公路顺层岩质边坡稳定及其影响因素分析
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摘要
本文以公路顺层岩质边坡为研究对象,采用有限元强度折减法、极限平衡法、敏感性分析的单因素法和正交设计法、可靠度分析的一次二阶矩法和响应面法等,针对边坡溉化模型和工程实例,进行了边坡稳定性、因素敏感性和可靠度等方面的研究。在边坡稳定性计算方面,量化分析了由通用有限元程序与传统极限平衡法得到的安全系数结果差异,以及参数选取对有限元计算结果的影响,提出并验证了一种在DP系列准则间进行安全系数转换的新方法和基于内摩擦角取值点的D-P系列准则与M-C准则的匹配方法；在因素敏感性分析中提出了采用参数的增量来分析层状边坡的思路,验证了方差分析法在边坡敏感性分析中的适用性；在边坡可靠度分析中提出了与因素敏感性分析相结合的思路,对因素敏感性在边坡可靠度分析中的应用开展了研究,并给出了可供工程设计参考的建议；根据模型计算以及工程实例分析,提出了防护设计的原则。主要内容和研究成果有：
通过对具一组贯通软弱结构面的顺层岩质边坡有限元计算模型的分析表明,边坡坡度陡于岩层倾角、存在临空面时对稳定不利,安全系数随边坡高度的增加而降低；坡顶荷载对边坡稳定性的影响跟其与潜在滑动面的相对位置以及荷载大小有关；挡墙和锚杆通过对塑性区贯通带的阻截使塑性区转移到更薄弱的结构面,从而提高安全系数,但锚杆必须贯穿塑性区才能发挥作用。
应用通用有限元程序计算公路顺层岩质边坡安全系数时,其计算结果偏于不安全,基于外接圆屈服准则的有限元计算结果比基于莫尔-库仑准则的极限平衡法计算结果平均高约22%。在有限元计算中,忽略剪胀角的计算结果较为保守；采用关联流动法则时的塑性区分布范围比非关联流动法则时明显缩小；杨氏模量和泊松比取值对边坡稳定安全系数计算结果几乎没影响,但模量下调将使边坡的位移增加,泊松比变小将使塑性区分布范围扩大。
D-P系列准则与M-C准则的研究表明,在基于系列DP准则的边坡稳定安全系数有限元计算中,可以用π平面上D-P系列准则半径之比进行边坡稳定安全系数转换；当D-P系列准则与M-C准则进行匹配时,传统的方法多从“平均”角度出发,对于具体边坡,从“平均”意义得出的匹配结论可能有较大偏差；本文提出了新的方法,只需将不同内摩擦角φ值时DP1准则和M-C准则计算得到的安全系数比值数据曲线,加入内摩擦角～系列DP准则半径比值的二维空间,通过比较各曲线在相应φ值的竖向截距即可得到最佳匹配准则,该法对具体边坡更具针对性,结果也更为准确。
均质边坡进行敏感性分析时可以直接取参数的不同水平值,由多层岩体组成的顺层岩质边坡,在敏感性分析考虑因素水平时,提出了采用参数增量的分析思路。通过单因素分析法、极差分析法和方差分析法的比较表明,三种敏感性分析法得出的结论基本一致,但方差分析法的分析效果最优。
基于因素敏感性的可靠度分析表明,敏感性较大的因素,不管是强度参数或者几何参数,若存在一定的变异性,在可靠度分析中都不应忽视,否则将对结果产生重大影响；在边坡可靠度分析中以敏感性较大的因素作为随机变量时的破坏概率大,在边坡可靠度分析前首先确定各个稳定影响因素的敏感性排序,再根据实际参数的变异性选取随机变量进行分析,结果往往更加合理；边坡可靠度求解结合参数敏感性分析,不仅对最终的计算结果影响很大,而且从某种程度上也关系到计算工作量和复杂程度,对于顺层岩质边坡等复杂边坡,合理地应用敏感性分析结果,剔除不敏感因素,可以使原本十分复杂的边坡可靠度求解变得相对简单。
杭千高速公路建德段典型顺层滑坡的分析表明,公路顺层岩质边坡的形成要素可以归结为层状基岩、岩层的不利走向和产状、层间软弱夹层、临空面。边坡防护设计总体原则为“下挡上缓”,即加强下部支挡,根据岩层倾角合理设计边坡坡率,有条件时尽量放缓边坡并降低边坡高度,坡面需及时防护,坡顶有荷载时,需查明其与潜在滑动面的相对位置,当边坡放缓受限时,可根据实际情况采用工程措施加强防护
Based on generalized model of highway bedding rock slope and engineering examples, the slope stability, factors sensitivity and reliability and so on were studied by using strength reduction of FEM, limit equilibrium method, single factor analysis and orthogonal design method of factors sensitivity, first order-two moment method and response surface method of reliability analysis. In the slope stability calculation, based upon the difference of safety coefficients obtained between general FEM program and traditional limit equilibrium method, and the influences of parameters selection on the results of FEM were quantitatively analyzed, a new transformation method of safety coefficients by different Drucker-Prager yield criterions, and matching method between Drucker-Prager yield criterions and Mohr Coulomb criteria based on value of the internal frictional angle were proposed. In the factors sensitivity analysis of layered slope, the idea of using parameter increment was put forward when considering the factors level, and the applicability of variance analysis method in slope sensitivity was verified. In the analysis of slope reliability, the idea of combining factors sensitivity was put forward, the application of factors sensitivity in slope reliability was studied, and reference for engineering design was proposed. According to the model calculation and analysis of engineering examples, the design principles of slope protection was suggested. The main contents and research results as follow:
Using nonlinear FEM strength reduction method, stability analysis was made on the model of bedding rock slope with a group of runned-through plane of weakness. Results show it is disadvantage for the stability when the slope steeper than the dip angle of rock stratum and the presence of free surface, and the safety coefficient decreases with the increase of slope height. The influence of load on the top of slope to safety coefficient depends on the magnitude of load and relative position between load and the runned-through plastic zone. Retaining wall or anchor rods can increase the safety coefficient of slope by block and intercept the runned-through plastic zone, then the plastic zone moves to other more weak structure plane, only when the plastic zone is runned through can anchor rod play a role.
The calculation results of highway bedding rock slope safety coefficient obtained by general FEM program are unsafe, for the results of FEM based on Drucker-Prager yield criterion are about22%higher than the results of traditional limit equilibrium method based on Mohr Coulomb criteria. In the finite element analysis, the calculation results are more conservative when the dilatancy angle is ignored. When using the associated flow rule, the distribution range of plastic zone reduced obviously than that of the non associated flow rule. The value of Young's modulus and Poisson's ratio almost have no effect on slope stability, but the cut of Young's modulus will make the displacement of slope increase obviously, the scope of plastic zone will increase with the reduce of Poisson's ratio.
By study on Drucker-Prager yield criterion and traditional Mohr Coulomb criteria shows, in slope stability by FEM based on different Drucker-Prager yield criterion, ratios of D-P radii can be used as conversion coefficient of safety factors under different Drucker-Prager yield criterion. When D-P yield criterion are to be matched to Mohr Coulomb criteria, traditional method is always from the perspective of "average", the matching conclusion from "average" may have a larger deviation for a specific slope. A new method is proposed in this paper:the ratios of safety factors under Mohr Coulomb hexagon circumcircle Drucker-Prager yield criterion(DP1) and M-C criteria vary with the value of the internal frictional angle, putting the numerical value of internal frictional angle and the ratios on two-dimensional space of internal frictional angle～ratios of D-P radii, it can get the best matching yield criterion by comparing the y-intercept under corresponding value of internal frictional angle among these curves, this method is more specific and the results will be more accurate.
For the sensitivity analysis of homogeneous slope, it may use the different level of parameters directly; but in the case of multi-layered rock mass, it is difficult to use the method mentioned above, instead a method of the available parameter increment is suggested. The comparison of single factor analysis, range analysis and variance analysis shows, the conclusion obtained from these methods are basically the same, but the effect of variance analysis is best.
Study of slope reliability analysis based on factors sensitivity shows, whether the strength parameters or geometric parameters, if there sensitivity are larger and there exists some variability, its influence to slope stability analysis of reliability cannot be ignored, or there will have a significant impact on the analysis results. The higher sensitivity level of factors selected as random variable, the larger failure probabilities, firstly determining the sorting of parameters sensitivity, and choosing random variable according to the variation coefficient of parameters, the results of slope reliability analysis maybe more reasonable. The slope reliability analysis combined with factors sensitivity can not only influence the final results greatly; to some extent, it is also related to the computational workload and complexity. For reliability analysis of bedding rock slope and other complex slope, reasonable application of the sensitivity analysis results can eliminates the un-sensitive factors and simplify the original complex analysis of slope reliability.
Analysis of typical bedding landslide in Jiande section of Hang Qian Expressway shows, the formation elements of highway bedding rock slope can be attributed to the layered rock, adverse trend and occurrence of rock, plane of weakness and free surface. The general design principle for bedding rock slope protection is "retaining at the bottom and slow slope above" that is strengthen the retaining of lower part of the slope, choosing reasonable slope ratio according to the obliquity of rock, when conditions permit, slowdown and reduce the height of slope as far as possible, the surface of slope should be timely protected, when there is load on the top of slope, it is necessary to identify the relative position between load and potential sliding surface, when the slowing of slope is restricted, engineering measures should be used to enhance the protection according to the actual situation.
通过对具一组贯通软弱结构面的顺层岩质边坡有限元计算模型的分析表明,边坡坡度陡于岩层倾角、存在临空面时对稳定不利,安全系数随边坡高度的增加而降低；坡顶荷载对边坡稳定性的影响跟其与潜在滑动面的相对位置以及荷载大小有关；挡墙和锚杆通过对塑性区贯通带的阻截使塑性区转移到更薄弱的结构面,从而提高安全系数,但锚杆必须贯穿塑性区才能发挥作用。
应用通用有限元程序计算公路顺层岩质边坡安全系数时,其计算结果偏于不安全,基于外接圆屈服准则的有限元计算结果比基于莫尔-库仑准则的极限平衡法计算结果平均高约22%。在有限元计算中,忽略剪胀角的计算结果较为保守；采用关联流动法则时的塑性区分布范围比非关联流动法则时明显缩小；杨氏模量和泊松比取值对边坡稳定安全系数计算结果几乎没影响,但模量下调将使边坡的位移增加,泊松比变小将使塑性区分布范围扩大。
D-P系列准则与M-C准则的研究表明,在基于系列DP准则的边坡稳定安全系数有限元计算中,可以用π平面上D-P系列准则半径之比进行边坡稳定安全系数转换；当D-P系列准则与M-C准则进行匹配时,传统的方法多从“平均”角度出发,对于具体边坡,从“平均”意义得出的匹配结论可能有较大偏差；本文提出了新的方法,只需将不同内摩擦角φ值时DP1准则和M-C准则计算得到的安全系数比值数据曲线,加入内摩擦角～系列DP准则半径比值的二维空间,通过比较各曲线在相应φ值的竖向截距即可得到最佳匹配准则,该法对具体边坡更具针对性,结果也更为准确。
均质边坡进行敏感性分析时可以直接取参数的不同水平值,由多层岩体组成的顺层岩质边坡,在敏感性分析考虑因素水平时,提出了采用参数增量的分析思路。通过单因素分析法、极差分析法和方差分析法的比较表明,三种敏感性分析法得出的结论基本一致,但方差分析法的分析效果最优。
基于因素敏感性的可靠度分析表明,敏感性较大的因素,不管是强度参数或者几何参数,若存在一定的变异性,在可靠度分析中都不应忽视,否则将对结果产生重大影响；在边坡可靠度分析中以敏感性较大的因素作为随机变量时的破坏概率大,在边坡可靠度分析前首先确定各个稳定影响因素的敏感性排序,再根据实际参数的变异性选取随机变量进行分析,结果往往更加合理；边坡可靠度求解结合参数敏感性分析,不仅对最终的计算结果影响很大,而且从某种程度上也关系到计算工作量和复杂程度,对于顺层岩质边坡等复杂边坡,合理地应用敏感性分析结果,剔除不敏感因素,可以使原本十分复杂的边坡可靠度求解变得相对简单。
杭千高速公路建德段典型顺层滑坡的分析表明,公路顺层岩质边坡的形成要素可以归结为层状基岩、岩层的不利走向和产状、层间软弱夹层、临空面。边坡防护设计总体原则为“下挡上缓”,即加强下部支挡,根据岩层倾角合理设计边坡坡率,有条件时尽量放缓边坡并降低边坡高度,坡面需及时防护,坡顶有荷载时,需查明其与潜在滑动面的相对位置,当边坡放缓受限时,可根据实际情况采用工程措施加强防护
Based on generalized model of highway bedding rock slope and engineering examples, the slope stability, factors sensitivity and reliability and so on were studied by using strength reduction of FEM, limit equilibrium method, single factor analysis and orthogonal design method of factors sensitivity, first order-two moment method and response surface method of reliability analysis. In the slope stability calculation, based upon the difference of safety coefficients obtained between general FEM program and traditional limit equilibrium method, and the influences of parameters selection on the results of FEM were quantitatively analyzed, a new transformation method of safety coefficients by different Drucker-Prager yield criterions, and matching method between Drucker-Prager yield criterions and Mohr Coulomb criteria based on value of the internal frictional angle were proposed. In the factors sensitivity analysis of layered slope, the idea of using parameter increment was put forward when considering the factors level, and the applicability of variance analysis method in slope sensitivity was verified. In the analysis of slope reliability, the idea of combining factors sensitivity was put forward, the application of factors sensitivity in slope reliability was studied, and reference for engineering design was proposed. According to the model calculation and analysis of engineering examples, the design principles of slope protection was suggested. The main contents and research results as follow:
Using nonlinear FEM strength reduction method, stability analysis was made on the model of bedding rock slope with a group of runned-through plane of weakness. Results show it is disadvantage for the stability when the slope steeper than the dip angle of rock stratum and the presence of free surface, and the safety coefficient decreases with the increase of slope height. The influence of load on the top of slope to safety coefficient depends on the magnitude of load and relative position between load and the runned-through plastic zone. Retaining wall or anchor rods can increase the safety coefficient of slope by block and intercept the runned-through plastic zone, then the plastic zone moves to other more weak structure plane, only when the plastic zone is runned through can anchor rod play a role.
The calculation results of highway bedding rock slope safety coefficient obtained by general FEM program are unsafe, for the results of FEM based on Drucker-Prager yield criterion are about22%higher than the results of traditional limit equilibrium method based on Mohr Coulomb criteria. In the finite element analysis, the calculation results are more conservative when the dilatancy angle is ignored. When using the associated flow rule, the distribution range of plastic zone reduced obviously than that of the non associated flow rule. The value of Young's modulus and Poisson's ratio almost have no effect on slope stability, but the cut of Young's modulus will make the displacement of slope increase obviously, the scope of plastic zone will increase with the reduce of Poisson's ratio.
By study on Drucker-Prager yield criterion and traditional Mohr Coulomb criteria shows, in slope stability by FEM based on different Drucker-Prager yield criterion, ratios of D-P radii can be used as conversion coefficient of safety factors under different Drucker-Prager yield criterion. When D-P yield criterion are to be matched to Mohr Coulomb criteria, traditional method is always from the perspective of "average", the matching conclusion from "average" may have a larger deviation for a specific slope. A new method is proposed in this paper:the ratios of safety factors under Mohr Coulomb hexagon circumcircle Drucker-Prager yield criterion(DP1) and M-C criteria vary with the value of the internal frictional angle, putting the numerical value of internal frictional angle and the ratios on two-dimensional space of internal frictional angle～ratios of D-P radii, it can get the best matching yield criterion by comparing the y-intercept under corresponding value of internal frictional angle among these curves, this method is more specific and the results will be more accurate.
For the sensitivity analysis of homogeneous slope, it may use the different level of parameters directly; but in the case of multi-layered rock mass, it is difficult to use the method mentioned above, instead a method of the available parameter increment is suggested. The comparison of single factor analysis, range analysis and variance analysis shows, the conclusion obtained from these methods are basically the same, but the effect of variance analysis is best.
Study of slope reliability analysis based on factors sensitivity shows, whether the strength parameters or geometric parameters, if there sensitivity are larger and there exists some variability, its influence to slope stability analysis of reliability cannot be ignored, or there will have a significant impact on the analysis results. The higher sensitivity level of factors selected as random variable, the larger failure probabilities, firstly determining the sorting of parameters sensitivity, and choosing random variable according to the variation coefficient of parameters, the results of slope reliability analysis maybe more reasonable. The slope reliability analysis combined with factors sensitivity can not only influence the final results greatly; to some extent, it is also related to the computational workload and complexity. For reliability analysis of bedding rock slope and other complex slope, reasonable application of the sensitivity analysis results can eliminates the un-sensitive factors and simplify the original complex analysis of slope reliability.
Analysis of typical bedding landslide in Jiande section of Hang Qian Expressway shows, the formation elements of highway bedding rock slope can be attributed to the layered rock, adverse trend and occurrence of rock, plane of weakness and free surface. The general design principle for bedding rock slope protection is "retaining at the bottom and slow slope above" that is strengthen the retaining of lower part of the slope, choosing reasonable slope ratio according to the obliquity of rock, when conditions permit, slowdown and reduce the height of slope as far as possible, the surface of slope should be timely protected, when there is load on the top of slope, it is necessary to identify the relative position between load and potential sliding surface, when the slowing of slope is restricted, engineering measures should be used to enhance the protection according to the actual situation.
引文
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