A practical procedure for the back analysis of slope failures in closely jointed rock masses

PII: S0148-9062(97)00335-5

Int. J. Rock Mech. Min. Sci. Vol. 35, No. 2, pp. 219±233, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0148-9062/98 $19.00 + 0.00

A Practical Procedure for the Back Analysis of Slope Failures in Closely Jointed Rock Masses H. SONMEZ R. ULUSAY C. GOKCEOGLU Where closely jointed rock masses are encountered in slopes, failure can occur both through the rock mass, as a result of combination of macro and micro jointing, and through the rock substance. Determination of the strength of this category of rock mass is extraordinarily dicult since the size of representative specimens is too large for laboratory testing. This diculty can be overcome by using a non-linear rock mass failure criterion or by back analysis of such slopes to estimate the rock mass strength. In this paper, a practical procedure and a computer program are presented for the back determination of shear strength parameters mobilized in slopes cut in closely jointed rock masses which obey a non-linear failure criterion rather than a linear one. The procedure shows that the constants to derive normal stress dependent shear strength parameters of the failed rock masses can be determined by utilizing a main cross-section and without a pre-determined value of rock mass rating (RMR). Trials are made for di€erent RMRm and RMRs values corresponding to various possible combinations of the constant m and s, which are used in the Hoek±Brown failure criterion, satisfying the limit equilibrium condition. It is also noted that the procedure provides a quick check for the rock mass rating obtained from the site investigations. The method is used in conjunction with the Bishop's method of analysis based on circular slip surfaces. The procedure outlined in this paper has also been satisfactorily applied to documented slope failure case histories in three open pit mines in Turkey. # 1998 Elsevier Science Ltd.

INTRODUCTION

In a rock mass with clearly de®ned discontinuity sets, failure mechanisms related to discontinuities can be analyzed and the stability of slopes excavated in that rock mass can be calculated providing the shear strength along the discontinuities is known. However, such an analytical approach might not be feasible for slopes containing multiple discontinuity sets with large variations in mechanical characteristics. Continuum calculations for engineering structures in or on a rock mass, whether analytical or numerical, cannot be appropriate, since over-simpli®cations result from presenting the rock mass as a continuum. In general, the slope stability determination methods depending on the material involved may be divided into three broad categories: Hacettepe University, Faculty of Engineering, Geological Engineering Department, Applied Geology Division, 06532 Beytepe, Ankara, Turkey. 219

(a) Methods suitable for slopes in soils or soil like materials where the strength of the material can be determined from testing small specimens of the material in the laboratory. (b) Methods suitable for slopes in hard jointed rocks where slope stability is controlled by the discontinuities in the rock material. The potential for failure is dependent on the presence and orientation of discontinuities, and shear strength along them. (c) Methods suitable for closely jointed rock masses where failure can occur both through the rock mass, as a result of a combination of macro and micro jointing, and through the rock substance. Determination of the strength of this category of rock mass is a much more dicult task. There are formidable diculties in the sampling and testing of undisturbed samples that are suciently large to represent the combined e€ects of rock material and discontinuities. The possibility for the measurement of the shear strength of such rock masses is usually based on some form of classi®cation

220

SONMEZ et al.: BACK ANALYSIS OF SLOPE FAILURES IN ROCK MASSES

Fig. 1. E€ect of scale on rock strength and possible mechanisms of failure in rock slopes.

techniques [1±3] in conjunction with a non-linear failure criterion [4±8]. A rock mass is described as closely jointed when the joint spacing is small in relation to the scale of the project in question. In closely jointed media it seems appropriate to assume that the material is approximately isotropic and homogeneous, i.e. there are no clearly de®ned joint planes or joint sets which control the form of the failure mode. In these rocks, the joint spacing is a fraction of meter, the individual particles of rock mass are very small compared to the dimension of slope and these particles are not interlocked due to their shape. Depending on the number and nature of the discontinuities, the intact rock pieces will translate, rotate or crush in response to stresses imposed on the rock mass. The behavior of the mass is thus a consequence of the combined action of a large number of individual joints. When the rock mass contains a number of discontinuity sets, having relatively small spacings in relation to the slope size, failure can occur along a shear surface similar to those observed in soil slopes. Therefore, the required conditions for a circular failure are mostly satis®ed in heavily jointed rock masses as illustrated in Fig. 1. The standard method for assessing the strength of a geotechnical material is to recover a sample and test it in laboratory. In the case of a closely jointed rock mass it is clearly not possible to recover a sample that is large enough to represent the joint system. Therefore, an empirical approach such as rock mass classi®cation can be attractive alternative, provided that the appropriate parameters are included in the classi®cation system. In order to overcome the diculties in laboratory determination of the shear strength of jointed rock masses; the Hoek±Brown failure criterion in conjunction with geomechanics classi®cation system [1] is commonly used. Rock mass classi®cation has been applied successfully in tunnelling and underground mining [1±3, 9]. A number of systems, introduced by Bieniawski [1] and by Romana [10], has also been suggested for rock slopes. It should be noted, however, that the use of rock mass classi®cations developed particularly for underground works may lead to unsatisfactory results

when applied to near-surface applications such as rock slopes. This is due to the restrictions of these systems which are not well considered. Recently, an empirical failure criterion developed by Hoek and Brown [5±8] has been adopted to the RMR rock mass classi®cation scheme [1] to assess the shear strength of the jointed rock masses in surface and underground excavations. This approach has been also employed in slope stability analyses by several investigators [11±14]. The slope mass rating (SMR) classi®cation scheme proposed by Romana [10] also involves the input parameters used by the RMR-system, but generally provides assessments on structurally controlled slope failures. The main input parameters used in various classi®cation systems are more or less the same. Namely, these systems consider intact rock strength, RQD, discontinuity spacing, condition and orientation of discontinuities and groundwater conditions. Although a number of additional input parameters and some modi®cations are required in the RMR classi®cation scheme, the advantage of the system is that it provides an easy connection to the Hoek±Brown failure criterion for jointed rock masses. The intact rock strength is one of the input parameters involved in the RMRSystem and is only of limited interest with regard to the stability of rock slopes in which failure is most often associated with the shear strength of discontinuities. Sometimes a rock mass having low intact rock strength is a consequence of the failed rock containing a large number of discontinuities. In addition to this, the purpose of including intact rock strength in the classi®cation system for slopes is to give an assessment of wall rock strength of the discontinuities. As stated by Hoek [15], the Hoek±Brown failure criterion is only applicable to intact rock or to closely jointed rock masses which can be considered homogeneous and isotropic. The rock mass parameters RQD and discontinuity spacing de®ne the block size and block form and are also very useful in analyzing stability of slopes. Therefore, these two parameters are considered by the authors to be the parameters of meaningful value in rock mass classi®cation, particularly for slopes excavated in closely jointed rock masses.

SONMEZ et al.: BACK ANALYSIS OF SLOPE FAILURES IN ROCK MASSES

The condition of discontinuities includes the items related to roughness, continuity, in®ll material, aperture and degree of weathering. Laubscher [9] takes into account in his ®nal RMR rating only the condition factor of the most prominent discontinuity set or the discontinuity set with the most adverse in¯uence on the stability of an underground excavation. This is too simple for slopes where the failure is often not determined by one main discontinuity set. Particularly for the slopes in a closely jointed rock mass, the condition rating becomes more important and it is taken as the mean value of the condition ratings of the di€erent discontinuity sets. For the rock slopes, the persistence has a considerable in¯uence on the stability and the RMR-System takes into account the persistence as a quantitative factor. Weathering a€ects the condition of discontinuities and discontinuity spacing. It is also noted that the state of weathering is considered to be a local feature which has changed the rock mass at a particular location. Within the lifespan of a cut slope, future weathering might lead to instability. Therefore, the weathering parameter included in the RMR-System is a very important factor in slope stability. The main problem of water in slopes is the pressure of the water in discontinuities. The presence of water in discontinuities reduces the stability of slopes by reducing the strength of discontinuity surfaces or of any in®ll material. The water pressure is taken into account in the slope stability analysis by estimating the pressure or the position of groundwater table in slope. But the softening or weakening e€ect of water on discontinuity surfaces becomes more important for slopes. Consequently, the groundwater rating is an integral part of the rock mass classi®cation and should be assigned for each particular outcrop for slopes. In closely jointed or crushed rock masses it is very dicult or impossible to determine the orientation of discontinuities. In such cases, the orientation is not meaningful, because part of the rock mass will fall into the underground opening and require immediate support regardless of discontinuity orientation. In the case of slopes excavated in such rocks, the situation is not di€erent. Bieniawski [1] in his RMR classi®cation scheme, suggests rating adjustments for discontinuity orientations, relative to proposed slope orientation, ranging between 0 and ÿ60. No guidelines have been published for the de®nition of each adjustment values, and no reference is given by Bieniawski to use of the RMR classi®cation in slopes. The reason for this lack of use is probably the extremely high values of the adjustment rating values which may sometime result in negative RMR values. Therefore, the ratings assigned for discontinuity orientation adjustments suggested by Bieniawski [1] is unrealistic. Singh and Gahrooee [16] proposed better and clearer descriptions for discontinuity orientation in slopes. This approach was quanti®ed on the basis of rating with regard to the number of possible modes of failure. The authors of the pre-

221

sent paper think that the above mentioned rating system is still questionable. First of all, Singh and Gahrooee [16] did not change the values of ratings which can reach up to ÿ60 points out of 100. As discussed before, such an adjustment is not applicable in practice. Secondly, in a closely jointed rock mass, the most probable mode of failure occurs in the form of a circular shape regardless of discontinuity orientation. Consequently, only one de®nition namely ``one possible mode of failure'' is considered to be more logical, and a single adjustment of ÿ5 for discontinuity orientation is more realistic for slope failures in closely jointed rock masses. Some factors such as method of excavation, major planes of weakness or change in stress are treated as local features which have in¯uenced the rock mass at a particular location and are not rock mass constants. These have been discussed by Laubscher [9], Romana [10] and Kendorski et al. [17]. The greatest in¯uence of the method of excavation will be on the spacing of discontinuities. Depending of the blasting damage, blasted slopes may have closer discontinuity spacing than natural slopes. Therefore, in order to compensate for the in¯uence of such local factors, necessary adjustments [1, 9, 17] are taken into consideration in rock mass classi®cation for the slope failures in closely jointed rock masses investigated in this study. On the other hand, during a classi®cation process, serious diculties are encountered in determining or describing some of the rock mass parameters, particularly in poor quality rock masses [18±20]. Due to such uncertainties, the calculated rock mass rating may erroneously a€ect the constants and shear strength parameters derived from the non-linear rock mass failure criterion. The most reliable way to obtain a mean value of the constants m and s employed by the Hoek±Brown failure criterion in an extended slope is by back-calculation and by comparison of the results of back-calculation with the available data derived from the Hoek±Brown criterion [21]. However, in some cases it is unlikely that an accurate assessment of the true strength parameters for a given rock mass will ever be available due to limitations, so RMR values cannot be precisely determined. Because the results of back-analysis provide a range of combinations of apparent friction angle and cohesion, the problem of parameter selection becomes dicult in such cases. The procedure presented herein is to perform a back-analysis of failed slopes cut in jointed rock masses to estimate the rock mass rating and shear strength parameters mobilized at the time of failure. The main philosophy of the method recognizes that it is unlikely that an accurate assessment of the value of RMR and shear strength parameters for a given rock mass will ever be available. A detailed description of the procedure which can be readily incorporated into the conventional back analysis of a slope failure in a jointed rock mass, where only a single cross-section is

222

SONMEZ et al.: BACK ANALYSIS OF SLOPE FAILURES IN ROCK MASSES

available, is presented with a computer solution developed for the purpose. The proposed method is also applied to failure case histories in jointed rock masses at three open pit mines located in Turkey to check its performance. METHOD OF ANALYSIS

Theoretical background-basic procedure One of the most dicult tasks in slope stability analysis is the determination of the shear strength parameters (c, f) along the sliding surfaces. In geotechnical engineering practice, failure of a slope can be regarded as a full scale ®eld test and an assessment of any failure is, therefore, of considerable value. Appropriate geomechanics models can be used to estimate the values of shear strength parameters on the basis of certain assumptions. These back calculated values may then be used for preventative and remedial

work for the redesign of failed slopes and for new projects in similar types of material. Therefore, it is considered that back analyses are an integral part of the slope design. The shear strength parameters of a failed slope have been back calculated by geotechnical engineers and engineering geologists in the following procedures: (a) Assuming the value of the angle of internal friction f or of the cohesion c to calculate another [22] (Fig. 2(a)). (b) Utilizing a main cross-section of a failed slope and another cross-section near the main one in the same failed slope or utilizing two cross-sections in two failed slopes which have similar geological and hydrogeological conditions to establish two equations and then evaluate the values of c and f (single solution; Fig. 2(b)). (c) Because of the variations in the mechanical properties of the same material in di€erent places, utilizing

Fig. 2. Basic back analysis approaches applied for the slope forming materials obeying linear failure envelopes: (a) derived range of c and f and determination of c from an assumed f; (b) single solution for two slides with di€erent geometry; (c) multiple solutions for four slides with di€erent geometry; and (d) multiple solutions with a comparison with laboratory derived strength test results.

SONMEZ et al.: BACK ANALYSIS OF SLOPE FAILURES IN ROCK MASSES

more than two slope cross-sections to obtain as many as n(n ÿ 1)/2 points of intersections (solutions) for n curves c(f) (multiple solutions; [23]; Fig. 2(c)). The set of continuous curves represents the range of back calculation solutions from which the most realistic solution can be obtained based on engineering judgement, experience and veri®ed with shear test results if these are available (Fig. 2(d)). The above procedures, however, are based on the back calculation of the shear strength parameters of the materials obeying linear Mohr±Coulomb failure criterion which are characterized by c and f values independent from the normal stress. But a consensus has gradually emerged among the rock mechanics community that the failure envelope for a closely jointed rock mass is curved rather than linear. The authors believe that the Hoek±Brown non-linear failure criterion [4±7], which has gained an increasing popularity in stability analyses made in conjunction with rock mass classi®cation systems, provides a meaningful estimate of rock mass behavior. Due to the nonlinear nature of this failure criterion, the above mentioned methods are unrealistic for use with closely jointed rock slopes, i.e. the shear strength parameters of a failure surface in closely jointed rock masses can be calculated for any speci®c normal stress value using the material constants (m and s) as a function of rock mass rating (RMR) from the following equation [24]; for disturbed rock masses:   m RMR ÿ 100 ˆ exp …1a† mi 14 

RMR ÿ 100 s ˆ exp 6

 …1b†

for undisturbed or interlocking rock masses:   m RMR ÿ 100 ˆ exp mi 28  s ˆ exp

RMR ÿ 100 9

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ing can be very dicult because of tendency of these materials to slake and de-laminate. In addition, as reported by Unal et al. [18], Ulusay et al. [19] and Unal [20], serious diculties are encountered in determining or describing some of the rock mass parameters, particularly in weak, strati®ed and claybearing rocks. In such circumstances overestimated rock mass ratings might be obtained and they result in deriving di€erent m and s values than those in real situation. On the other hand, in some areas where slope failures have occurred, because of the limited number of outcrops or no borehole data, the rock mass rating can not be precisely determined. Therefore, a back analysis based on such limited or questionable data may yield unrealistic results. The strategy of this study is aimed at overcoming the diculties associated with the limitations discussed above. In this strategy, a procedure is suggested to identify the most reasonable and a common rock mass rating (RMR) value which corresponds to the pair of m and s satisfying the limit equilibrium condition. In jointed rock masses obeying the Hoek±Brown failure criterion, a function F, the conventional factor of safety commonly speci®ed in the limit equilibrium methods of slope stability analysis, depends on several variables and for any particular sliding surface may be written in the following form: F ˆ FfRMR…m, s†, GW, G g

…3†

where RMR: rock mass rating (m and s are the material constants), GW: groundwater conditions prevailing in the slope, G: geometry of the slope and the failure surface.

…2a†

 …2b†

where mi is the material constant of intact rock sample and can either be calculated form laboratory triaxial test on intact samples or taken from the tables proposed by Hoek [24], and Hoek et al. [8]. In the case of a slope instability with accurately speci®ed failure geometry in a closely jointed rock mass, if the value of RMR is precisely determined and the triaxial test data are available, back analysis of the failure provides a realistic comparison between the rock mass strength obtained from the failure surface yielding a safety factor of unity and the failure envelope derived with the updated Hoek±Brown failure criterion as reported by Ulusay and Aksoy [21] (Fig. 3). However, in weak sedimentary rocks, such as shales, marls and siltstones, and in heavily fractured schistose rock masses, preparation of specimens for triaxial test-

Fig. 3. Comparison between the rock mass shear strength obtained from the failure surfaces yielding safety factors of unity and the failure envelope with the updated Hoek±Brown criterion for coal-bearing rocks (after Ref. [21]).

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The real factor of safety F is considered to be known and equal to one for a case study concerned with a slope that has failed. The value of the geometry data G in Equation (3) can be delineated from the results of ®eld inspection or by surveying the actual failed slope. The values of the constants m and s at the time of failure are unknowns and groundwater condition, GW, may be either known or unknown. The suggested approach involves the determination of various possible combinations of m and s satisfying the following equation: 1 ˆ FfRMR…m, s†, GW, G g

…4†

where G and GW are considered as known in the procedure. The back analysis method presented herein is based on the following assumptions: (1) The geometry of the slope before and after failure, the position of the sliding surface, and the groundwater conditions are known. (2) The mechanism of the movement is known. (3) A condition of static equilibrium at the point of failure (limit equilibrium) exists at the time of failure. (4) In closely jointed media, it seems appropriate to assume that material is approximately homogeneous. (5) What is obtained by back calculation is a weighed mean value of RMR and corresponding m and s values along the failure surface at the time of failure. (6) A set of relations between the RMR from the Bieniawski's rock mass classi®cation [1] and the constants given in Equations (1a)±(b) and (2a)±(b) are used in conjunction with the equations given by the updated Hoek±Brown failure criterion [24]. (7) Uniaxial compressive strength (sc) and the material constant mi are the input parameters. The back analysis procedure starts with the fact that the constants m and s of a given rock mass depend upon an RMR value (Equations (1a)±(b) and (2a)± (b)), and therefore, various possible combinations of (m, s) pairs at the time of failure (F = 1) can be derived from di€erent RMR values. The procedure which performs back calculations for three unknown parameters can be carried out using the following algorithm. Step 1. One variable, RMR, out of three unknown geomechanical parameters (RMR, m, s) is selected and the second unknown, the constant s, is calculated by the utilization of Equation (1b) or Equation (2b) depending on the condition of disturbance (blasted and/or excavated rock, or none) of the rock mass. The RMR value selected to calculate the parameter s is denoted by RMRs. Step 2. By utilizing the position of the sliding surface, normal stress acting on each slice base is calculated. Keeping the previously chosen RMRs value and the corresponding RMR (RMRm) which lead a value of safety factor of unity are calculated by trial and error technique in conjunction with the equations

given by the updated Hoek±Brown failure criterion [24]. Step 3. Trials are made for di€erent values of RMRs(s) to obtain various possible combinations of RMRs and RMRm satisfying the limit equilibrium condition. The results of the back analysis are best presented in a RMRs±RMRm function forms, i.e. RMRs plotted against RMRm considering each combination to lead to a value of the factor of safety F = 1 (Fig. 4). All the points (or RMR pairs) located on the curve indicate a safety factor of unity. Because the closely jointed rock mass is an approximately homogeneous material, it is logical to consider that the rock mass must have a unique RMR value from which a pair of m and s representing a given rock mass can be derived using Equations (1a)±(b) and (2a)±(b). Thus, if a straight line passing from the origin of the graph (see Fig. 4) with an inclination of 458 is drawn, it intersects the RMRs±RMRm curve at a certain point which indicates a common RMR (RMRRM:the actual RMR for the rock mass) value for both constants at the time of failure and utilization of this back analyzed RMRRM value will yield the right combination of the two constants, m and s, of the rock mass. Software description The method described above has been used to develop a computer program for conventional deterministic slope stability analysis and back calculation. The computer program was written in QBasic and can run on any type of IBM PC or compatible equipped with a graphics card and monitor. The program HOBRSLP, which has routines that search the more critical failure surface in a grid system or automatically, can handle slope stability analysis of circular slip surfaces for slopes involving many benches with di€erent geometries, various materials and di€erent groundwater conditions, and includes simpli®ed Bishop's method of analysis [25]. Two options are included in the program: (a) conventional stability analysis for searching the most critical failure surface and corresponding lowest factor of safety; (b) back analysis of a failed slope with known failure geometry. Input data for the program includes the coordinates of the points specifying slope geometry, water conditions prevailing in the slope, and material properties. It will also prompt users to enter the tension crack position. Output consists of a table of input data, safety factor, a cross-section of the slope showing all strata, water table, the failure surface, and a list of ci, fi, sn, t for each slice base if the case consists of materials having non-linear failure envelopes. Three di€erent methods of shear strength data input are incorporated in the program with keyboard selection of the input mode for conventional analysis. These three modes are as follows: (1) Input of the known shear strength parameters derived from linear Coulomb equation.

SONMEZ et al.: BACK ANALYSIS OF SLOPE FAILURES IN ROCK MASSES

Fig. 4. Basic concept of the proposed back analysis technique.

(2) Calculating the shear strength parameters from input data for rock types, RMR value, sc, and material constant mi. (3) Calculating the shear strength parameters from normal stress (sn) acting on each slice base, and the constants A and B for the materials ®tted to power curve strength equation (t = AsB). The back calculation option provides the use of the ®rst two modes mentioned above. In the back analysis option, mi and sc are given as material properties with the condition of rock mass (disturbed or undisturbed). The existing program can analyze slopes with up to 150 slices. The steps to be followed during the execution of the program are shown diagrammatically in the ¯ow chart illustrated in Fig. 5.

EXAMINATION OF THE PROCEDURE ON ACTUAL EXAMPLES

The procedure outlined above has been applied to failed slopes in three open pit mines located in the western and central parts of Turkey (Fig. 6). All the slopes presented in the particular and well documented case histories were cut in jointed rock masses where the joint spacing is a fraction of a meter. It is, therefore, very much smaller than the scale of the cut slopes which are tens of meters high. An externally loaded highwall slope failure (Case 1) The particular case history presented and described below is concerned with the instability of a highwall in Eskihisar strip coal mine (Yatagan±Mugla) in southwestern Turkey. No sign of instability in highwalls was observed until 1989. During a comprehensive slope stability research project by Ulusay [14], the highwall of the ninth slice was found to be unstable after loading the slope by a temporary spoil pile (Fig. 7). The failed highwall, located at the southern end of the ninth slice, was excavated in the compact marls which lie above the coal seam with a thickness of 15± 20 m. In the failed highwall and in the entire pit, continuous cross joints are well developed within the compact marl. Except local deviations, there are three dominant joint sets developed parallel and/or subpar-

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allel to the normal faults crossing the Tertiary deposits. Excepting local deviations, three dominant joint sets dipping 758±858 NE and SW were identi®ed. Their persistence is high and reaches up to 8 m in some places. The presence of cross joints, faults and ¯at lying bedding planes result in a closely jointed rock mass. The groundwater level rises above the coal seam into the compact marls and where seepage occurs it tends to decline toward the compact marl±coal seam boundary. Thus, the failed part of the investigated slope was dry. In the strip coal mine, the overburden rocks composed of the compact marls were evaluated based on Bieniawski's 1989 classi®cation [1]. The data required for rock mass rating determinations were obtained from the geotechnical logs recorded and the scanline surveys carried out in accordance with the procedure suggested by ISRM [26]. Values of RMR for the rock mass were determined for a number of individual sections from seven fully cored geotechnical boreholes considering drill-run lengths ranging between 1 to 3 m. In addition, a total of seven scanline sections were also evaluated. Joint systems show negative exponential distribution. Mean joint spacing (x) and the average number of joints per meter (l) of the rock mass were calculated as 0.386 m and 2.59 mÿ1, respectively. In the compact marls overlying the coal, excepting occasional laminated levels, spacing between bedding planes ranged 0.3 to 1 m. Discontinuity surfaces observed on the faces of the benches were normally dry. However, moisture appeared in some places when the surfaces were scraped by a geologist hammer. The ranges of the ®ve main parameters employed in the determination of RMR values are tabulated in Table 1. As explained in the ®rst section, the adjustment rating for discontinuity orientation was quanti®ed on the basis of rating with regard to the number of possible modes of failure [16]. In this study, only one mode of failure, circular failure through the rock mass, was considered for discontinuity orientation adjustment. Mining applications include dynamic processes. In the studied pit a controlled blasting with a slight damage to loosen the overburden, compact marls, is made. For this condition, a blasting damage adjustment of 0.94 [17] to the RMR values of the compact marls was assigned. Using the statistical methods, individual RMR values were assessed and then RMR values ranging between 50 and 62 with a mean value of 53 were obtained. Due to light blasting carried out in the compact marls to loosen the overburden, disturbed rock mass condition is considered and the value of mi (9.87) for intact rock was calculated by linear regression analysis on the measured triaxial data pairs from the intact rock, and the constants m and s were found to be 0.344 and 0.0004, respectively [14]. To assess the various controls on slope movements, the development of mobilized shear strength and the failure mechanism under the in¯uence of the loads exerted by the spoil pile were investigated by Ulusay and Aksoy [21] using determi-

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SONMEZ et al.: BACK ANALYSIS OF SLOPE FAILURES IN ROCK MASSES

Fig. 5. The ¯ow chart for the proposed method of analysis code HOBRSLP.

SONMEZ et al.: BACK ANALYSIS OF SLOPE FAILURES IN ROCK MASSES

Fig. 6. Location map of the back analyzed case study sites.

nistic and numerical (FEM) methods. For this purpose, available monitoring record, structural data and groundwater information were examined, and a rock mass shear strength envelope was derived from the Hoek±Brown criterion in conjunction with rock mass classi®cation for the highwall material. Ulusay and Aksoy [21] back analyzed the failure utilizing four cross-sections and indicated that the updated Hoek± Brown failure criterion used with rock mass classi®cation gives strength values equal to those obtained by the mobilized strength curve, and results of the back analyses con®rm the applicability of the loaded slope model proposed for the case. The procedure presented herein was applied to the case summarized above. Taking into consideration the loaded slope model (symmetrical vertical triangular external loading condition), the program HOBRSLP [14] was modi®ed by the authors to incorporate external loading conditions (Fig. 8). Considering that the predicted (based on the site observations and monitoring data) surfaces were con®rmed by the calculated failure surfaces [21], four failure surfaces given in Fig. 9 were employed in the

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back analyses. A mean uniaxial compressive strength of 4.15 MPa determined from 40 test specimens for the compact marl, and average values of unit weight of 13 kN/m3 and 16 kN/m3 were utilized for the spoil material (in-situ) and the compact marl, respectively. For each cross-section, starting from an arbitrarily chosen initial RMR value of 18 for the calculation of the constant s, the values of the constant m and corresponding RMRm which satisfy a factor of safety of unity for the given failure surfaces are calculated. The results of the analyses are plotted in the form of RMRm±RMRs graphs (Fig. 10). It is evident from Fig. 10(a)±(d) that common values of RMR for the constants m and s along the failure surfaces in section 1-1' is 51, along section 2-2' is 52 and along section 33' is 53. The RMR values back calculated for four failure surfaces are equal to or nearly identical to 53 and, thus they con®rm the average value of RMR (53) obtained from the comprehensive geotechnical logging and scanline surveys performed by Ulusay [14]. Shear strength values calculated for the base of each slice involved by the four failure surfaces con®rmed by the predicted surfaces (at F = 1 condition) were plotted against normal stresses acting at the slice bases onto the original failure envelope of the rock mass derived from the Hoek±Brown failure criterion by utilizing an average RMR value of 53 (Fig. 11(a)). This comparison indicates that the mobilized strength plots match the original failure envelope of the investigated rock and the method proposed gives identical results to those obtained in a previous study by Ulusay and Aksoy [21]. The resulting curvilinear failure envelopes with RMR values of 51±53 given in Fig. 11(b). Figure 11(b) suggest that failure envelopes for the range of calculated normal stress levels (sn) in the back ana-

Fig. 7. Initiation of the slide in the highwall externally loaded by a spoil pile (Case 1).

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SONMEZ et al.: BACK ANALYSIS OF SLOPE FAILURES IN ROCK MASSES Table 1. Range of parameters employed in rock mass classi®cations for three cases considered in the study

Parameter

Uniaxial compressive strength (MPa) RQD (%) Spacing of discontinuities (mm) Condition of discontinuities

Groundwater Adjustment for discontinuity orientation Blasting damage adjustment Adjustment for major plane of weakness Adjusted RMR'76 Adjusted RMR'89

Range (mean)/description case 1

case 2

case 3

1.14±6.41 (4.15)

4.20±6.15 (5.2)

35.4±44.3 (40.2)

37±98 0 joints: 250±410 (386) bedding: 300± 30±40 1000 aperture 0±1 mm; very thin soft aperture 1±3 mm; soft in®lling; coating; planar-smooth surfaces; slickensided surfaces; highly fresh/slightly weathered; high weatered; high persistence persistence dry-damp one mode of failure ÿ5

dry one mode of failure ÿ5

smooth blasting 0.94 ÿ

ÿ very close to discrete fault zones 0.7 21 20.6

not determined 50±62 (53)

90±95 310±390 (370) apertures <1 mm and 1±5 mm between bedding and joint planes, respectively; soft coating <1 mm; smooth-slightly rough surfaces; fresh to slightly weathered; high persistence dry one mode of failure ÿ5 fair blasting 0.90 ÿ not determined 40±47 (43)

The values given in the parentheses indicate mean value.

lyzed slope show negligible and/or slight di€erences which result from probably due to small variations in the mechanical properties of the same rock in di€erent places. Slope failure in a closely jointed schist rock mass at a barite open pit mine (Case 2) The Baskoyak mine at the central part of Turkey is an open pit mine operated for the extraction of barite. A comprehensive slope stability project was carried out to determine the engineering properties of the rock mass, and to assess the failure mechanism and the alternatives for improving the overall stability between 1987 and 1988, and the investigation was published by Ulusay and Yucel [27]. Based on the scanline surveys consisting of 90 schistosity and 160 joint measurements and geotechnical logging of a borehole of 75 m deep, Ulusay and Yucel [27] reported that the schists should be regarded as comprising two rock mass types. The ®rst type consists of a schist rock mass heavily broken by closely spaced discontinuities (Fig. 12), and the second type is a weathered schist in di€erent degrees both in the hangingwall and footwall, particularly observed at the

Fig. 8. The model with the parameters for the slope under the in¯uence of a symmetrical vertical triangular spoil loading used in the back analysis (Case 1).

middle and lower benches. The unit weight of the schists ranges between 17.2 kN/m3 and 28.5 kN/m3 with a mean value of 22.2 kN/m3. The uniaxial compressive strength of the intact rock determined on a limited number of specimens due to the diculties in sample preparation was 5.2 MPa. Slope failures covering a single bench or two benches were observed at three locations in the pit. The failures were circular and one of them occurred in the closely jointed rock mass. Back analysis of the failures indicated that the calculated sliding surfaces con®rm the actual failure surfaces delineated from the site measurements [27]. No any sign of groundwater was encountered through the geotechnical and previously drilled boreholes and on the benches. Thus, the pit slopes was considered as dry for stability assessments. The overburden material and the ore are removed by the excavators without any blasting. The rock mass parameters of the heavily broken part of the rock mass are given in Table 1. Ulusay and YuÈcel [27] declared an RMR value of 21 in their report based on Bieniawski's 1976 classi®cation [28]. However, the authors of this recent study also calculated the RMR value of the rock mass based on 1989 version of the RMR classi®cation [1] using the parameters given in Table 1 for this case. In this calculation a discontinuity adjustment of ÿ5 considering one mode of failure, mass failure, was assigned. Because the presence of discrete fault zones running very close to the failed slope, a major structure adjustment of 0.7 [17] was also considered to obtain ®nal RMR value. An RMR value of 20.6 which is identical to that derived from Bieniawski's 1976 classi®cation was obtained. Utilizing the well delineated circular slip surface illustrated in Fig. 13 and the geomechanical parameters given above, the proposed method was applied to the failure occurred in closely jointed part of the schists. Choosing an initial RMR value of 10 for the calcu-

SONMEZ et al.: BACK ANALYSIS OF SLOPE FAILURES IN ROCK MASSES

229

Fig. 9. Slope pro®les, and the predicted and calculated failure surfaces employed in the back analyses for the loaded highwall case (Case 1).

lation of the constant s, the analysis was started. The pairs of RMRm and RMRs which lead a value of safety factor of unity are plotted and then the RMRRM value which satis®es limit equilibrium condition for the constants of m and s is found as 21 (Fig. 14(a)). Besides, on the basis of normal stresses acting at the bottom of 10 slices in the failed mass, the

rock mass shear strength values obtained from the failure surface yielding F = 1 are plotted on the original s±t curve derived from the updated Hoek±Brown criterion utilizing an RMR value of 21 (Fig. 14(b)). These results indicate that the back calculated RMR value and the mobilized shear strength plots match the RMR derived from site investigations, and the original

Fig. 10. Back analysis plots illustrating the derivation of RMRs±RMRm pairs satisfying the limit equilibrium condition for the slope pro®les examined (Case 1).

230

SONMEZ et al.: BACK ANALYSIS OF SLOPE FAILURES IN ROCK MASSES

Fig. 11. (a) Comparison between the rock mass shear strength obtained from the back analysis and the failure envelope derived with the Hoek±Brown criterion considering the average RMR value (53) for the rock mass; (b) failure envelopes based on empirical failure criterion for mean and lower bound RMR values derived from the proposed method (Case 1).

failure envelope of the investigated rock mass. Thus, it is concluded that the procedure outlined above also yielded realistic results for this case. A slope instability in a coal mine (Case 3) As an example of the proposed method, back analysis on a typical instability was carried out in Kisrakdere open pit mine which is located at Soma lignite basin (see Fig. 6). The necessary geotechnical data were collected by the authors from this pit. The coal seam is generally 20 m thick, but becomes thinner towards the basin margins where the failed slope is located. Figure 15(a) shows the geometry of the slope in which a single thin coal seam with a thickness of 4.5 m is overlain by a sequence consisting of compact marl, and soft clay beds about 10 m thick. The observations on the slope surfaces, measurements through the blast-holes, and the records of the previously

Fig. 13. Slope geometry before and after failure and circular slip surface in closely jointed schist rock mass (Case 2).

drilled holes in the vicinity of the investigated slope indicated that the groundwater table lies below the failed marly rock mass. As being in the ®rst case, the coal seam acts an aquifer, and therefore, the failed slope is dry. Bedding planes dip into opposite direction of the slope. The marly rock which forms the majority of the sequence has a carbonate content considerably higher than its clay content. The actual slip surface was in circular shape, which was evident from the ®eld inspection and topographical measurements carried out along the failure surface, and passed through the compact marl rock mass and the clay, above the coal seam. Because the thickness of the coal seam reduces in this part of the pit, highly steep slopes were cut to extract the coal. In addition to this application, it is concluded that the presence of a weak and soft clay, and the jointed nature of the marly rock in the sequence made the failure easier. Scanline surveys were carried out in the close vicinity of the failed slope to collect data for the discontinuities and to assess rock mass conditions. Three main joints moderately and

Fig. 12. A view from the schist rock mass heavily broken by closely spaced joints and schistosity planes at a barite open pit mine (Case 2).

SONMEZ et al.: BACK ANALYSIS OF SLOPE FAILURES IN ROCK MASSES

231

Fig. 14. (a) Back analysis plots illustrating the derivation of RMRs± RMRm pairs satisfying the limit equilibrium condition for the failure in the schist; (b) comparison between the rock mass shear strength obtained from the back analysis and the failure envelope derived with Hoek±Brown criterion utilizing the RMR value (21) determined from the site investigation (Case 2).

closely spaced, and bedding planes in the marly sequence resulted in a jointed rock mass. In this study, Bieniawski's 1989 [1] classi®cation scheme was used and the data for the rock mass rating determinations were obtained from the scanline surveys carried out at twenty®ve locations in the studied pit. The range of the rock mass parameters determined in this study is given in Table 1. It is also noted that a discontinuity adjustment of ÿ5 for the case of one mode of failure and a blasting damage adjustment of 0.90 for fair blasting carried out in the compact marls, which have considerable higher strength when compared to those mentioned in Case 1, were considered. A histogram of RMR values based on the assessment of the line survey data (Fig. 15(b)) has a normal form which indicates that RMR values are concentrated between 42 and 44 with a mean value of 43. The geotechnical properties of the marl and the clay determined by an experimental program are listed in Table 2. Considering the similarities between engineering behavior of the clays in this site and the clays in a transition zone at Yatagan coal mine, which were back analyzed by Ulusay and Doyuran [29], the residual

Fig. 15. (a) Cross-section illustrating the geometry of the failed slope and the position of the strata; (b) RMR histogram for the marly rock mass (Case 3).

shear strength parameters of the clay given in Table 1 were assumed to be used for back analysis. The procedure presented was applied to the failed slope by utilizing data available for the site for the assessment of shear strength parameters of the jointed marly rock mass. The results are presented as a plot of RMRs vs RMRm (Fig. 16(a)). The method suggests that the RMRRM value satisfying limit equilibrium condition is 42.5. The back calculated RMRRM value (42.5) con®rms the actual RMR (43) previously determined by the authors through the site investigations. It is also evident from Fig. 16(b) that there is a good agreement between the back calculated shear strengths at the base of slices and the failure envelope derived from the Hoek±Brown failure criterion utilizing the actual RMR value of 43.

232

SONMEZ et al.: BACK ANALYSIS OF SLOPE FAILURES IN ROCK MASSES Table 2. Material properties employed in the black analysis of Kisrakdere open pit mine (Case 3)

Material Marl rock mass Soft clay

Unit weight (kN/ U.C.S. (MPa) m3) 23.7 18.0

40.2 ÿ

mi

cp (kPa)

cr (kPa)

fp (8)

fr (8)

9.04 ÿ

ÿ 17.7

ÿ 14.9

ÿ 21

ÿ 18

cp, cr: Peak and residual cohesion, respectively. fp, fr: Peak and residual internal friction angle, respectively. U.C.S.: Uniaxial compressive strength.

CONCLUSIONS

Conventional back analysis of slope failures can provide functional relations between shear strength parameters c and f for slopes of homogeneous materials with linear failure envelopes provided all the other parameters are known. But in closely jointed rock masses shear strength determination, particularly due to the scale e€ect, is very dicult. In addition, such back analyses have limited practical application because these rocks obey a non-linear failure criterion. In this study, the diculty of determining the shear strength of such rocks and applicability of rock mass classi®cation to rock slopes are explained and a practical procedure with a computer solution for the back analysis of failed slopes is put forward as a means of

Fig. 16. (a) Back analysis plots; (b) comparison between the back analyzed shear strength and the failure envelope derived with the Hoek±Brown criterion for an RMR value of 43 (Case 3).

estimating the mobilized shear strength required to explain existing states of stability. This study is based on the conventional deterministic analysis framework. However, the procedure outlined, which is based on the Hoek±Brown failure criterion, is suitable for back calculations with a maximum of three unknown parameters (RMR and the constants m and s), and requires iterations. The main emphasis in this paper is the application of the method where no procedure of direct strength or RMR measurement is possible. The rock mass rating (RMR) of the rock and the corresponding constants, m and s, satisfying limit equilibrium condition can be readily obtained from a graphic representation of the possible range of solutions. Three examples have been given to illustrate the application of the method in practical geotechnical engineering. In the application of this approach, it was found that the back calculated and predetermined values of RMR with the constants m and s were identical. However, it should be kept in mind that the classi®cation systems which have been mainly developed for underground works may give unrealistic results when applied to rock slopes if their limitations are not well considered. Adjustment for the discontinuity orientation is one of the most important questionable parameter in the RMR system when it is applied to rock slopes. Particularly in closely jointed rock masses, which obey the non-linear Hoek±Brown failure criterion, slope failures occur only in the form of a circular shape regardless of discontinuity orientation. Therefore, in such rock masses expecting of one possible mode of failure and assignment and adjustment value of ÿ5 for the discontinuity orientation seems to be more realistic. This approach was also con®rmed by the results of the stability analysis. On the other hand, consideration of the factors such as method of excavation, major planes of weakness and change in stress which in¯uence the rock mass at a particular location and thus an adjustment for these factors become necessary in rock mass classi®cation applied to rock slopes. It is also noted that the Hoek±Brown failure criterion in conjunction with the RMR classi®cation system is only applicable to intact rock or to closely jointed rock masses, otherwise unrealistic results may be obtained. Therefore, it is reasonable to conclude that the method seems to be a practical tool for back analyzing of slopes in jointed rock masses and to check the rock mass rating obtained from site and laboratory investi-

SONMEZ et al.: BACK ANALYSIS OF SLOPE FAILURES IN ROCK MASSES

gations. In other words, the method may lead to the development of possible modi®cations in describing the rock mass parameters particularly for the slopes, if necessary. A better understanding of the mechanics of jointed rock mass behavior is a problem of major signi®cance in geotechnical engineering. The authors believe that the Hoek±Brown failure criterion provides a good estimate for the shear strength of jointed rock masses. However, the authors hope that the application of the proposed method on various failure case histories in the future may lead to provide a better tool for more precise input data and to check the equations employed by the non-linear failure criterion. AcknowledgementsÐThe authors express their gratitude to Professor Evert Hoek of Canada, and to Professor Hasan Gercek of Karaelmas University, Turkey for their valuable comments and suggestions in preparing the manuscript. Accepted for publication 26 November 1997

REFERENCES 1. Bieniawski, Z. T., Engineering Rock Mass Classi®cation. John Wiley, 1989, 237 pp. 2. Barton, N. R., Lien, R. and Lunde, J., Engineering classi®cation of rock masses for the design of tunnel support. Rock Mech., 1974, 6, 189±239. 3. Grimstad, E. and Barton, N. R., Updating the Q-System for NMT. Proc. Int. Symp. on Sprayed Concrete Ð Modern use of wet mix sprayed concrete for underground support, Fagernes, ed. Kompen, Opsahl and Berg. Oslo, Norwegian Concrete Assoc., 1993. 4. Hoek, E. and Brown, T., Underground Excavations in Rock. Inst. Min. Metall. Stephen Austin and Sons, London, 1980. 5. Hoek, E. and Brown, E. T., Empirical strength criterion of rock masses. J. Geotech. Eng. Div. Am. Soc. Civil Eng. , 1980, 106, 1013±1035. 6. Hoek, E. and Brown, T., The Hoek±Brown failure criterion Ð a 1988 update. Proc. 15th Canadian Rock Mech. Symp. Univ. of Toronto, 1988, pp. 31±38. 7. Hoek, E., Wood, D. and Shah, S., A modi®ed Hoek±Brown criterion for jointed rock masses. Proc. Eurock'92, ed. J. A. Hudson. Thomas Telford, 1992, pp. 209±213. 8. Hoek, E., Kaiser, P. K. and Bawden, W. F., Support of Underground Excavations in Hard Rock. A. A. Balkema, Rotterdam, 1995. 9. Laubscher, D. H., A geomechanics classi®cation system for the rating of rock mass in mine design. J. South Afr. Inst. Miner. Metall., 1990, 90(10), 257±273. 10. Romana, M., A geomechanical classi®cation for slopes: Slope Mass Rating. in Comprehensive Rock Engineering, Vol. 3, Ch. 22, ed. J. A. Hudson. Pergamon Press, London, 1993, pp. 575± 599.

233

11. Priest, S. D. and Brown, E. T., Probablistic stability analysis of variable rock slopes. Trans. Inst. Miner. Metall. A Miner. Ind., 1993, 92(10), A1±A12. 12. Pender, M. J. and Free, M. W., Stability assessment of slopes in closely jointed rock masses. Proc. Eurock'93, ed. A. Sousa and P. Grossmann. A. A. Balkema, 1993, pp. 863±870. 13. Singh, R. N. and Gahrooee, D. R., Deterministic stability and sensitivity analyses of slopes in jointed rock masses. Mining Sci. Technol. , 1990, 10(10), 265±286. 14. Ulusay, R., Geotechnical considerations and deterministic design considerations for pitwall slopes at Eskihisar (Yatagan±Mugla) strip coal mine. Unpublished Ph.D. dissertation. Middle East Technical University, Ankara, Turkey, 1991. 15. Hoek, E., Strength of rock and rock masses. News J. ISRM, 1995, 2(2), 4±16. 16. Singh, R. N. and Gahrooee, D. R., Application of rock mass weakening coecient for stability assessment of slopes in heavily jointed rock masses. Int. J. Surf. Mining, 1989, 3(2), 207±219. 17. Kendorski, F. S., Cummings, R. A., Bieniawski, Z. T. and Skinner, E. H., Rock mass classi®cation for block caving mine drift support. Proc. 5th Int. Cong. Rock Mech. ISRM. Melbourne, 1983, pp. B51±B63. 18. Unal, E., Ozkan, I. and Ulusay, R., Characterization of weak, strati®ed and clay Ð bearing rock masses. ISRM Symposium: Eurock' 92 Ð Rock Characterization, Chester, UK, 14±17 September, 1992, ed. J. A. Hudson. British Geotechnical Society, London, 1992, pp. 330±335. 19. Ulusay, R., Ozkan, I. and Unal, E., Characterization of weak, strati®ed and clay Ð bearing rock masses for engineering applications. Fractured and Jointed Rock Masses Conference, ed. L. R., Myer, N. G. W., Cook, R. E., Goodman, and C. F., Tsang, 3±5 June, 1992, CA. A. A. Balkema, Rotterdam, 1995, pp. 229± 235. 20. Unal, E., Modi®ed rock mass classi®cation: M-RMR System. The Bieniawski Jubilee Collection Ð Milestones in Rock Enginering. A. A. Balkema, 1996, pp. 203±222. 21. Ulusay, R. and Aksoy, H., Assessment of the failure mechanism of a highwall slope under spoil pile loadings at a coal mine. Eng. Geol. , 1994, 38(2), 117±134. 22. Fookes, P. G., Reeves, B. J. and Dearman, W. R., The design and construction of a rock slope in weathered slate at Fowey, South-West England . Geotechnique, 1977, 27(2), 533±556. 23. Sancio, R. T., The use of back-calculations to obtain shear and tensile strength of weathered rocks. Proc. Intnl. Symp. on Weak Rock, 21±24 September, 1981, Tokyo, Vol. 2. 1981, pp. 647±652. 24. Hoek, E., Estimating Mohr±Coulomb friction and cohesion values from Hoek±Brown failure criterion. Int. J. Rock Mech. Miner. Sci. Geomech. Abstr., 1990, 27(2), 227±229. 25. Bishop, A. W., The use of slip circle in the stability analysis of earth slopes. Geotechnique, 1955, 5(2), 7±17. 26. ISRM (International Society for Rock Mechanics), ISRM Suggested Methods: Rock Characterization, Testing and Monitoring, ed. E. T. Brown. Pergamon, London, 1981, 211 pp. 27. Ulusay, R. and Yucel, Z., An example for the stability of slopes excavated in weak rocks: Baskoyak Barite Open Pit. Earthsciences (Bull. of Earth Sciences Application and Research Center of Hacettepe University), 1989, 15(2), 15±27in Turkish. 28. Bieniawski, Z. T., Rock mass classi®cation in rock engineering. Exploration for Rock Engineering, Proc. of the Symp., Vol. 1, ed. Z. T. Bieniawski. Balkema, CapeTown, 1976, pp. 97±106. 29. Ulusay, R. and Doyuran, V., Characteristics of a multiple retrogressive failure in a coal mine in southwest Turkey. Eng. Geol. , 1993, 36(2), 79±89.