INTRODUCTION

 

The slope stability analyses in geotechnical engineering have followed closely the developments in soil and rock mechanics as a whole. Slopes either occur naturally or are engineered by humans. Slope stability problems have been faced throughout history when men and women or nature has disrupted the delicate balance of natural soil slopes. Slope stabilization methods involve an understanding of geology, hydrology, and soil properties. Slope analyses must be based upon a model that accurately represents site subsurface conditions, ground behavior, and applied loads. Factor of safety is calculated to assess the results of analyses and generally calculated at the beginning, and sometimes throughout the life, of projects during planning, design, construction, improvement, rehabilitation, and maintenance. Planners, engineers, geologists, contractors, technicians, and maintenance workers become involved in this process (Abramson et. al., 2002).

The primary purpose of slope stability analysis is to contribute to the safe and economic design of excavations, embankments, earth dams, landfills, and spoil heaps. There are mainly are mainly concerned with identifying critical geological, material, environmental, and economic parameters that will affect the project, as well as understanding the nature, magnitude, and frequency of potential slope problems. When dealing with slopes in general and slope stability analysis in particular, previous geological and geotechnical experience in an area is valuable. The aims of slope stability analyses are

 

1.1 Factors Affecting Slope Failure

Slope failure occurs when the downward movements of material due to gravity and shear stresses exceeds the shear strength.  The major factor affecting slope stability is given in table below.

 

Sr. No

Name of the parameters and properties

Details

1

Geological Discontinuities

Fault, Joint, bedding plane,

2

Water

Ground water, drainage pattern, rainfall, permeability, aquifer

3

Strength

Shear strength, compressive strength, tensile strength

4

Geotechnical parameters

Gran size, moisture content, atterberg limit, etc.

5

Method of construction

Shovel, dumper, BWE or combination

6

Dynamic forces

Blasting, Seismic activity

7

Geometry of slope

Height and angle of slope, bench height and angle,

 

1.3 Types of rock slope failure

Plane, wedge, toppling, rockfall and rotational (circular/non-circular) types of failure are common in slopes (Figure 1). The first four are more predominant in rock slopes and are primarily controlled by the orientation and the spacing of discontinuities planes with respect to the slope face.  The pattern of the discontinuities may be comprised of a single discontinuity, or a pair of discontinuities that intersect each other, or a combination of multiple discontinuities that are linked together to form a failure mode. Circular and non circular failure occurs in soil, mine dump, heavily jointed or fractured rock mass and very weak rock. The types of slope failure are primarily controlled by material properties, water content and foundation strength.

        Figure 1: Common types of slope failure

 

1.4 Rock Slope Stability Analysis: Limit Equilibrium Method

·         Plane failure analysis

·         Wedge failure analysis

·         Toppling failure analysis

 

1.5 Stability analysis of slope : circular failure

Most conventional stability analyses of slopes have been made by assuming that the curve of potential sliding is an arc of a circle. The procedures of stability analysis may be divided into two major categories. Slip circle method of circular failure analysis uses the theory of limiting equilibrium. It solves a two-dimensional rigid body stability problem using potential slip surface of circular shape. This method is used to investigate the equilibrium of a soil mass tending to move down the slope under influence of gravity.

The trial slip circle is drawn and the material above the assumed slip surface is divided into a number of vertical strips or slices. In the ordinary slip circle. the forces between slices are neglected and each slice is assumed to act independently as a column of soil of unit thickness and width. The weight of each slice is assumed to act at its centre. The factor of safety is assumed to be the same at all points along the slip surface. The surface with the minimum factor of safety is termed the critical slip surface. Such a critical surface and the corresponding minimum factor of safety represent the most likely sliding surface. 

 

1.6 Stability Analysis in Presence of Water

Water is the most important factor in most of the slope stability analysis. Pore water in soil can strongly influence the physical interaction among soil grains. Changes in pore pressures can directly impact the effective stresses, which in turn, affect both the shear strength and consolidation behaviour of soil. Therefore, analysis of pore fluid seepage plays an important role in the solution of many geotechnical problems, especially those concerning the stability analysis of slopes and retaining structures.

  

Failure of soil slopes, both natural and man-made, during or shortly after rainfall is a commonly occuring phenomena. Such rainfall related failures are often associated with tropical areas, where intense rainfall may occur seasonally, and the soils are residual soils derived from the underlying rock. Under these conditions, infiltration may result in large volume of water entering into unsaturated soil slope. Such infiltration may lead to the soil becoming fully saturated, or an increased degree of saturation, without full saturation being achieved.

 

Whenever loads are applied to the surface of a soil, they set up stresses within it. As the pore-fluid has a low compressibility, it will not easily change its volume. As a result, pore-fluid pressures are set up. In soils of low permeability, these excess pore-fluid pressures cannot escape except after the passage of much time, and are therefore likely to have a major influence on the behavior of the soil. Conversely, in soils of high permeability, the excess pore-fluid pressures escape so readily that to all intents and purposes they may be ignored. The term 'drained' is used here to denote absence of excess or stress change induced by pore water pressures, whereas, the term 'undrained' is used to denote their presence. It is also possible to have partly drained conditions after the escape of some of the excess pore fluid pressures.

 

There are two types of water flow in surface or subsurface: steady state flow and transient flow. In the steady state flow, the pore water pressure is constant whereas, it is always chaining in transient flow. Transient pore pressure is developed in response to short but  intense rainfall and plays an important role in slope failure occurrences.

 

1.8 Seismic Analysis

 

Stability of a slope can be affected by seismicity in two ways: earthquake and blasting.  These seismic motions are capable of inducing large destabilizing inertial forces. In general, three methods of analysis have been proposed for the evaluation of slopes response under such conditions.

1.      Pseudostatic Method: The earthquake’s inertial forces are simulated by the inclusion of static horizontal and vertical forces in limit equilibrium analysis.

2.      Newmark’s Diaplacement Method: This method is based on the concept that the actual slope accelerations may exceed the static yield acceleration at the expense of generating permanent displacements (Newmark, 1965)

3.      Dynamic Finite Element Analysis: This is a coupled two or three dimensional analyses using appropriate constitutive material model that will provide details of concerning stresses, strains, and permanent displacement. 


 

1.9 Slope Stabilization

Safer operation of highways and railways, power generation and transmission facilities, and the safety of residential and commercial developments often require stable slopes and control of rock falls. Many transportation systems were constructed over a century ago in the case of railroads, and decades ago in the case of many highways. At that time, the blasting techniques that were often used in construction caused significant damage to the rock. Further, deterioration of stability conditions is likely due to weathering of the rock since the time of construction, and loosening of the surficial blocks by ice and water, and also by the growth of tree roots. All these effects can result in on-going instability that may justify remediation programs. A number of methods have been used to stabilize slopes, each of them found to be appropriate for a particular set of conditions.

Various geotechnical, construction and environmental issues must be considered while selecting and designing stabilization measures appropriate for a site. Construction and environmental issues, which can affect the cost and schedule of the work should also be addressed during design phase of the project. Other issues that are frequently important are equipment access, available work time during traffic closures, and disposal of waste rock and soil. The Slope stabilization methods can be classified into three categories:

(a)    Removal and Protection

(b)   Drainage of water

(c)    Reinforcement

 

1.10 Slope Monitoring: Techniques and Instruments

Slope movement is common in open pit mines and several mines continue to operate safely with moving slopes with the help of monitoring system to enable timely waring against deteriorating stability conditions. Slopes are designed with a factor of safety to control the risk of injury and equipment damage due to likely danger of slope failures and rock falls. Geological structures, rock mass properties, and hydrologic conditions are important elements for design of safe and efficient slope structures.  Groundwater, surface water, and precipitation runoff can be controlled to abate their deleterious effects on stability. Benches and berms are normally used to stop rocks before they fall far enough to pose a significant hazard. Mechanical rock fall catchment systems or secondary supports may also be used to stabilize slopes in particular locations. However, even a carefully designed and constructed slope may fail because of unidentified geological structures, unexpected weather conditions, or seismic activities. For these reasons, regular examination and systematic monitoring of slopes are important for early detection of failure and associated hazard.

Slope failures do not occur spontaneously. Prior to failure, measurable movement and/or the development of tension cracks may occur. In contrast to this, landslide is a result of long-term movement of slopes creeping for hundreds of years resulting in accumulative movement of tens of meters. Such movement may be superimposed for short periods of more rapid movement resulting from major events like earthquakes. Under such conditions, monitoring of slope stability and landslides involve selecting certain parameters and observing their behaviour with time. The two most important parameters are, displacement and groundwater levels. Slope displacement can be characterized, in terms of depth of failure plane(s), direction, magnitude, and rate, using conventional slope monitoring, whereas, piezometers can be used for determination of water levels. Surveying of fixed surface monuments deploying extensometers, inclinometers, and tiltmeters allow determination of direction and rate of slope movement and depth and areal extent of the failure plane.

 

1.11 Landslide

Landslides are geological phenomena causing flow of rock, earth, or debris flows on slopes due to gravity in coastal, offshore or onshore environment. It also known as mud flows, debris flows, earth failures, slope failures, etc., and can be triggered by rains, floods, earthquakes, and other natural causes as well as human-made causes, such as grading, terrain cutting and filling, excessive development, etc. The factors affecting landslides can be geophysical or human-made, they can occur in developed areas, undeveloped areas, or any area where the terrain was altered for roads, houses, utilities, and buildings. The down-slope movement of material is further subdivide into two broad categories i.e. Slope Failures and Sediment Flows. 

 

Figure 6: Different types of load slide or Mass wasting Process.


 

 

1.12 Mine Waste Dump

The Overburden of waste and uneconomic mineralized rock is required to be removed to mine the useful mineral resource in a surface mining operation. In this process a dump is formed by casting the waste material and dumping it in nearby area. Waste dump may be classified as internal and external dump. External dump is created outside the pit whereas internal dump is created inside back of the mining area. These waste rock dumps are heterogeneous in terms of grain size and structure. The fragmentation of rock in a dump is a product of number of mechanical processes, like drilling, blasting, ripping, etc. Consequently, dump rock may range in size from clay particles to boulders (e.g. less than 0.1 mm to greater than 1 m in diameter). Natural gravity sorting of rock poured from a haulage truck onto a waste dump face may result in a vertical size distribution, finer materials tend to remain near the top and coarse materials tend to roll down the face toward the toe of the dump.

As most of the waste rock disposal facilities at open pit mines are constructed with run off mine materials using trucks, there is very little control over the exact size distribution of these materials. However, modern blasting technology allows considerable control on the size of largest particles. In-pit crushing of waste rock is also done at a few mines to reduce the size of material, to transport it by belt conveyors out of the pit to the disposal facility. Often overburden and waste rocks are end-dumped from the trucks and the excess material is bulldozed over the storage facility edge to construct slopes at the angle of repose, where the outer slope is just stable under the static loading conditions at the site and is typically 37–40°.

The manner in which a waste rock dump is designed and constructed can also result in significant differences in structure. Commonly, construction of a dump progresses by addition of material to its top at the face, allowing waste rock to form a continuously renewed veneer on the face. The dump progresses outward horizontally, as successive layers are added to the face. However, some dumps are engineered in other ways, resulting in significantly different internal structures. For instance, in order to enhance stability and minimize the release of fine sediments into the down-stream environment, some dumps are designed with a French drain, a layer of coarse and durable rock such as chert, placed at the base to allow unrestricted flow of stream through base of the dump. Waste rock dumps are also constructed in layers resulting in a sequence or stack of dumps.

 

Almost all waste materials produced at a mining and milling operation can be divided into two classes. Mine waste is that product which is mined but which is not processed before being placed on a waste dump. Tailing is that product which is discarded after mining and processing to remove the economic products. Processing may range from simple mechanical sorting to crushing and grinding followed by physical or chemical processing. It contains all other constituents of the ore except majority of the extracted metal. It may also contain heavy metals and other substances at concentration levels that can be toxic to biota in the environment. The mechanical stability of the tailings mass is poor because of its small grain size and high water content. The ultimate purpose of a tailing impoundment is to contain fine-grained tailings. The long-term cost of tailings disposal depend in part on mechanical stability and environmental integrity.

Tailings were disposed off where convenient and most cost-effective, often in flowing water or directly into drainages. Definition of impending stability concerns are raised in part by the use of tailings material in tailings dams or embankments. to mitigate these concerns, such embankments often rely on a certain amount of controlled seepage to enhance stability, which in turn affects environmental performance. Products are removed from their original location, broken up and placed in piles in which the conditions of oxidation, seepage, leaching and erosion differ considerably from those at their original location. This increases the potential considerably for wind or water erosion of surface materials and their transport into the environment. The potential for oxidation and leaching is also increased with the result that dissolved contaminants may be carried away from the pile into the environment. Design of tailing impoundments depends on the quantity and the individual characteristics of the tailings produced by mining and milling operation as well as the climatic, topographic, geologic, hydro-geologic and geotechnical characteristics of the disposal site, apart from regulatory requirements related to dam safety and to environmental performance.


 

 

1.13 Sensitivity, Probability And Reliability Analysis

 

Traditional slope stability analysis methods are defined as those which treat slopes as deterministic condition with using uniquely defined parameters. It uses principles of static equilibrium to evaluate the balance of driving and resisting forces. The factor of safety is defined as the resisting forces divided by the driving forces, or alternatively as the shear strength divided by the calculated shear stresses.

In deterministic analysis, single fixed values (typically, mean values) of representative samples or strength parameters or slope parameters are used in the analysis. The deterministic is unable to account for variation in slope properties and parameters and other variable conditions. Geotechnical properties of Slope parameters have always pose some uncertainties in the simulation. This uncertainty imposes a limit on our confidence in the response or output of the model.

Probabilistic analysis in slope stability involves quantity the task of quantitatively the source uncertainty. A probabilistic analysis is based on a correct randomness determination of the parameters affected by uncertainties. Therefore, the probability density function of each of the random variable is demined  which governs the stability problem.

The accuracy of an experimental probability density distribution depends on the number of observations. Geometrical features of rock discontinuities such as spacing, orientation and persistence are gathered at lower costs than shear strength features of discontinuities. A probabilistic analysis model requires the knowledge or the reliable estimation of: The independence of the random variables or the correlation between random variables.

Many variables are involved in slope stability evaluation and the calculation of the factor of safety. It requires geometrical data, physical data on the geologic materials and their shear-strength parameters (cohesion and angle of internal friction), pore-water pressures, geometry of slope, and the unit weights, water pressure, seismic acceleration and friction angle, etc. Traditional slope stability analysis uses single value  for each variable in the calculate of factor of safety equations. The output of a traditional stability analysis is a single-value of factor of safety in deterministic estimate of whether the slope will stand or collapse.

Single value of the factor of safety approach cannot quantify the probability of failure, or level of risk, associated with a particular design situation. A probabilistic approach to studying geotechnical issues offers a systematic way to treat uncertainties, especially slope stability.

The variable associated with slope design are uncertain due to many reasons. Therefore, to account for uncertainty the probabilistic method can be used for assessing the stability of slope. These are many source of uncertainty in slope stability analysis. The amount of uncertainty varies from one analysis to another and from one site to another.  These uncertainties are

 

A probabilistic approach, on the other hand, allows for the systematic analysis of uncertainties and for their inclusion in evaluating slope performance. Important geotechnical parameters such as shear strength parameters and pore water pressures may be regarded as random variables, each with a probability distribution, rather than deterministic values or constants. Consequently, the factor of safety F of a slope under specified conditions must also be regarded as a random variable with a probability distribution.

If one could compute factors of safety with absolute precision, a value of F=1.1 or even 1.01 would be acceptable. However, because the uncertainties involved in computing factors of safety, so the computed values of F are never absolutely precise.  It can be said that this definition of factor of safety is based on the assumption that F is the same for every point along the slip surface. This calls into question whether such analyses are reasonable, because it can be shown, for example by finite element analyses, that the factor of safety for every slice is not the same, and limit equilibrium analysis is not true. The reliability of a slope (R) is an alternative measure of stability that considers explicitly the uncertainties involved in stability analyses. The reliability of a slope is the computed probability that a slope will not fail and is 1.0 minus the probability of failure:

 


 

 

1.15 Classification systems in slope stability analysis

A number of classification system are available for analysis of slope stability. Some of the most commonly referred classification system are :

Slope Mass Rating (SMR)

Chinese Slope Mass Rating System (CSMR)

Rock slope rating (RSR)

Slope stability rating (SSR) classification system, and

Dump mass rating

 

Artificial Neural Network

Fuzzy Inference System