Kinematic and Block Theory Analyses for Shiplock Slopes of the Three Gorges Dam Site in China

The granitic rock mass that exists in the shiplock region of the Three Gorges dam site contains a number of major discontinuities and about four sets of minor discontinuities. One hundred and thirty three major discontinuities have been mapped around the shiplock covering an area of 1740×600 m. These major discontinuities were used to perform rock slope kinematic and block theory analyses. Kinematic analyses were performed under the following two cases: (1) assuming all the mapped discontinuities cross the shiplock; (2) using only discontinuities that actually intersect the shiplock. Under case (1) and case (2) the shiplock faces in the proposed permanent shiplock region in fresh rock were found to be stable up to a cut slope of about 45° and 58°, respectively. Block theory was applied to identify different block types that exist on the shiplock faces and to estimate the maximum safe slope angles on the shiplock faces. The orientations of the major discontinuities that actually intersect the shiplocks were considered in this analysis. The total length of the shiplock (1750 m) was divided into 50 m segments. From the stereo-plots, the key blocks (Type I) and/or potential key blocks (Type II) were found for only five segments of the shiplock slopes. It was found that the dip of the cut slope should be less than about 60° to avoid creation of a key block on the proposed shiplock slopes. However, it is important to keep in mind that these conclusions are based on the kinematic analyses performed using only the major discontinuities. Further kinematic as well as kinetic analyses are recommended incorporating minor discontinuities, water forces, earthquake forces etc. before making the final conclusions about the maximum safe slope angle for the shiplock region.     

Probabilistic block theory analysis for a rock slope at an open pit mine in USA

A new formulation is given to conduct a probabilistic block theory analysis. A new computer code (PBTAC) is developed to perform both deterministic and probabilistic block theory analysis. The variability of the discontinuity orientation and shear strength is incorporated in the probabilistic block theory analysis. Discontinuity orientation is treated as a bivariate random variable including the correlation that exists between the dip angle and dip direction. PBTAC code was applied to perform both deterministic and probabilistic block theory analyses for a part of an open pit mine in USA. Needed geological and geotechnical data for the analyses were obtained from field and laboratory investigations. The variability of the discontinuity orientations resulted in important differences between the probabilistic and deterministic block theory analyses results. The results confirmed that the design value selected for the maximum safe slope angle (MSSA) for a particular region in the open pit mine based on the deterministic block theory analysis can be on the unsafe side. In summary, the results showed clearly the superiority of probabilistic block theory analysis over the deterministic block theory analysis in obtaining additional important information with respect to designing rock slopes. The calculated values agree very well with the existing almost stable bench face angles reported by the mining company.     

Probabilistic analysis of rock slope stability and random properties of discontinuity parameters, Interstate Highway 40, Western North Carolina, USA

Probabilistic analysis has been used as an effective tool to evaluate uncertainty so prevalent in variables governing rock slope stability. In this study a probabilistic analysis procedure and related algorithms were developed by extending the Monte Carlo simulation. The approach was used to analyze rock slope stability for Interstate Highway 40 (I-40), North Carolina, USA. This probabilistic approach consists of two parts: analysis of available geotechnical data to obtain random properties of discontinuity parameters; and probabilistic analysis of slope stability based on parameters with random properties. Random geometric and strength parameters for discontinuities were derived from field measurements and analysis using the statistical inference method or obtained from experience and engineering judgment of parameters. Specifically, this study shows that a certain amount of experience and engineering judgment can be utilized to determine random properties of discontinuity parameters. Probabilistic stability analysis is accomplished using statistical parameters and probability density functions for each discontinuity parameter. Then, the two requisite conditions, kinematic and kinetic instability for evaluating rock slope stability, are determined and evaluated separately, and subsequently the two probabilities are combined to provide an overall stability measure. Following the probabilistic analysis to account for variation in parameters, results of the probabilistic analyses were compared to those of a deterministic analysis, illustrating deficiencies in the latter procedure. Two geometries for the cut slopes on I-40 were evaluated, the original 75° slope and the 50° slope which has developed over the past 40 years of weathering.     

Controls on Block Toppling Using a Three-Dimensional Distinct Element Approach

Analysis methods for block toppling are most commonly undertaken in two dimensions. This paper investigates the influence of discontinuity orientations on three-dimensional block toppling mechanisms using a three-dimensional distinct element code. The three-dimensional models allow one to kinematically appraise if toppling conditions derived for two-dimensional geometries can be extended into three dimensions. Two conceptual model geometries were considered in order to represent a road cut or open-pit bench. The first geometry examined a slope with fixed vertical lateral boundaries, while the second geometry assumed an unrestrained lateral slope as a model boundary condition. This “along-strike slope profile” of the models was found to play an important role in the failure mechanism and displacement direction. The dip direction and dip angle of the toppling, basal and lateral release discontinuities were varied one at the time using angular ranges of up to 30° from an assumed mutual orthogonal relationship. This made it possible for the influence and importance of each discontinuity set to be independently evaluated. The results are presented in a stereographic format with preliminary zones outlining discontinuity aspect combinations that potentially result in block toppling failures.     

Influence of discontinuities and clay minerals in their filling materials on the instability of rock slopes

To assess the influence of discontinuities and clay minerals in their filling materials on the instability of rock slopes, seven rock slopes along the margin of Ganjnameh–Shahrestaneh Road, Hamedan Province, Western Iran were selected, and the physical and mechanical properties of their rocks and discontinuities were determined. By statistical studies of the discontinuities, rock slope stability analysis has been performed using kinematic and limit equilibrium methods so that safety factors for the rock slopes can be calculated. Also, sampling of filling materials and X-ray diffraction tests have been done to identify the clay minerals in the filling materials. The lithologies of the studied rock slopes are granite, diorite and hornfels. The presence of discontinuities and weakness planes with different orientations and clay minerals in filling materials of discontinuities are effective factors that cause plane, wedge and toppling failures in the rock slopes. Clay minerals as filling materials of discontinuities in the studied rock slope facilitate their instability by two different methods. First, absorption of water by infilling clay minerals causes the friction angle of discontinuity surfaces that leads to plane and wedge failures to be reduced. Second, water absorption causes the swelling of clay infilling minerals that leads to toppling failure.     

Evaluating Kinematic Controls on Planar Translational Slope Failure Mechanisms Using Three-Dimensional Distinct Element Modelling

This paper investigates the importance of kinematic release mechanisms on planar translational slope failure using three-dimensional distinct element codes. The importance of the dip and dip direction of the rear, basal and lateral release surfaces and their influence on failure mechanism, dilation, and the development of step-path failures is illustrated. The three-dimensional block shape and volume of the unstable rock masses simulated with the different discontinuity set geometries are characterized. Two assumed three-dimensional slope models are investigated in order to assess the importance of varying kinematic confinement/release mechanisms. These two assumed boundary conditions are shown to be critical in the development of asymmetrical rock mass deformation patterns. Scale effects due to the block size and discontinuity persistence are shown to control the calculated displacement and failure mechanisms. The numerical modelling results are also demonstrated to be sensitive to the assumed normal and shear stiffness of the discontinuities. The influence of the factors investigated on the failure of a single rock block versus a rock mass are compared and discussed.     

A graphical approach for slope mass rating (SMR)

Slope mass rating (SMR) is a commonly used geomechanical classification for the characterization of rock slopes. SMR is computed adding to basic rock mass rating (RMR) index, calculated by characteristic values of the rock mass, several correction factors depending of the discontinuity–slope parallelism, the discontinuity dip, the relative dip between discontinuity and slope and the employed excavation method. In this work a graphical method based on the stereographic representation of the discontinuities and the slope to obtain correction parameters of the SMR (F₁, F₂ and F₃) is presented. This method allows the SMR correction factors to be easily obtained for a simple slope or for several practical applications as linear infrastructures slopes, open pit mining or trench excavations.     

Plane failure analysis of rock slopes

Summary Hoek and Bray (1981) gave an analytical approach for plane failure analysis for rock slopes that is limited to those slopes in which the upper slope surface is horizontal and the tension crack is vertical. An analysis is presented here which can take these factors into account. It is found that varying the angle of the upper slope from 0° to 30° causes a significant reduction in the factor of safety. Varying the tension crack from vertical to 70° only has an effect when the upper slope angle is less than 20°.     

双临空面岩质边坡滑动与倾倒破坏的运动学分析

临空面的几何形状在边坡破坏模式与稳定性分析中起着举足轻重的作用。运动学分析是确定边坡破坏模式与评价边坡稳定性的一种有效方法。目前基于运动学分析的边坡稳定性研究主要集中于单临空面边坡的破坏模式与最大安全开挖边坡角的确定。本文将此项研究扩展至双临空面边坡,将其破坏模式细分为4种,分别为沿结构面发生单平面滑动、沿结构面发生楔形体滑动、沿两个结构面的交线发生楔形体滑动以及倾倒破坏。在立体投影中得出,平滑滑动与楔形体滑动的滑动区为双临空面真倾向线与摩擦圆所组成的区域,单个结构面倾角矢量与两个结构面交线矢量位于该区城内;倾倒破坏区为双临空面真倾向线、摩擦圆与基圆所组成的区域,结构面的法向矢量位于该区城内。提出了双临空面边坡最大安全开挖边坡角的确定方法及边坡设计原则。最后将上述方法应用于三峡库区湖北省秭归县郭家坝镇郭家坝村生基坡高边坡,研究了该双临空面边坡的破坏模式并给出了最大安全边坡角的建议值     

Effect of rock mass disturbance on the stability of rock slopes using the Hoek–Brown failure criterion

The process of creating man made or “cut” slopes in rock invariably leads to stress relief within the rock mass which in turn induces a certain degree of fracturing and disturbance. The level of disturbance can be particularly significant when the slope is formed using blasting techniques. However, the effects of this disturbance on the overall rock slope stability have not been investigated thoroughly in the current literature. In order to account for rock mass disturbance during construction, a disturbance factor has been included in the Hoek–Brown failure criterion [1]. This paper uses finite element upper and lower bound limit analyses to estimate rock slope stability based on the Hoek–Brown failure criterion whilst including the effect of rock mass disturbance. A rigorous set of analyses have been performed where the level of disturbance is considered as constant or linearly varying throughout the slope. The results are then compared to a number of reported case histories for verification purposes. From the results of this study, the disturbance factor was found to have significant influence on the rock slope stability assessment, especially for poorer quality rock masses. Hence, cautious engineering judgement must be exercised when estimating the level of disturbance. In addition, utilising stability charts to estimate the stability of cut rock slopes without considering the rock mass disturbance may lead to significant overestimations.     

Cut Slope Design Recommendations for Sub-Horizontal Hard Sedimentary Rock Units in Ohio, USA

Although most cut slopes in Ohio consist of inter-layered, sub-horizontal units of hard and soft sedimentary rocks (sandstone, limestone, dolostone, shale, claystone, mudstone), slopes consisting of relatively thick hard rock units are not uncommon. Design of stable cut slopes in hard rock units needs to consider rock mass strength and orientation of discontinuities with respect to slope face. Results of kinematic stability analyses show that hard-rock cut slopes are less likely to have conventional plane and wedge failures, caused by unfavorable orientation of discontinuities. The main cause of failure is identified to be the undercutting-induced toppling, which is not amenable to traditional kinematic or rock mass strength-based analyses. Therefore, to recommend a suitable slope angle, numerical models, using UDEC software, were employed to study how various slope angles affect the process of undercutting-induced toppling failures. The UDEC models showed a slope angle of 45° (1H:1 V) to be the most stable angle. However, a 63° (0.5H:1 V) slope angle can significantly reduce the potential for such failures and is therefore more appropriate than the widely used angle of 76° (0.25H:1 V).     

Fuzzified kinematic analysis of discontinuity-controlled rock slope instabilities

In this study, it is aimed to bring a different approach to kinematic analyses of discontinuity-controlled rock slope instabilities. For this purpose, the data of a detailed discontinuity survey carried out in Ankara, the capital city of Turkey, were updated and reevaluated. Serious discontinuity-controlled instability events were observed in the andesites covering large areas with dense population in the city. Instead of analyzing the effects of the planes belonging only to the major discontinuity sets on the stereographic projection net, all discontinuities were taken into consideration, and kinematic analyses were carried out for planar, wedge, and toppling type failures on pixel basis of the Digital Elevation Model (DEM) of the study area. By doing so, it could be possible to compensate for the deficiency created by neglecting the planes in the lower concentration zones of the stereographic projection. A computer program named FUDIKA (Fuzzified Digital Kinematic Analyses) was written to perform modular kinematic analyses and fuzzy operations, having four modules and operating in three stages. First, Potential Instability Index (PII) was introduced to define instability potential of the rock slopes based on the number of possible instability events for each failure type. Next, the PII values were normalized and fuzzified to obtain PII map of the area. It was seen that when tested on previously occurred instabilities in the area, the PII values obtained through the methodology proposed in the study showed quite a high performance.     

顺层岩质边坡开挖模型试验及稳定性影响因素分析

用地质力学模型试验方法,对顺层岩质边坡进行开挖破坏试验。同时在有限元分析的基础上,采用多层结构模型对顺层岩质路堑边坡稳定性的影响因素进行了分析。指出当边坡走向与岩层走向夹角超过30后,边坡发生顺层滑动破坏的可能性很小,基本上可不视为顺层边坡。同时也阐明了岩层倾角以及结构面抗剪强度对顺层岩质边坡稳定性的影响。文中结论可为顺层岩质边坡的科研、设计和施工提供参考。     

Influence of Stochastic Discontinuity Network Parameters on the Formation of Removable Blocks in Rock Slopes

Summary  We study the effects of discontinuity network parameters on the formation of removable wedges in rock slopes. Discontinuities are simulated using the Poisson disk model, and removable wedges are identified using block theory. The formation of removable wedges of different sizes is assumed to follow a Poisson process. Poisson regression and Monte Carlo simulation are then used to identify statistically relevant parameters of the model, and to study the effects that variations in their values have on formation of removable blocks. The sensitivity of the results as a function of the mean orientations of the discontinuity sets forming the blocks is also studied by means of a parametric study. The volumetric intensity of discontinuities in the rock mass is found to have a significant impact on the computed estimates of removable block formation. As predicted by theory, our results indicate that, everything else being equal, the expected rate of formation of removable wedges is proportional to the square of the intensity measure. Estimates are also sensitive to changes in discontinuity size, especially in cases in which discontinuities are smaller than one to two times the height of the slope. The interaction between the mean size of discontinuities and the coefficient of variation of discontinuity sizes is found to be significant as well. Finally, results of our sensitivity analysis suggest that the orientation of discontinuity sets significantly affects the rate of formation of removable blocks in rock slopes. Author’s address: Dr. Rafael Jimenez-Rodriguez, ETS Ing. de Caminos, Canales y Puertos. Universidad Politecnica de Madrid, Spain     

Rock slopes risk assessment based on advanced geostructural survey techniques

The rock mass structure determines the possible unstable blocks that can induce rock fall phenomena. The stability analyses must therefore be based on an accurate geo-structural survey. In this work, the stability conditions of several steep slopes along a motorway in the Far East have been evaluated through key block analysis based on traditional surveys and on laser scanner acquisitions. Discontinuity orientations and positions on the rock face are derived from the point cloud in order to perform the reconstruction of the rock mass and to identify blocks in the slope. Results obtained from both the traditional and the new method is in good agreement. Stability analyses have been performed for evaluating the kinematic feasibility of different failure mechanisms. The rock block shapes and volumes are computed by performing 2D and 3D analyses whereas the failure mechanisms are examined using the key block method. Parametrical analyses have been carried on to evaluate the influence of slope angle variation. DEM models have also been set up. The relative hazard is determined by statistically evaluating the kinematical feasibility of different failure mechanisms. Hazard mapping has been utilized to identify the best methodology for risk mitigation.     

Discontinuity controlled probabilistic slope failure risk maps of the Altindag (settlement) region in Turkey

The evaluation of potential rock slope problems using stereographic projection techniques known as kinematic analysis is one of the most important parts of a slope stability investigation to be carried out in jointed rock media. In conventional stereoprojection techniques for the assessment of possible rock slope failures, the peak orientations of joints together with the slope geometry and the friction angle of the weakness planes are used. Other possible joint orientations which may be encountered in the rock media are ignored, although they belong to the group of joint peak orientations. In this study, nearly vertical jointed andesites cropped out at the Altindag settlement region in Ankara were studied in order to evaluate the relevance of this ignored discontinuity orientation data on slope stability. As a result, probabilistic risk maps for planar, toppling and wedge failures were produced using the kinematic rules and digital elevation model of the study area. The comparison of the distribution of the actual failures in the area and the probabilistic risk maps prepared for the study area revealed that all of the identified failures are found to be located in the higher risk zones on the probabilistic risk maps.     

Assessment of rock slope stability along the proposed Ankara–Pozantı autoroad in Turkey

 The main objective of this study is the determination of the slope stability and excavatability category of discontinuous rock exposed between 53+000 and 58+000 km of the proposed Ankara–Pozantı autoroad in Turkey to provide secure access. The study area is mostly in the outcrops of highly jointed sandstone with minor layers of marl. This Maastrichtian–Eocene Group also contains conglomerate and limestone bands of flysch character called the Pas˙ada* Group. Quaternary alluvial deposits occur throughout the site. The area was divided into four design sectors based on cut slope locations. Rock slope stability was assessed kinematically as well as through utilizing limit equilibrium analyses. The excavation category was determined to range from hard to extremely hard ripping. Remedial measures for unstable rock slopes are discussed. Received: 22 July 1997 · Accepted: 14 April 1998     

Rock Slope Stability Assessment Using Geomechanical Classification and its Application for Specific Slopes along Kodaikkanal-Palani Hill Road,Western Ghats,India

Linear infrastructure networks like roads play a vital role in the socio-economic development of hill towns centered on tourism. Stability of the slopes along the hill roads are therefore a major concern and slope failures lead to disruption of traffic and loss of property/life or both. This study analyses the stability of cut-slopes along the Kodaikkanal – Palani hill road in the Western Ghats, India using rock mass classification systems like rock mass rating (RMR), slope mass rating (SMR) and continuous slope mass rating (CSMR). These geomechanical classifications provide a preliminary assessment of rock quality based on rock strength, discontinuity properties, hydrogeological condition of the slopes and slope stability based on the inherent rock strength parameters, discontinuity orientation and method of excavation. The results showed that both rock quality and discontinuity orientation contribute to type of failure in rock slopes with RMR > 40. SMR results are conservative while CSMR classification is matches more closely to the failures obtained from the field survey. CSMR classification represents continuous slope stability conditions and hence are more suitable for development of spatial database. Cutting of roads, thereby, steepening slopes has a definite influence on the stability of slopes.     

Charnockite bedrock,Chennai coast,Tamil Nadu: Micromorphology and geochemical signatures in stages of the weathering processes

Occurrences of landslide are most common and critical issue in North-East India. The various types of slope failures have been affected most part of slopes and road section between Malidor to Sonapur area (approx 30 Km) along NH-44 within Jaintia hills district, Meghalaya, India. These slope failures causes considerable loss of life and property along with many inconveniences such as disruption of traffic along highways. The unscientific excavations of rock slopes for road widening or construction purposes may weaken the stability of the slopes. The rocks exposed in the area are highly jointed sandstone and shale of Barail Group of Oligocene age. The Sonapur landslide is most dangerous and destructive rock fall-cum debris flow. The present study includes the kinematic analysis of the slope to assess the potential failure directions as the rocks are highly jointed in some parts of road cut sections. The continuous slope mass rating (CSMR) technique has been applied for slope stability analysis at five vulnerable locations. Kinematic analysis indicates mainly wedge type of failure along with few toppling and planar failures. These failure required immediate treatment to prevent the slide and long term stability of the slope.     

基于底摩擦试验的硬岩岩质边坡变形过程及破坏机制研究

针对不同倾向、不同倾角条件下,边坡变形破坏特征不同但缺乏相互对比分析研究的现状,在充分考虑硬岩岩质边坡变形破坏特征的基础上,配制硬岩相似材料,采用底摩擦试验方法,分析不同倾向、不同倾角边坡变形破坏模式,并借助PIVlab技术进行分析。结果表明:顺倾和反倾边坡变形破坏模式和破坏范围有明显区别。在45°坡度条件下,当顺倾边坡倾角由30°→45°→60°→80°转换时,变形破坏模式由滑移-拉裂→轻微滑移-弯曲（或滑移-剪切）→未有明显变形（整体稳定）→浅表部倾倒-拉裂逐渐演化。在45°坡度、反倾边坡条件下,变形破坏模式由岩层倾角30°和45°条件下无明显变形,逐渐向60°和80°条件下的倾倒-拉裂演化。当岩层倾角较陡时,反倾边坡破坏范围相对顺倾边坡更大,倾倒弯曲转折端更深。PIVlab结果反映出不同结构边坡条件下,不同位置的速度和位移矢量特征不同,且与宏观观察结果相吻合。研究成果能够为同类边坡的稳定性评价和治理设计提供一定参考。