线以内选取；在未知滑移线位置的情况下,选取坡脚作为监测点是不合适的；同一点在不同位移方式下,得到的安全系数相等；
(5)采用边坡的位移等值线对滑动面进行判断,并利用自编FISH程序将该曲线和边坡线数据取出,从而量化滑动面上各点的位置,实现了滑动面直接确定方法；设置不同弹性区高度,得到多滑动面的确定方法；
(6)分析影响因素粘结力,内摩擦角,抗拉强度,剪胀角和弹性模量对边坡安全系数和滑动面的影响,得到：内摩擦角和粘结力对安全系数和滑动面位置的影响最大;定义了新的参数λcφ=ccr/(γhtanφcr),统一了滑动面随粘结力和内摩擦角的变化趋势；安全系数随着抗拉强度的增大而呈现递增的规律；探讨了不同工况下,剪胀角和弹性模量对安全系数的影响,完善了以往稳定性分析对这些参数的处理方法；
(7)采用双弹簧锚杆单元,模拟了边坡开挖过程中,锚杆的加固效应,讨论了强度折减法在考虑锚杆加固情况下的实施过程以及锚杆参数对稳定性的影响,得到一些新的见解对科学研究和工程应用都有一定参考价值；
(8)为了在Hoek-Brown准则中实施强度折减法,并使其得到的结果与Mohr-Coulomb准则中强度折减法得到的结果等效,通过理论推导得到Hoek-Brown准则与Mohr-Coulomb准则参数之间的关系；采用等效粘结力和内摩擦角,计算边坡的安全系数,从而间接得到Hoek-Brown准则下边坡的安全系数,该方法方便可行,具有实用价值；
(9)将强度折减法与描述层状岩体的Ubiquitous-Joint准则相结合,通过数值计算,分析了层状岩质边坡稳定性的影响因素,扩展了强度折减法的应用范围；
(10)进一步探讨Hoek-Brown准则强度折减法在三维边坡稳定性分析中的应用,以某露天矿边坡为工程背景,利用快速拉格朗日差分法(FLAC3D),建立三维数值分析模型,计算边坡的安全系数和破坏模式,从宏观角度揭示出边坡开挖后,不同区域的位移变形响应,为工程实践提供指导；
(11)采用FLAC3D对层状边坡的破坏模式进行模拟,利用低强度弹塑性单元模拟软弱结构面的变形；通过数值分析得到的结果与试验相符,推广了FLAC3D强度折减法在工程中的应用。
Slope stability analysis is the most basic and important stage in slope engineering, which is also the most difficult and emergent problem need to be solved. In the recent year, with the development of compute technology, the strength reduction method (SRM) is becoming a new trend in the area of slope stability analysis. When compared to the traditional limit equilibrium method (LEM), SRM not only meets the mechanical equilibrium condition, but also takes into consideration of the stress-strain relationship; During calculation, SRM does not have to make any assumption, it can search for the critical slip plane and find out the minimum safety factor for the slope in the automatic way, while the failure of slope and development of plastic zone can be reflected in the result of SRM, as well, which indicates that SRM has more advantages than LEM for it is based on the more precisely theories. Although many people have done much work on SRM, and get many achievements. The SRM is still far away from the perfect state. So the present paper has done the studies on some details for SRM which needs to be renovated. The main contents and conclusions are:
(1) The different definitions of safety factor for strength reduction method are discussed, and the relationship of safe factor for SRM and LEM is obtained, which shows the consistency of definitions for SRM and LEM;
(2) The impact of cohesion c and internal friction angleφto the stability of slope are analyzed, which studied the influential factors for stability of slope in the microscopic mechanism of shear strength; the equivalent influential angleθe is proposed; whenβ=θe, the c andφhave the same impact on the stability of slope; whenβ<θe,φhas the larger impact on the stability of slope than that of c; whenβ>θe, c has larger impact on the stability of slope than that ofφ; the equivalent influential angleθe is suitable in different homogenous slopes, whose value isθe=34.1°;
(3) Three critical failure criterions, the connectivity of plastic zone criterion, the convergence of numerical computations criterion and the mutation of displacement criterion, are founded in the same homogenous slope; The elasto-plastic analysis is done to the stability of slope by the method of fast lagrangian analysis of continua three dimensions (FLAC3D). Safety factors obtained from the three criterions are compared with that from Janbu's procedure of limit equilibrium. The analysis results show that, the automatic characteristic for the connectivity of plastic zone criterion is not obvious, it need observation and judgment from people; The calculation theory of the numerical computations convergence criterion is easy to understand, and convenient to be programmed, with great precision for its result is in small differences with that from LEM; the physical meaning of displacement mutation criterion is clear;
(4) In order to analyze the rationality of the chosen point's location and the displacement mode, numerical calculation models are founded for isotropic soil slope and joint rock slope, separately. Some monitoring points are located in slope while some in the internal of slope. The relationships between displacement and reduction factor are analyzed. According to the displacement mutation characteristic of displacement-reduction factor curves, hyperbola fitting equations are founded. The fitting results show that (a) fitting data are in good correlation with the monitoring data; (b) the points on and below the critical slip line can be chosen as the monitoring points of displacement mutation criterion; the top of slope is recommended to be chosen as the monitoring point in the universal slope with the consideration that the top of slope is sure to be below the critical slip line and its location is easy to obtained; If the location of slip plane is not certain, it is not proper to choose the toe of slope as the monitoring point; All the three displacement modes can lead to the same safety factor for the same monitoring point;
(5) A numerical model was founded in plane strain mode by FLAC3D for homogeneous soil slope, whose parameters were reduced until slope reached the critical state. Then FISH program was used to get the location data of slip plane from displacement contour lines, which are used to determine the critical slip plane. Furthermore, method to determine multiple slip planes is also proposed by setting different height of elastic areas;
(6) The influences of cohesion, internal friction angle, tensile strength, dilation angle and elastic modulus to the safety factor and slip plane of slope are obtained, which show that, cohesion and friction angle have the largest impact on the safety and slip plane; the parameter ofλcφ= ccr/(γhtanφcr) is defined, and the variation trends of slip plane with cohesion and internal friction angle are unified; The safety factor increases with the increase of tensile strength; The influences of dilation angle and elastic modulus to the safety factor are obtained for different practical situation, which prefect the past dealing method for influence of these parameters to the stability of slope;
(7) The dual-spring element is adopted to simulate the characteristic of cable. A numerical calculation model for slope reinforced by cable is founded by FLAC3D. The excavation procedure of slope is simulated during the calculation. The procedure of SRM and parameters of cable to the stability of slope are discussed, the analysis results can give some guidance for both science research and engineering project;
(8) In order to apply the SRM in Hoek-Brown criterion, and make the result the same with that from Mohr-Coulomb criterion, the relationship between parameters of Hoek-Brown criterion and Mohr-Coulomb criterion is analyzed; the equivalent cohesion and friction angle are adopted to calculated the safety factor of slope, which explores a new way to indirectly calculate the safety factor of slope based on the Hoek-Criterion; The new is convenient and practical to be processed;
(9) The SRM is combined with the ubiquitous-joint criterion; the influential factors of the stratified rock slope are analyzed according to the numerical calculation, which expands the application of SRM;
(10) The SRM in Hoek-Brown criterion is further expanded in the three dimensional stability analysis; Rock slope in one surface mine is chosen as the analysis object. Three dimensional numerical analysis model is founded by FLAC3D, the safety factor and failure mode of slope are calculated, the deformation responses of different areas in slope are recorded in the macroscopic way, which can give guidance for engineering practices;
(11) The failure modes of stratified rock slope are simulated by FLAC3D, during simulation, the elastic-plastic elements are adopted to simulate the deformation of weakness plane; the results from the numerical simulation are in accordance with that from laboratory tests, which extends the application area of SRM with FLAC3D.
引文
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