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Estimation of large-scale mechanical properties of a large landslide on the basis of seismic results
International Journal of Rock Mechanics & Mining Sciences 38 (2001) 877–883
Estimation of large-scale mechanical properties of a large landslide on the basis of seismic results E. Brueckl*, M. Parotidis Institute of Geodesy and Geophysics, Vienna University of Technology, Gusshaustrasse 27-29, A-1040 Vienna, Austria Accepted 17 July 2001
Abstract Knowledge of large-scale mechanical properties is essential for estimating the stability of rock slopes being deformed by deep creep and especially for predicting a transition to rapid sliding. Standard geomechanical testing procedures may not result in significant values as the volume of the mass movements under consideration exceeds the volume of even the largest in situ tests by several orders of magnitude. Seismic measurements may help to estimate some of the relevant mechanical properties by direct correlation with the seismic velocities. However, not all parameters necessary for a stability analysis correlate closely with seismic velocities. An alternative approach could be the geomechanical modelling of the structures and properties of the creeping or sliding mass, as determined from seismic exploration. In this paper, we present an application of this approach to the giant landslide of Koefels. The development of the creeping rock mass, which represents the initial phase of the mass movement, has been successfully modelled by assuming a transition of the originally compact rock mass to ‘‘soft’’ rock, controlled by a Mohr–Coulomb and no tension yield criterion. Geomechanical parameters are determined by fitting the geomechanical model to the seismic results. An apparent angle of internal friction has been determined in the range 20–241. These low values are compatible with the fact that a transition to rapid sliding took place in the past. r 2001 Elsevier Science Ltd. All rights reserved.
1. Introduction For the stability analysis of high mountain slopes, knowledge of the large-scale mechanical properties is important. This issue is most essential if these slopes are deformed by deep creep with an imminent danger of a transition to rapid sliding. The volume of such mass movements ranges from 106 to 1010 m3 and therefore, exceeds the volume of even the largest in situ tests by orders of magnitude. Seismic measurements may help to estimate some of the relevant mechanical properties by direct correlation with the seismic velocities. However, not all parameters are necessary for a stability analysis to correlate closely with seismic velocities. A promising supplement could be the geomechanical modelling of the structures of the creeping or sliding rock masses. Such a geomechanical model must have the potential to describe the process of the generation and development of a creeping rock mass out of an originally compact rock. Geomechanical parameters, *Corresponding author. Tel.: +43-1-58801-12820; fax: +43-1-5044232. E-mail address: [email protected] (E. Brueckl).
which are not in close direct correlation to seismic parameters, may be determined by fitting the geomechanical model to the structures as determined from seismic exploration. In this paper, we present an application of this approach to the giant Koefels landslide, which has been explored quite well within the scope of the Austrian contribution to the International Decade of Natural Disaster Reduction.
2. The Koefels landslide . The Koefels landslide (Otztal, Tirol, Austria) is recognized as the largest landslide in the crystalline Alps. The location of this landslide may be seen in Fig. 1a. Despite the fact that this event took place about 8700 years ago, it is a promising task to apply the approach mentioned above to this unique landslide. From 1986 to 1997, several refraction and reflection seismic lines were carried out to explore the seismic structure and parameters of this landslide [1]. A model of the basal sliding surface was constructed on the basis of the seismic results (Fig. 1b). As the Koefels landslide
1365-1609/01/$ - see front matter r 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 3 6 5 - 1 6 0 9 ( 0 1 ) 0 0 0 5 3 - 3
878
E. Brueckl, M. Parotidis / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 877–883
Fig. 1. Location (a), sliding surface (b), topography just after the landslide (boundary line bn2) (c), and pre-failure topography (boundary line bn1) (d) of the giant landslide of Koefels.
is an ancient one, erosional losses took place, which had to be compensated in order to represent the situation just after the landslide event (Fig. 1c). The P-wave velocity of the compact rock basis could be determined at only one seismic line to 5200 m/s. The P-wave velocities of the landslide mass were approximated by an average velocity–depth profile (VP FD) which can be described by [2]: VP ¼ 402D0:324 : The units are m/s for VP and m for D. The average depth of the sliding surface is 300 m and the corresponding P-wave velocity of the landslide mass at this depth is 2550 m/s or, approximately, 50% of the value of the compact rock. Porosities of the landslide mass were estimated using an empirical relation between porosity and P-wave velocity. The pre-failure topography was
reconstructed, considering the morphological plausibility and observing the conservation of mass (Fig. 1d). The volume confined by the pre-failure topography and the sliding surface is identical with the landslide mass in the initial state (before rapid sliding took place). A representative cross-section containing all information for the modelling and defined by the pre- and postfailure location of the landslide mass centres is shown in Fig. 2. A compilation of the most important parameters derived from the structural models and the estimated porosity is given in the following table. Pre-failure base area Post-failure base area Pre-failure volume Post-failure volume
10.98 106 m2 12.87 106 m2 3.280 106 m3 3.880 106 m3
E. Brueckl, M. Parotidis / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 877–883
879
Fig. 2. Cross-section and elastic parameters of compact rock and sediment of the giant landslide of Koefels used for FEM calculations.
Post-failure mean porosity Vertical displacement of the centre of mass Horizontal displacement of the centre of mass Mean sliding angle Initial sliding angle
23% 676 m 2090 m 17.901 32.91
3. Mechanical modelling We assume that the development of a giant or large landslide follows the three states of creep, which are Primary creep: corresponding to the initial phase of development of the mass movement. An originally compact rock will be transformed to a damaged or soft rock, including small-scale fractures, by concentrations of high stresses. Secondary creep: is assumed as a quasi-stationary phase. The softened rock exhibits a more or less spatially continuous creep. The creep rate is mainly controlled by pore pressure, and the motion may be continuous or of the stick-slip type. Primary and secondary creeps correspond to the mechanism of Sackung failure (sagging of the whole slope). Tertiary creep: is the transition from a quasistationary phase to rapid and eventually catastrophic sliding. This possibility is the most important issue in analyzing historical and active mass movements. At the present state of our investigation, we concentrate on the modelling of the initial phase. However, the hypothesis we are going to test is whether parameters derived from the analysis of the initial phase of the movement are relevant for the secondary creep and the ultimate stability of the slope. If this hypothesis is true, the analysis of the initial phase could supply important data for predicting the future behaviour of an active mass movement. The numerical modelling of stress and strain is done by 2D-FEM calculations using the geometry and the
parameters of the cross-section shown in Fig. 2. These parameters are Young’s modulus, Poisson’s ratio, and the density of the compact rock. We assume plane strain and horizontal stresses resulting only from gravity. The influence of additional tectonic stresses is not considered at present. We further assume ideal elastic behaviour up to a yield stress defined by Mohr–Coulomb parameters (cohesion and angle of internal friction). We tested two models for the behaviour of the material exceeding the yield stress: Model A: Plastic behaviour with zero or little strain softening is introduced into all the cells of the FEM mesh exceeding the yield stress. The values of the cohesion at low strain and the strain softening were adjusted to maximize the area of plastic deformation under the constraint of slope stability. Model B: For this model, the no-tension condition is introduced as an additional yield criterion. The calculation starts with an initial state where all cells of the FEM mesh have the properties of compact rock. After the first calculation of the stress distribution, all cells of the FEM mesh exceeding the yield stress are considered to change from compact rock to a zone of damaged or softened rock mass. We model this transition from compact to soft rock by a reduction of the shear modulus by a factor ko1. After mapping the reduced shear modulus to the zone of softened rock, a next FEM-calculation of the state of stress is carried out and the procedure of mapping the properties of soft rock to the cells exceeding the yield criterion is repeated. The cohesion defined in the yield criterion is chosen to add n more cells to the zone of softened rock after each recalculation. The whole process of recalculating the stress field and mapping a reduced shear modulus to the cells exceeding the yield criterion is stopped when the value of the cohesion dropped considerably, or when the calculated zone of soft rock fitted best, the landslide mass in its initial state. In our numerical experiments applying model B, we chose n ¼ 16 and k ¼ 1=4: This value of n; guarantees
880
E. Brueckl, M. Parotidis / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 877–883
reasonable progress in the growth of the zone of softened rock after each recalculation. The value of k corresponds to a 50% reduction of the S-wave velocities. From our seismic field data, we did not get information about the S-wave velocities of the compact rock. However, assuming the same Poisson’s ratio for compact and softened rock, we may estimate a reasonable value of k from the P-wave velocities. Inserting the average depth of the landslide mass (300 m) to the (VP 2D) relation given before, we get a P-wave velocity of 2550 m/s for the softened rock in the vicinity of the sliding plane. The task of the numerical calculations is to adjust the free parameters in our models to fit the numerically determined zone of softened rock to the landslide mass in its initial state. The absolute value of the Young’s modulus does not effect the stress distribution within the elastic range, the cohesion being determined by the
procedures described above, and the softening of the rock exceeding the yield criterion is fixed for these tests. Therefore, the only parameters to be adjusted are Poisson’s ratio n of the compact rock and the angle of internal friction f1 : To prevent yielding at great depth due to the increasing difference between vertical and horizontal stresses, we selected the angle of internal friction to be equal or greater than f1min ¼ arcsinð1 2nÞ: 4. Results In Fig. 3, we present two examples of our calculations applying model A with parameters as follows: n ¼ 0:30
f1 ¼ 301
C ¼ 2:2 MPa;
ðaÞ
n ¼ 0:32
f1 ¼ 281
C ¼ 2:2 MPa:
ðbÞ
Fig. 3. Zones of plastic deformation applying model A with parameter selection (a) and (b) as calculated with the FEM.
E. Brueckl, M. Parotidis / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 877–883
Despite the fact that the zone of plastic deformation is confined to the lower part of the slope, decreasing the cohesion or introducing significant strain softening did not considerably enlarge this zone, but made the calculation unstable. At the present state of our experience with this model, we were not successful in producing a plastic zone comparable to the actual creeping mass in its initial phase. Therefore, we cannot derive any information about Poisson’s ratio and the angle of internal friction from the application of model A. Model B is a purely elastic model, therefore, stability is always guaranteed. The numerically determined zone of softened rock reacted sensitively to the selected parameters n and f1 : A quite satisfactory fit to the actual creeping mass was possible. The following combination of parameters has already been tested: n ¼ 0:40
f1 ¼ 121;
ðcÞ
881
n ¼ 0:40
f1 ¼ 181;
ðdÞ
n ¼ 0:30
f1 ¼ 241:
ðeÞ
Fig. 4 shows the maximum shear strains and the zone of softened rock at the 11th calculation step applying the parameter combination (c). There is a concentration of shear strain near the actual sliding surface; however, yielding started to penetrate deeply and unrealistically into the slope. Therefore, we discard the parameter combination (c) and classify the angle of internal friction f1 ¼ 121 as too low. Fig. 5 shows two calculation steps applying the parameter combination (d). The actual sliding surface and landslide mass is modelled quite well during the first two-thirds of the growth of the zone of maximum shear strain and softened rock. Approaching the end of the development, an unrealistically deep-penetrating zone of softened rock and high shear strain is generated. As the
Fig. 4. Zones of softened rock (red zone corresponds to soft rock and blue to compact rock) (left column) and maximum shear strains (right column) of the 11th FEM calculation step.
Fig. 5. Zones of softened rock (red zone corresponds to soft rock and blue to compact rock) (left column) and maximum shear strains (right column) of the FEM calculation steps 30 and 43. The colour bars of Fig. 4 are valid.
882
E. Brueckl, M. Parotidis / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 877–883
Fig. 6. Zones of softened rock (red zone corresponds to soft rock and blue to compact rock) (left column) and maximum shear strains (right column) of the FEM calculation steps 1, 10, 25 and 31. The colour bars of Fig. 4 are valid.
cohesion had to be reduced several times, we can expect that the whole development is slowing down continuously. Fig. 6 shows a sequence of four calculation steps corresponding to Fig. 5, but with the parameter combination (e). The difference from Fig. 5 is a shallower zone of maximum shear strain and softened rock. During the first half of the whole process, the calculated structures are clearly above the actual sliding surface. In the final state, the total volume of softened rock fits well the actual creeping mass in its initial phase. By inspection of the spatial distribution of the maximum normal and shear stress for each calculation step, it turns out that tension occurs only very sporadically at isolated spots, and the linear Mohr– Coulomb yield criterion is responsible for the softening of the rock.
5. Discussion and outlook At the present state of our investigations, the elastoplastic model (model A) turns out to be ineffective in modelling the development of a zone of softened rock corresponding to the creeping mass in its initial state. However, more numerical tests have to be carried out to prove this first conclusion. In contrast to the elasto-plastic model, the pure elastic model (model B), introducing only a reduction of the shear modulus after reaching the Mohr–Coulomb yield criterion, is very effective in modelling the initial phase of the landslide. A zone of softened rock starts at the toe of the slope, expands near the actual sliding surface and finally comprises a volume comparable to the actual creeping mass. The thickness of the zone of softened rock may be controlled by the choice of Poisson’s ratio n
E. Brueckl, M. Parotidis / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 877–883
and the angle of internal friction f1 of the compact rock. Therefore, estimates of n and f1 may be derived from this type of modelling. A first guess could be 0:30ono0:35;
201of1 o241:
However, more parameter combinations have to be tested for the verification of this estimate. In our procedures, the pore water pressure was not taken into account. Therefore, f1 is the apparent angle of internal friction, which bears the following relation to the true angle of internal friction f: tan f1 ¼ ð1 p=sn Þ tan f: The quantities sn and p are the total normal stress and the pore water pressure. An estimate of f of the creeping mass at a normal pressure corresponding to the depth of the sliding plane by the method of Hoek and Brown [3] gives f ¼ 261: The equation for f and f1 may be satisfied by assuming quite reasonable ratios
883
creep phase. Future developments will make it possible to use the observed P-wave velocityFdepth relation as an input to model the reduction of the shear modulus. Furthermore, the pore water pressure will be introduced explicitly, the dilatancy will be considered, and the fracture mechanical conception of subcritical crack growth will be applied instead of the strength of material approach defined by the Mohr–Coulomb and no tension criterion.
Acknowledgements This work is part of a project within the International Decade of Natural Disaster Reduction and we thank the Austrian Academy of Sciences for funding. Additionally, we express our thanks to the two anonymous reviewers for their valuable remarks and suggestions.
References
0:09op=sn o0:25: The estimates of f1 are also in reasonable relation with the initial sliding angle of a0 ¼ 331; the mean sliding angle of the centre of mass am ¼ 181; and the fact is that a transition to tertiary creep and rapid sliding took place. The next steps in our work will be sensitivity tests for parameters including k and the application of the method to other large landslides in the quasi-stationary
[1] Brueckl E, Brueckl J, Castillo E, Heuberger H. Present structure and pre-failure topography of the giant landslide of Koefels. Proceedings of the Fourth EEGS-ES Meeting, 14–17 September 1998, Barcelona, Spain. p. 567–70. [2] Brueckl E, Parotidis M. Seismic velocities of large rockslide masses. Proceedings of the 62nd EAGE Conference & Technical Exhibition, 29 May–2 June, Glasgow, Scotland. p. 169. [3] Hoek E, Brown E. Practical estimates of rock mass strength. Int J Rock Mech Min Sci 1997;34(8):1165–86.
Estimation of large-scale mechanical properties of a large landslide on the basis of seismic results E. Brueckl*, M. Parotidis Institute of Geodesy and Geophysics, Vienna University of Technology, Gusshaustrasse 27-29, A-1040 Vienna, Austria Accepted 17 July 2001
Abstract Knowledge of large-scale mechanical properties is essential for estimating the stability of rock slopes being deformed by deep creep and especially for predicting a transition to rapid sliding. Standard geomechanical testing procedures may not result in significant values as the volume of the mass movements under consideration exceeds the volume of even the largest in situ tests by several orders of magnitude. Seismic measurements may help to estimate some of the relevant mechanical properties by direct correlation with the seismic velocities. However, not all parameters necessary for a stability analysis correlate closely with seismic velocities. An alternative approach could be the geomechanical modelling of the structures and properties of the creeping or sliding mass, as determined from seismic exploration. In this paper, we present an application of this approach to the giant landslide of Koefels. The development of the creeping rock mass, which represents the initial phase of the mass movement, has been successfully modelled by assuming a transition of the originally compact rock mass to ‘‘soft’’ rock, controlled by a Mohr–Coulomb and no tension yield criterion. Geomechanical parameters are determined by fitting the geomechanical model to the seismic results. An apparent angle of internal friction has been determined in the range 20–241. These low values are compatible with the fact that a transition to rapid sliding took place in the past. r 2001 Elsevier Science Ltd. All rights reserved.
1. Introduction For the stability analysis of high mountain slopes, knowledge of the large-scale mechanical properties is important. This issue is most essential if these slopes are deformed by deep creep with an imminent danger of a transition to rapid sliding. The volume of such mass movements ranges from 106 to 1010 m3 and therefore, exceeds the volume of even the largest in situ tests by orders of magnitude. Seismic measurements may help to estimate some of the relevant mechanical properties by direct correlation with the seismic velocities. However, not all parameters are necessary for a stability analysis to correlate closely with seismic velocities. A promising supplement could be the geomechanical modelling of the structures of the creeping or sliding rock masses. Such a geomechanical model must have the potential to describe the process of the generation and development of a creeping rock mass out of an originally compact rock. Geomechanical parameters, *Corresponding author. Tel.: +43-1-58801-12820; fax: +43-1-5044232. E-mail address: [email protected] (E. Brueckl).
which are not in close direct correlation to seismic parameters, may be determined by fitting the geomechanical model to the structures as determined from seismic exploration. In this paper, we present an application of this approach to the giant Koefels landslide, which has been explored quite well within the scope of the Austrian contribution to the International Decade of Natural Disaster Reduction.
2. The Koefels landslide . The Koefels landslide (Otztal, Tirol, Austria) is recognized as the largest landslide in the crystalline Alps. The location of this landslide may be seen in Fig. 1a. Despite the fact that this event took place about 8700 years ago, it is a promising task to apply the approach mentioned above to this unique landslide. From 1986 to 1997, several refraction and reflection seismic lines were carried out to explore the seismic structure and parameters of this landslide [1]. A model of the basal sliding surface was constructed on the basis of the seismic results (Fig. 1b). As the Koefels landslide
1365-1609/01/$ - see front matter r 2001 Elsevier Science Ltd. All rights reserved. PII: S 1 3 6 5 - 1 6 0 9 ( 0 1 ) 0 0 0 5 3 - 3
878
E. Brueckl, M. Parotidis / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 877–883
Fig. 1. Location (a), sliding surface (b), topography just after the landslide (boundary line bn2) (c), and pre-failure topography (boundary line bn1) (d) of the giant landslide of Koefels.
is an ancient one, erosional losses took place, which had to be compensated in order to represent the situation just after the landslide event (Fig. 1c). The P-wave velocity of the compact rock basis could be determined at only one seismic line to 5200 m/s. The P-wave velocities of the landslide mass were approximated by an average velocity–depth profile (VP FD) which can be described by [2]: VP ¼ 402D0:324 : The units are m/s for VP and m for D. The average depth of the sliding surface is 300 m and the corresponding P-wave velocity of the landslide mass at this depth is 2550 m/s or, approximately, 50% of the value of the compact rock. Porosities of the landslide mass were estimated using an empirical relation between porosity and P-wave velocity. The pre-failure topography was
reconstructed, considering the morphological plausibility and observing the conservation of mass (Fig. 1d). The volume confined by the pre-failure topography and the sliding surface is identical with the landslide mass in the initial state (before rapid sliding took place). A representative cross-section containing all information for the modelling and defined by the pre- and postfailure location of the landslide mass centres is shown in Fig. 2. A compilation of the most important parameters derived from the structural models and the estimated porosity is given in the following table. Pre-failure base area Post-failure base area Pre-failure volume Post-failure volume
10.98 106 m2 12.87 106 m2 3.280 106 m3 3.880 106 m3
E. Brueckl, M. Parotidis / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 877–883
879
Fig. 2. Cross-section and elastic parameters of compact rock and sediment of the giant landslide of Koefels used for FEM calculations.
Post-failure mean porosity Vertical displacement of the centre of mass Horizontal displacement of the centre of mass Mean sliding angle Initial sliding angle
23% 676 m 2090 m 17.901 32.91
3. Mechanical modelling We assume that the development of a giant or large landslide follows the three states of creep, which are Primary creep: corresponding to the initial phase of development of the mass movement. An originally compact rock will be transformed to a damaged or soft rock, including small-scale fractures, by concentrations of high stresses. Secondary creep: is assumed as a quasi-stationary phase. The softened rock exhibits a more or less spatially continuous creep. The creep rate is mainly controlled by pore pressure, and the motion may be continuous or of the stick-slip type. Primary and secondary creeps correspond to the mechanism of Sackung failure (sagging of the whole slope). Tertiary creep: is the transition from a quasistationary phase to rapid and eventually catastrophic sliding. This possibility is the most important issue in analyzing historical and active mass movements. At the present state of our investigation, we concentrate on the modelling of the initial phase. However, the hypothesis we are going to test is whether parameters derived from the analysis of the initial phase of the movement are relevant for the secondary creep and the ultimate stability of the slope. If this hypothesis is true, the analysis of the initial phase could supply important data for predicting the future behaviour of an active mass movement. The numerical modelling of stress and strain is done by 2D-FEM calculations using the geometry and the
parameters of the cross-section shown in Fig. 2. These parameters are Young’s modulus, Poisson’s ratio, and the density of the compact rock. We assume plane strain and horizontal stresses resulting only from gravity. The influence of additional tectonic stresses is not considered at present. We further assume ideal elastic behaviour up to a yield stress defined by Mohr–Coulomb parameters (cohesion and angle of internal friction). We tested two models for the behaviour of the material exceeding the yield stress: Model A: Plastic behaviour with zero or little strain softening is introduced into all the cells of the FEM mesh exceeding the yield stress. The values of the cohesion at low strain and the strain softening were adjusted to maximize the area of plastic deformation under the constraint of slope stability. Model B: For this model, the no-tension condition is introduced as an additional yield criterion. The calculation starts with an initial state where all cells of the FEM mesh have the properties of compact rock. After the first calculation of the stress distribution, all cells of the FEM mesh exceeding the yield stress are considered to change from compact rock to a zone of damaged or softened rock mass. We model this transition from compact to soft rock by a reduction of the shear modulus by a factor ko1. After mapping the reduced shear modulus to the zone of softened rock, a next FEM-calculation of the state of stress is carried out and the procedure of mapping the properties of soft rock to the cells exceeding the yield criterion is repeated. The cohesion defined in the yield criterion is chosen to add n more cells to the zone of softened rock after each recalculation. The whole process of recalculating the stress field and mapping a reduced shear modulus to the cells exceeding the yield criterion is stopped when the value of the cohesion dropped considerably, or when the calculated zone of soft rock fitted best, the landslide mass in its initial state. In our numerical experiments applying model B, we chose n ¼ 16 and k ¼ 1=4: This value of n; guarantees
880
E. Brueckl, M. Parotidis / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 877–883
reasonable progress in the growth of the zone of softened rock after each recalculation. The value of k corresponds to a 50% reduction of the S-wave velocities. From our seismic field data, we did not get information about the S-wave velocities of the compact rock. However, assuming the same Poisson’s ratio for compact and softened rock, we may estimate a reasonable value of k from the P-wave velocities. Inserting the average depth of the landslide mass (300 m) to the (VP 2D) relation given before, we get a P-wave velocity of 2550 m/s for the softened rock in the vicinity of the sliding plane. The task of the numerical calculations is to adjust the free parameters in our models to fit the numerically determined zone of softened rock to the landslide mass in its initial state. The absolute value of the Young’s modulus does not effect the stress distribution within the elastic range, the cohesion being determined by the
procedures described above, and the softening of the rock exceeding the yield criterion is fixed for these tests. Therefore, the only parameters to be adjusted are Poisson’s ratio n of the compact rock and the angle of internal friction f1 : To prevent yielding at great depth due to the increasing difference between vertical and horizontal stresses, we selected the angle of internal friction to be equal or greater than f1min ¼ arcsinð1 2nÞ: 4. Results In Fig. 3, we present two examples of our calculations applying model A with parameters as follows: n ¼ 0:30
f1 ¼ 301
C ¼ 2:2 MPa;
ðaÞ
n ¼ 0:32
f1 ¼ 281
C ¼ 2:2 MPa:
ðbÞ
Fig. 3. Zones of plastic deformation applying model A with parameter selection (a) and (b) as calculated with the FEM.
E. Brueckl, M. Parotidis / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 877–883
Despite the fact that the zone of plastic deformation is confined to the lower part of the slope, decreasing the cohesion or introducing significant strain softening did not considerably enlarge this zone, but made the calculation unstable. At the present state of our experience with this model, we were not successful in producing a plastic zone comparable to the actual creeping mass in its initial phase. Therefore, we cannot derive any information about Poisson’s ratio and the angle of internal friction from the application of model A. Model B is a purely elastic model, therefore, stability is always guaranteed. The numerically determined zone of softened rock reacted sensitively to the selected parameters n and f1 : A quite satisfactory fit to the actual creeping mass was possible. The following combination of parameters has already been tested: n ¼ 0:40
f1 ¼ 121;
ðcÞ
881
n ¼ 0:40
f1 ¼ 181;
ðdÞ
n ¼ 0:30
f1 ¼ 241:
ðeÞ
Fig. 4 shows the maximum shear strains and the zone of softened rock at the 11th calculation step applying the parameter combination (c). There is a concentration of shear strain near the actual sliding surface; however, yielding started to penetrate deeply and unrealistically into the slope. Therefore, we discard the parameter combination (c) and classify the angle of internal friction f1 ¼ 121 as too low. Fig. 5 shows two calculation steps applying the parameter combination (d). The actual sliding surface and landslide mass is modelled quite well during the first two-thirds of the growth of the zone of maximum shear strain and softened rock. Approaching the end of the development, an unrealistically deep-penetrating zone of softened rock and high shear strain is generated. As the
Fig. 4. Zones of softened rock (red zone corresponds to soft rock and blue to compact rock) (left column) and maximum shear strains (right column) of the 11th FEM calculation step.
Fig. 5. Zones of softened rock (red zone corresponds to soft rock and blue to compact rock) (left column) and maximum shear strains (right column) of the FEM calculation steps 30 and 43. The colour bars of Fig. 4 are valid.
882
E. Brueckl, M. Parotidis / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 877–883
Fig. 6. Zones of softened rock (red zone corresponds to soft rock and blue to compact rock) (left column) and maximum shear strains (right column) of the FEM calculation steps 1, 10, 25 and 31. The colour bars of Fig. 4 are valid.
cohesion had to be reduced several times, we can expect that the whole development is slowing down continuously. Fig. 6 shows a sequence of four calculation steps corresponding to Fig. 5, but with the parameter combination (e). The difference from Fig. 5 is a shallower zone of maximum shear strain and softened rock. During the first half of the whole process, the calculated structures are clearly above the actual sliding surface. In the final state, the total volume of softened rock fits well the actual creeping mass in its initial phase. By inspection of the spatial distribution of the maximum normal and shear stress for each calculation step, it turns out that tension occurs only very sporadically at isolated spots, and the linear Mohr– Coulomb yield criterion is responsible for the softening of the rock.
5. Discussion and outlook At the present state of our investigations, the elastoplastic model (model A) turns out to be ineffective in modelling the development of a zone of softened rock corresponding to the creeping mass in its initial state. However, more numerical tests have to be carried out to prove this first conclusion. In contrast to the elasto-plastic model, the pure elastic model (model B), introducing only a reduction of the shear modulus after reaching the Mohr–Coulomb yield criterion, is very effective in modelling the initial phase of the landslide. A zone of softened rock starts at the toe of the slope, expands near the actual sliding surface and finally comprises a volume comparable to the actual creeping mass. The thickness of the zone of softened rock may be controlled by the choice of Poisson’s ratio n
E. Brueckl, M. Parotidis / International Journal of Rock Mechanics & Mining Sciences 38 (2001) 877–883
and the angle of internal friction f1 of the compact rock. Therefore, estimates of n and f1 may be derived from this type of modelling. A first guess could be 0:30ono0:35;
201of1 o241:
However, more parameter combinations have to be tested for the verification of this estimate. In our procedures, the pore water pressure was not taken into account. Therefore, f1 is the apparent angle of internal friction, which bears the following relation to the true angle of internal friction f: tan f1 ¼ ð1 p=sn Þ tan f: The quantities sn and p are the total normal stress and the pore water pressure. An estimate of f of the creeping mass at a normal pressure corresponding to the depth of the sliding plane by the method of Hoek and Brown [3] gives f ¼ 261: The equation for f and f1 may be satisfied by assuming quite reasonable ratios
883
creep phase. Future developments will make it possible to use the observed P-wave velocityFdepth relation as an input to model the reduction of the shear modulus. Furthermore, the pore water pressure will be introduced explicitly, the dilatancy will be considered, and the fracture mechanical conception of subcritical crack growth will be applied instead of the strength of material approach defined by the Mohr–Coulomb and no tension criterion.
Acknowledgements This work is part of a project within the International Decade of Natural Disaster Reduction and we thank the Austrian Academy of Sciences for funding. Additionally, we express our thanks to the two anonymous reviewers for their valuable remarks and suggestions.
References
0:09op=sn o0:25: The estimates of f1 are also in reasonable relation with the initial sliding angle of a0 ¼ 331; the mean sliding angle of the centre of mass am ¼ 181; and the fact is that a transition to tertiary creep and rapid sliding took place. The next steps in our work will be sensitivity tests for parameters including k and the application of the method to other large landslides in the quasi-stationary
[1] Brueckl E, Brueckl J, Castillo E, Heuberger H. Present structure and pre-failure topography of the giant landslide of Koefels. Proceedings of the Fourth EEGS-ES Meeting, 14–17 September 1998, Barcelona, Spain. p. 567–70. [2] Brueckl E, Parotidis M. Seismic velocities of large rockslide masses. Proceedings of the 62nd EAGE Conference & Technical Exhibition, 29 May–2 June, Glasgow, Scotland. p. 169. [3] Hoek E, Brown E. Practical estimates of rock mass strength. Int J Rock Mech Min Sci 1997;34(8):1165–86.