考虑能量-时间分布的边坡动力可靠性分析新方法

提出一种考虑能量-时间分布的边坡动力可靠性分析方法。该方法将动态最危险滑动面及其稳定系数以时间序列加以刻画,并根据边坡动力反应的能量分布特征,提取持续时间统计窗,用于对上述时间序列的统计分析,以获取边坡动力模糊失效概率、边坡动力可靠度指标和基于保证率的边坡动力稳定系数。以澳大利亚计算机应用协会边坡稳定考核题为例,应用上述新方法考察其在芦山7.0级主震波形条件下的稳定性,研究了在不同统计窗下的边坡动力可靠性。案例分析表明： （1）新方法能够抓住影响边坡动力稳定的主要时间段,使分析结果更为凝练、可信。（2）通过引入边坡失效状态的模糊判别,使得可靠性评价中能够考虑模糊性,解决了以往常规方法区分度不够的问题。（3）基于保证率的边坡动力稳定系数具有很好的应用前景,它在内涵上体现了可靠性分析,在形式上与静力稳定系数的定义兼容,在数值上反映了边坡瞬时动力稳定系数的保守估计值,在实践上与现行规范的拟静力法具有良好的可比性,因而具有多方面的优势。（4）就本案例而言,动力条件下最危险滑动面的发育位置趋向于静力条件下的最危险滑动面,体现了依据静力和拟静力理论框架所进行的防护工程设计,在动力条件下仍然具有积极的意义。（5）新方法对定量研究现行边坡规范的抗震设计冗余提供了一条途径。提出的新方法为边坡抗震研究提供了新的思路、方法和可供参考的实例。     

Seismic stability analysis of a layered rock slope

In general, the determination of the factor of safety and the location of the critical slip surface are two major challenges in seismic slope stability analysis. In this paper, a new approach for determining the factor of safety and the corresponding critical slip surface of a layered rock slope subjected to seismic excitations is presented, through a case study based on the combination of the shear strength reduction technique and distinct element method. According to this proposed method, the seismic factor of safety and the critical slip surface of the slope are estimated and compared with those obtained by the pseudo-static approach, combined with the limit equilibrium method. It is found that the factor of safety obtained from the proposed method is slightly greater than that computed by the pseudo-static analysis, with a difference of 4.2%, and that the critical slip surface obtained from the two methods is identical, which confirms the reasonability and feasibility of the proposed method.     

A simplified approach for studying the influence of vertical accelerations on seismic response of slopes

ABSTRACT

A simplified approach is presented for estimating permanent displacements in slopes as a result of both vertical and horizontal seismic accelerations. A study of 52 earthquake records showed that the time difference between maximum horizontal and vertical accelerations varied between 0 and 10.3 s. The approach is illustrated for an earth dam embankment by analysing the effects of five of the above earthquake records. The approach combines a pseudo-static slope stability analysis for estimation of the critical (or yield) horizontal-vertical acceleration combinations, and a Newmark type displacement analysis. Guidelines are presented for conservative choice of soil strength parameters of saturated clays for use in the stability analysis. While permanent displacements of up to 40 cm were predicted without considering the vertical acceleration component, no additional displacement above 3.5 cm resulted when this component was included. The predicted additional displacement was consistently less than 10%, and in 50% of the analyses, vertical acceleration led to smaller predicted displacements. The simple approach may be applied in analysis for any slope using real earthquake records. Using existing, empirical expressions for permanent displacement, based only on horizontal accelerations, the effect of the vertical accelerations may be conservatively estimated by increasing the displacement by 10%.     

锚固岩石边坡地震稳定性拟动力分析

地震易发地区的锚固岩石边坡,需要研究其地震稳定性。对于锚固典型岩石边坡,在考虑水平与竖向地震力、张裂缝积水深度、坡顶超载、锚索倾角、锚索位置、锚索拉力及静水与动水压力等的条件下,运用拟静力和拟动力方法分别推导了不同工况条件下其抗滑和抗倾覆地震安全系数。分析表明,竖向向上地震力有利于锚固岩石边坡的抗滑稳定,而竖向下的地震力有利于锚固岩石边坡的抗倾覆稳定;在相同工况条件下,当岩体放大系数等于1.0时,拟动力与拟静力方法所得锚固岩石边坡地震安全系数相差无几,但是,当岩体放大系数逐渐增大时,拟动力方法所得地震安全系数越来越明显地小于拟静力方法所得地震安全系数。因此,在抗震设计当中适当的考虑岩体放大系数,将会有利于锚固岩石边坡的安全设计。     

Seismic rock slope stability charts based on limit analysis methods

Earthquake effects are commonly considered in the stability analysis of rock slopes and other earth structures. The standard approach is often based on the conventional limit equilibrium method using equivalent Mohr–Coulomb strength parameters (c and ?) in a slip circle slope stability analysis. The purpose of this paper is to apply the finite element upper and lower bound techniques to this problem with the aim of providing seismic stability charts for rock slopes. Within the limit analysis framework, the pseudo-static method is employed by assuming a range of the seismic coefficients. Based on the latest version of Hoek–Brown failure criterion, seismic rock slope stability charts have been produced. These chart solutions bound the true stability numbers within ±9% or better and are suited to isotropic and homogeneous intact rock or heavily jointed rock masses. A comparison of the stability numbers obtained by bounding methods and the limit equilibrium method has been performed where the later was found to predict unconservative factors of safety for steeper slopes. It was also observed that the stability numbers may increase depending on the material parameters in the Hoek–Brown model. This phenomenon has been further investigated in the paper.     

土石坝拟静力抗震稳定分析的强度折减有限元法

基于拟静力抗震设计概念,提出利用强度折减有限单元法分析土石坝的抗震稳定性,给出了两种确定地震惯性力的方法：（1）依据《水工建筑物抗震设计规范》[1],并结合有关土石坝动态分布系数计算了沿坝高分布的地震惯性力;（2）直接利用土石坝有限元地震动力反应分析得到的单元节点加速度反应,依据建议的方法确定坝体各单元节点的地震惯性力。将上述计算确定的地震惯性力与其他形式的外荷载共同作用到土石坝上,采用强度折减有限元法确定土石坝坝体的拟静力抗震安全系数。对于稳定渗流期,水位降落期等不同工况,或需要考虑振动孔隙水压力作用的饱和无黏性土填筑坝等不同计算条件,给出了使用折减强度有限元法分析坝体抗震稳定性的实现途径和方法。研究表明,有限元法对边界条件、复杂断面条件和材料分区及荷载组合均具有较强的适应能力,因此,使用有限元法分析土石坝抗震稳定性具有显著的优越性。     

地震效应和坡顶超载对均质土坡稳定性影响的拟静力分析

基于强度折减技术和极限分析上限定理,假定机动容许的速度场破坏面,考虑坡顶超载、水平和竖向地震效应影响推导了边坡稳定性安全系数的计算表达式。采用序列二次规划迭代方法（和内点迭代方法）对边坡安全系数目标函数进行能量耗散最小化意义上的优化计算,与多个算例的对比验证了其方法和程序计算的正确性;对影响土质边坡动态稳定性的一些因素进行了参数分析,分析表明：随着边坡倾角?、坡顶超载q、水平和竖向地震效应影响系数的增大,边坡稳定性安全系数显著下降;随着坡顶超载q、水平地震效应影响系数kh的增大、竖向地震效应影响系数kv的减小,边坡的潜在滑动面越来越深,潜在破坏范围越来越大。竖向地震效应对边坡稳定性也有一定影响,强震条件下的设计计算必须考虑竖向地震效应的影响。     

基于离散元的强度折减法分析岩质边坡稳定性

将通用离散元UDEC与强度折减法结合,对含多结构面的岩质边坡的稳定性进行了分析。通过对节理岩质边坡的UDEC模型中的可变形块体和节理单元的强度参数进行折减,使模型不能再达到平衡状态,此时的折减系数就是边坡的安全系数,另外,由对应的边坡块体的速度矢量可以确定滑动面和边坡的破坏形态。通过与传统的条分法的结果比较,表明基于UDEC的强度折减法是一种可靠、有效的方法,为复杂节理岩质边坡的滑动面确定与安全系数计算开辟了新的途径。     

An important pitfall of pseudo-static finite element analysis

Finite Element (FE) pseudo-static analysis can provide a good compromise between simplified methods of dynamic analysis and time domain analysis. The pseudo-static FE approach can accurately model the in situ, stresses prior to seismic loading (when it follows a static analysis simulating the construction sequence) is relatively simple and not as computationally expensive as the time domain approach. However this method should be used with caution as the results can be sensitive to the choice of the mesh dimensions. In this paper two simple examples of pseudo-static finite element analysis are examined parametrically, a homogeneous slope and a cantilever retaining wall, exploring the sensitivity of the pseudo-static analysis results on the adopted mesh size. The mesh dependence was found to be more pronounced for problems with high critical seismic coefficients values (e.g. gentle slopes or small walls), as in these cases a generalised layer failure mechanism is developed simultaneously with the slope or wall mechanism. In general the mesh width was found not to affect notably the predicted value of critical seismic coefficient but to have a major impact on the predicted movements.     

Vertical acceleration effect on landsides triggered by the Wenchuan earthquake,China

The 2008 Wenchuan earthquake with Ms8.0 triggered extensive throwing-pattern landslides in the area within or near the seismic faults. The resultant landslides from this earthquake brought to the fore the effect of vertical earthquake acceleration on landslide occurrence. The pseudostatic analysis and the dynamic response on landslide stability due to the Wenchuan earthquake are studied with the Chengxi (West Town) catastrophic landslide used as a case study. The results show that the epicenter distance is an important factor which affects the vertical acceleration and thus the stability of landslide. Also, the vertical acceleration was found to have a significant impact on the FOS of landslide if the earthquake magnitude is quite large. Within the seismic fault, the amplitude effect of vertical acceleration is very dominant with the FOS of landslide, for vertical acceleration ranging from positive to negative, having a variation of 25 %. The variation of FOS of landslide for vertical acceleration ranging from positive to negative are 15 and 5 % for landslides near seismic fault and outside seismic fault, respectively. For landslide with a slope angle <45°, the FOS of landslide with both horizontal and vertical accelerations is significantly greater than the one without vertical acceleration. Further, the results computed from both the pseudostatic method and dynamic analysis reveal that the FOS during the earthquake varied significantly whether vertical acceleration is considered or not. The results from this study explain why lots of throwing-pattern catastrophic landslides occurred within 10 km of the seismic fault in the Wenchuan earthquake.     

Lined Circular Tunnels in Elastic Transversely Anisotropic Rock at Depth

Closed-form solutions for displacements and stresses of both the liner and the rock are presented for a deep circular tunnel excavated in transversely anisotropic rock above or below the water table subjected to static or seismic loading. The solutions are obtained with the assumption of elastic response of rock and liner, tied contact between rock and liner, impermeable liner, plane strain conditions along the tunnel axis and simultaneous excavation, and liner installation. The liner of a tunnel placed below the water table must support, in addition to the rock stresses, the full water pressure, while a tunnel located above the water table must support only the rock pressures. The solutions presented for static loading show, however, that displacements and stresses of the liner and rock are the same when the tunnel is placed above or below the water table as long as the total far-field stresses are the same. With rapid loading, e.g. seismic loading, excess pore pressures may be generated in saturated rock, which induce a different response than that of a tunnel excavated in dry rock. The analyses indicate that stresses and displacements are more uniform when excess pore pressures are produced, which seems to indicate that pore pressure generation tends to reduce non-uniform response in anisotropic rock.     

Reliability analysis of slope stability under seismic condition during a given exposure time

Evaluating the failure probability of a slope under the seismic condition during a given exposure time is important for performance-based assessment of slope stability. In this paper, a two-stage method is suggested to study the seismic stability of a slope during a given exposure time. In the first stage, the exceedance probability of the horizontal pseudo-static acceleration is evaluated. In the second stage, the vulnerability curve of the slope, which shows the relationship between the horizontal pseudo-static acceleration and the failure probability of the slope, is established. The failure probability of the slope during a given exposure time is then assessed by combining the exceedance probability curve of the horizontal pseudo-static acceleration and the vulnerability curve of the slope. Examples investigated show that the reliability of a slope under the seismic condition is controlled by multiple slip surfaces. A slope may have different failure probabilities during the same exposure time when it is at different locations because of different levels of ground shaking. Event at the same site, different slopes may have different failure probability because of the difference in factors like slope geometries and geological conditions. The method suggested in this paper can be used to quantify the effect of the above factors on the reliability of a slope.     

Seismic landslide simulations in discontinuous deformation analysis

Discontinuous deformation analysis (DDA) is a numerical approach used to simulate the post-failure behavior of a blocky assembly. Three available algorithms incorporate seismic impacts into DDA simulations for earthquake-induced slope failure. The following methods are used: directly applying time-dependent accelerations to falling/sliding blocks (Method 1); adding time-dependent accelerations to base block (Method 2); and time-dependently constraining seismic displacements of the base block (Method 3). However, incorrect absolute movements of falling/sliding and base blocks were obtained using Method 1. Additionally, relative movements between falling/sliding blocks and the base block are opposite to those simulated by the other two algorithms—Methods 2 and 3. Since locating an earthquake-induced landslide before an earthquake is extremely difficult, the seismic movements of base rock are recorded. Method 1 applies recorded seismic data to sliding blocks in conflict with d’Alembert’s principle of mechanics. Additionally, in Method 2, when the computation time step must be longer than the time in seismic data, computational results reveal abnormal base block displacements due to the non-zero velocity recorded at the end time of seismic data in seismic DDA. In this study, a novel algorithm to diminish the velocity of the base rock in the seismic analysis is utilized to modify Method 2. Furthermore, this work confirms that DDA with the modified Methods 2 and 3 is a practical approach for earthquake-induced landslide simulations.     

Seismic stability analysis of a rock block using the block theory and Newmark method

Seismic stability analysis of a rock block is an important issue in the field of rock mechanics and rock engineering. To solve this problem, the block theory and the Newmark method are combined, and a general method for seismic response of a rock block is introduced. First, the formation method of a three-dimensional rock block, which includes establishing a topological relationship among the block-polygon face-edge-vertex and dividing a complex block into convex subblocks, is presented, and the simplex integration method is employed to calculate the volume of a rock block and the areas of the polygonal faces. Second, the assumptions and algorithms of the general method for seismic response of a rock block are detailed. The dynamic analysis is carried out in time step. In each time step, the key technologies including analysis of the seismic force and motion mode, trial of the incremental displacement, check for the block entrance, and update of the motion parameters are performed in order. Last, two verification examples and three application examples including a wedge, a rock block of slope, and a combined rock block are used to analyze the correctness and practicality of the general method. The results show that, for a given ground motion record, the Newmark program can effectively simulate the dynamic response process of the motion mode, velocity, and safety factor of the rock block, and the permanent displacement under the earthquake action is obtained, which provides a quantitative parameter to evaluate the dynamic stability of a rock block.     

A resilience framework for safety management of fossil fuel power plant

In the present study, cut slope stability assessment along ghat road section of Kolli hills was carried out by using various geotechnical parameters of rock and soil slope sections and structural kinematics of major discontinuities is presented. The rock slope (RS) stability assessment was carried out using Rock Mass Rating basic (RMR_basic) and Slope Mass Rating (SMR) classification systems. The type of failure and their Factor of Safety (FOS) for individual RS was calculated using Hoek and Bray method. In the case of soil slopes (SS), the FOS was calculated using Circular Failure Chart (CFC) and Limit Equilibrium (LE) methods. The input data for the slope stability analyses were collected through extensive field work followed by stereonet plotting and laboratory test. There are six rock slope sections, and five soil slope sections were taken into consideration for the cut slope stability analyses. The area depicts class II (RS-1, 2, & 6) and class III (RS-3, 4, & 5) of RMR classes. The SMR result depicts for RS-1, RS-2, and RS-6 are 64.40, 60.02, and 60.70, respectively, and falls in class II stable condition. The SMR values of RS-3 and RS-5 were 44.33 and 57, respectively, and come under the class III partially stable condition. The RS-4 with SMR value of 17.33 falls under the class I completely unstable condition. The FOS of planar failure case indicates that RS-3 (FOS = 0.22) is more unstable, while all other sections are having greater than 1 FOS. The calculated FOS values using CFC method reveals that the FOS is very close to 1 for all the SS sections that fall under completely saturated condition which indicates that these slope sections may fail during heavy rainfall. In LE method, the sections SS-3 and SS-4 are unsafe under partially and completely saturated (natural slope) condition. In average slope condition, all the SS sections are unsafe under partially or completely saturated conditions. The facets 2, 3, 4, and 5 required mitigation measures, to improve the stability of slopes. Site-specific mitigation measures were suggested for partially or completely unstable rock and soil cut slopes.     

地震作用下堆积体边坡的坡面变形与失稳机制

地震作用下堆积体边坡的动力响应特性十分复杂,单一抗震安全系数不足以评价其动力稳定性。通过大型振动台试验,研究了连续多级地震荷载作用下,地震波的类型、卓越频率及峰值加速度对堆积体边坡坡面永久位移的影响,并初步分析其失稳机制。试验结果表明,相同峰值加速度下振动型地震波比冲击型地震波更容易产生坡面永久位移,地震波卓越频率对坡面永久位移也有重要影响;堆积体边坡在峰值加速度apeak=0.2g时开始有大颗粒石砾滚落,对应的坡面永久位移在apeak=0.2g～0.3g之间开始产生并显著增大,另外利用考虑坡面几何形态变化的改进Newmark法对坡顶的永久位移进行了估算。通过坡面永久位移评价堆积体边坡的动力稳定性有一定合理性。     

地震效应下三维非均质土坡稳定性极限分析

基于极限分析上限定理,采用拟动力法研究了地震效应下非均质土坡的三维稳定性,并通过重度加大法（GIM）推导出边坡安全系数的显式表达式。此外,采用遗传算法进行优化,将所得结果进行对比验证,详细分析了地震条件下相关参数对边坡稳定性的影响。分析结果表明：边坡高度一定时,宽高比、边坡倾角的增大以及土体内摩擦角、非均质系数的减小均会造成安全系数的降低;拟静力法获得的结果相比于拟动力法较大,两种方法结果的差值会随着水平地震系数、有效内摩擦角的增大而增大,随着边坡倾角的增大而减小;土体放大系数的增大会导致安全系数减小,而地震波周期及波速的变化几乎对安全系数没有影响;滑动面轨迹受水平地震系数的影响较大,而受非均质系数的影响相对较小。     

三峡链子崖危岩体非线性动力响应分析

采用非线性有限元法研究岩质边坡的动力响应问题，模拟了软弱夹层的材料非线性及断层或裂缝的接触问题，假定岩块弹性体，推导了非线性动力响应迭代格式并编制了适于岩质边坡动力响应分析的三维非线性有限元程序，利用该程序对三峡链子崖危岩体进行了动力响应分析，得出了一些有价值的结论，计算结果与模型试验结果基本相符，证明本文数值计算的正确性。     

Advanced seismic slope stability analysis

The objective of this study was to present an advanced methodology for assessing seismic slope stability by taking into account the uncertainties related to the main input parameters. The methodology was applied on a real landslide in order to show the advantages of using the proposed procedure and establish the baseline trends of dynamic response and calculated permanent seismic displacements. It involves the following steps: preliminary analysis, probabilistic static and seismic factor of safety analysis, and permanent seismic displacement analysis. Estimating post-failure maximum seismic deformation of landslide mass and sounding properties is the most important part of this study. It involves both Newmark sliding block method and continuum mechanics approach, applied for characteristic set of input values in order to have more accurate assessment of slope performance and determine the relative importance of input parameters. The results of the analysis showed the benefits of using the proposed step-by-step methodology. The obtained difference in the results between the two methods depends strongly on the set input data for a particular analysis.     

基于有限元强度折减法的边坡动力稳定性可靠性分析

传统有限元强度折减法在边坡稳定性数值分析中取得了一定的成功,但由于未考虑岩土体材料参数的变异性等不确定性因素,尚不能直接应用于边坡稳定性特别是动力稳定性可靠性分析问题。为此提出了基于有限元强度折减法的地震边坡动力稳定性可靠性分析方法。将有限元极限分析法、动力分析法和可靠性分析法三者耦合,分析求解边坡在地震作用下的动力稳定性可靠性问题,并将这一过程在数值计算程序中得以实现。在计算分析过程中,克服了原方法需不断人工试算才能得到边坡安全系数而无法量化处理问题,并对边坡动力失效准则进行了适用于程序化的改进,使其计算过程完全实现自主运行。结合典型算例分析结果表明,该方法显著的特点是能较全面地反映岩土体的动力特性和边坡岩土体材料强度参数的变异性及相关性,所得结果相对更加合理且更符合工程实际。该方法既是对有限元强度折减法的应用范围的有益推广,也为边坡动力稳定性可靠性问题研究提供了一条新的有效途径。