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** BACKGROUND TO THE PROBLEM**

**BACKGROUND TO THE PROBLEM**

Most textbooks on soil mechanics or geotechnical engineering include references to several alternative limit equilibrium methods of slope-stability analysis. In a survey of these methods, undertaken by Wright et al. (1973), the characteristics of all accepted methods were summarised, including the ordinary method of slices (Fellenius, 1936), Bishop’s Modified Method (Bishop, 1955), force equilibrium methods (e.g. Lowe and Karafiath, 1960), Janbu’s procedure for slices (Janbu, 1957), Morgenstern and Price, (1965) and Spencer’s method (Spencer, 1967). There seems to be some consensus that the Morgenstern-Price method is one of the most reliable. All limit equilibrium methods are based on an assumption that the failing soil mass could be divided into slices. This slicing requires further assumptions regarding the magnitude and direction of the side forces influencing equilibrium. The assumption made about side forces is one of the main characteristics that distinguishes one limit equilibrium method from another, and yet is itself an entirely artificial distinction (Bromhead, 1992).

**Common features of the failures**

**Common features of the failures**

There are four features common to the failures. The first one is related to the post-failure profile, similar to that reported by Boyd (1983) in Figure 1.1. The failure mode has horizontal movement towards the pit by an almost undisturbed front block (passive block) and vertically downward movement of the block behind it (active block), with a final elevation significantly lower than that of the original slope profile. The second feature of the failures is that in all cases the slope is situated on an undulated stratum with strata dipping towards the pit. The failure surface is at the contact between shale that overlies the second coal seam, i.e. the contact between a relatively weak and relatively strong layer respectively.

** MODEL DEVELOPED FOR VIRGIN STRESS ESTIMATION**

**MODEL DEVELOPED FOR VIRGIN STRESS ESTIMATION**

The rock properties used in this development are defined by six parameters, and shown in Table 2.1. Following shear test results (Karparov, 1998), it was estimated that the shale specimens would have approximately 30% lower shear strength parallel to bedding, compared to the shear strength normal to bedding. For simulating this anisotropy, the application of the “ubiquitous joints” model in FLAC (Itasca, 1999) has been used with the properties set out in Table 2.2. In this model, which accounts for the presence of an orientation of weakness in a FLAC MohrCoulomb model, yield may occur in either the solid or along the weak plane, or both, depending on the stress state.

**ESTIMATION OF HORIZONTAL TO VERTICAL STRESS**

RATIO Skempton (1961) states that Samsioe first put the idea forward in the 1930’s that the k-ratio (k), defined as the ratio between the horizontal and vertical stresses in soil or rock, could be larger than unity. By reconstructing the geological history of London clay in Bardwell, Skempton (1961) showed that in this case, k > 2.5 and that the 10-15m thick upper layer of the subsoil is at the passive limit state of stress (cf. Terzaghi, 1961). Lambe and Whitman (1979) concede that in overconsolidation, the k – ratio can reach as high a value as 3.

** VIRGIN STRESS DISTRIBUTION IN MODEL**

**VIRGIN STRESS DISTRIBUTION IN MODEL**

To verify the reliability of the new grid for its further application, a model with homogeneous material was run first. The undulated strata formation was chosen to have maximum limb inclination angles of 50 and 150 at the intersection with the horizontal line AA at a depth of 30m (See Figure 2.3). The finite difference grid consists of 25000 1m x 1m zones, which correspond to 250m in length and 100m in height respectively, with the undulated strata formation positioned between 130m and 230m from the left model boundary. The trial run of these examples used geotechnical parameters for massive sandstone (Table 2.1), a k-ratio of 2 and an unmined ground surface. Such a long model has been chosen to accommodate the undulated strata and for modelling an advancing excavation cut approaching this formation.

**VIRGIN STRESS ON AND ABOVE SHALE-COAL CONTACT**

Failure in the mine took place on the bottom contact of the shale layer (i.e. at the top of the middle coal seam) when the strata were dipping toward the pit. This section concentrates on the virgin stress state along this contact, and along a vertical line above the crest of the undulating formation. Figure 2.9 presents part of the model showing the shale layer, indicating the future slope position and the two profile lines for the representation of virgin and post-mining stress state data. The thickness of the embedded shale layer (h) in the first run of the model was 2m and, in the second run, 8m with an overburden thickness (H) of 28m and 22m respectively.

**TABLE OF CONTENTS :**

- Page
- DEDICATION
- ACKNOWLEDGMENTS
- DECLARATION
- ABSTRACT
- LIST OF FIGURES
- LIST OF PICTURES
- LIST OF TABLES
- LIST OF NOTATIONS
- Chapter 1: INTRODUCTION
- Introduction
- Background to the problem
- 1.1.1 Geological history and its effect on
- geotechnical complexity
- 1.1.2 Slope failures in complex
- geotechnical conditions
- 1.1.3 Common features of the failures
- Thesis overview

**Chapter 2: NUMERICAL MODEL OF GEOTECHNICAL CONDITIONS AND STRESS BEFORE MINING**- Introduction
- Model developed for virgin stress estimation
- Estimation of horizontal to vertical stress ratio
- Grid development for a model with undulated strata
- Virgin stress distribution in model
- Virgin stress on and above shale-coal contact
- Conclusions

**Chapter 3: STRESS STATE AT THE SLOPE AFTER MINING**- Introduction
- Effect of high k-ratio on failure potential
- Simplified FLAC model for mined slope
- Stress state in the slope profile after mining
- Investigation of potential pillar instability as a result of opencast mining
- Conclusions

**Chapter 4: MECHANISM OF FAILURE SURFACE GROWTH IN SLOPE AFTER MINING**- Introduction
- Initial flaw for crack initiation and binocular microscope observations
- Mode of interaction
- Development of single carbon flake-based crack model for shale-coal contact
- Periodic collinear crack model for shalecoal contact
- Determination of the critical tensile zone
- length along the upper and bottom shale contact surfaces
- Discussion and conclusions

**Chapter 5: PROPOSED THRUST FAILURE MECHANISM FOR SLOPE STABILITY ANALYSES IN COMPLEX GEOTECHNICAL CONDITIONS**- Introduction
- Determining shear failure zones in the profile
- Assumptions regarding the proposed thrust failure mechanism
- Proposed thrust failure mechanism
- 5.5.1 Calculation of the forces applied from the passive block to the failure surface
- 5.5.2 Calculation of active block forces
- 5.5.3 Calculation of the pore water forces
- 5.5.4 Criterion for the existence of the inner shear surface
- 5.5.5 Calculation of the outer shear failure surface factor of safety
- 5.5.6 Calculation of the basal failure surface factor of safety
- 5.5.7 Slope stability safety factor
- Conclusion

**Chapter 6: CALCULATED EXAMPLES AND DISCUSSION**- Summary
- Example 1: Pit A-2 slope failure
- 6.2.1 Example 1a: Safety factor calculations along the upper contact surface
- 6.2.2 Example 1b: Safety factor calculations along the bottom contact surface
- Example 2: Pit A-1 slope failure
- Discussion
- Practical implication of thrust failure mechanism for active mining slopes

**Chapter 7: CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK**- Conclusions
- Future work
- APPENDIX 1. FLAC MODELS AND DERIVATIONS
- APPENDIX 2. FIGURES
- APPENDIX 3. GRAPHS
- APPENDIX 4. SLOPE STABILITY CALCULATIONS
- APPENDIX 5. SAFETY FACTORS FOR OPENCAST MINING
- REFERENCES

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SLOPE STABILITY ANALYSES IN COMPLEX GEOTECHNICAL CONDITIONS –THRUST FAILURE MECHANISM