Victoria, Australia, is known as its huge brown coal reserves in the world. Brown coal has been mined by open cut mining method in Victoria, Australia, almost over a century. Due to the long-term mining activity, coal batter instability has become one of the major geo-hazards in Victoria, and batter failures have not been rare in this area. Both geological structures and hydrogeology affect the pit stability in Victorian brown coal mines. The strength of weak seams beneath coal, the orientation of joints and bedding planes, high-level underground water and water pressure in joints were believed as the main reasons to cause slope failure in Victorian brown coal open pits . Brown coal batter with overburden tends to lead a circular sliding while the coal batter after overburden removal has a blocking slide trend at Maddingley brown coal mine, Victoria . High tensile strain behind the batter and high shear strain underneath the coal seam could be developed after the overburden is stripped in the brown coal batter, and cracking propagation is a result of stress relief due to the overburden removal . The unique batter failure type, block failure, often occurred not long after cracks (opened joints) emerging on coal batter surface and heavy rainfall event in Victorian brown coal open pits, as reported in Yallourn mine in 1950  and 2007 . It is noted that batter failures are prone to occur in summer or close to summertime in Victoria. There is a significant amount of rainfall throughout the year in Victoria; an average annual rainfall amount is between 1800 and 2500 mm, with heavy downpours in summer months. The recorded highest rainfall in a single day was 375 mm in the Otway Ranges in 1983 (rainfall by region: Victoria, n.d.). Water plays a critical role in the initiation of brown coal batter instability due to the relatively low unit weight of Victorian brown coal. Rainfall can accelerate the cracking propagation process in the brown coal batter .
To monitor the ground movement, eight survey markers were installed along the major cracks in November 2013. The locations of these survey markers (from Marker 1 to Marker 8) are demonstrated in Fig. 3. The monitored data were collected weekly. Monitored data are shown in Fig. 4.
To study the stability of the brown coal batter with opened cracks under rainfall conditions, a three-dimensional geological model of MBC north batter was developed based on the MBC north batter on 13 February 2014 when the emergency buttress had been in place and crack deformations had been monitored. One day later, a 26-mm rainfall event occurred. The model was 400 m in length from west to east and 250 m in width from north to south. The grid division diagram of the model after fine meshing is shown in Fig. 5. The model covered the whole north batter, part of east and west batter of MBC open pit.
From top to the bottom, the model consisted of 5 layers that were Fyansford formation (overburden, RL 87 m to RL 100 m), brown coal layer (RL 50 m to RL 87 m), emergency buttress (RL 60 m to RL 72 m) and engineering fill layer (RL 55 m to RL 60 m), broken brown coal layer (RL 50 m to RL 55 m) and Werribee formation (RL 0 m to RL 50 m). Groundwater flew towards pit bottom. Based on the measured borehole logs in the field, the top groundwater level was set at RL 92 m in the Fyansford formation at the initial state, which flew down to the pit bottom (RL 60 m). The opened cracks in the model included the major crack and the subsequent minor cracks, which are shown in Fig. 6. The major crack was approximately 20 m back from the coal face, and the two minor cracks were on the south of the major one.
The numerical modelling was designed to simulate the initial state of the coal batter (after buttress in position and before the recorded 26-mm rainfall event), the state after the 26-mm rainfall, the states with 26 mm/day rainfall intensity lasting for 3 days, 6 days, 9 days and 78 mm/day rainfall intensity lasting for 1 day, 2 days, 3 days, respectively. The simulated deformations after the 26-mm rainfall were compared with the monitored batter movements. With the purpose of studying the effect of precipitation, rainfall intensity and lasting time on the cracked batter stability, three total precipitation conditions (78 mm, 156 mm, 234 mm) were set and each precipitation was reached by 26 mm/day and 78 mm/day rainfall intensity for different lasting times, respectively. To be specific, the calculation conditions of 26 mm/day for 3 days and 78 mm/day for 1 day were designed to reach 78-mm precipitation; 26 mm/day for 6 days and 78 mm/day for 2 days were for 156-mm precipitation; in terms of the 234-mm precipitation, the simulation conditions were 26 mm/day for 9 days and 78 mm/day for 3 days. There were three calculation types involved in the model simulation. Gravity loading was to simulate the initial phase of the model. The fully coupled flow-deformation calculation type was employed to calculate the rainfall process on the model. All precipitation was assumed being evenly distributed in the set lasting term. Each calculation phase was followed by a safety analysis phase that was to compute the global safety factors of the model. As a result, there were total 16 calculation phases (Fig. 7) included in the integrated simulation design of the model, namely 1 gravity calculation phase (initial state), 7 fully coupled flow-deformation calculation phases (rainfall process) and 8 safety analysis phases.
Victorian brown coal is a material with high organic content and low permeability [24, 25], whose strength is between normal engineering soil and rock, and its stiffness is similar to very stiff clay. It is also a highly deformable and low-density material. The unit weight of saturated MBC brown coal is about 11.5 kN/m3 while the dry unit weight is about 5 kN/m3. The low density means the batter stability is very susceptible to the water pressure from groundwater or rainfall run-off, and the deformable character tends to cause the formation of cracks and open of existing joints in Victorian brown coal . Table 2 lists the adopted geotechnical parameters in the model. These parameters are from direct shear tests, triaxial tests, permeability tests and technical reports provided by MBC.
In summary, the failure mechanism of rainfall-induced block sliding of brown coal batter with cracks is graphically summarized in Fig. 13. When a large rainfall event occurs, the hydrostatic forces in the exposed crack and in the aquifer underneath the coal seam will both increase, the former increases the driving force, and the latter decreases the resisting force. The compounded results of hydrostatic forces from the crack in the rear of the batter and from the clay layer underlain the batter is pushing the block to slide towards the pit bottom, or batter failure, e.g. the factor of safety is dramatically declined to less than 1.0.
A three-dimensional model was developed using Plaxis 3D to study the effects of rainfall on the brown coal batter stability with open cracks in Maddingley brown coal open pit, Victoria. The following conclusions can be made.
From the safety analysis, the safety factor of the batter was 1.340 at the initial state (with cracks and buttress). After the 26-mm precipitation in 24 h, the safety factor dropped to 1.316. This rainfall event did not cause the batter instable; even some deformations were observed by the surveying markers installed around cracks. Some rebound of the deformations was attributed to the recession of hydrostatic pressure in the cracks. With the further increase in precipitation and rainfall lasting time in the numerical study, the safety factor continuously dropped under the conditions of both 26 mm/day and 78 mm/day rainfall intensity. The coal batter would fail with the 26 mm/day rainfall intensity lasting for 9 days. It revealed that both the short-term high rainfall intensity precipitation and long enduring low rainfall intensity precipitation could lead the brown coal batter with opened cracks to an instability state.
From this study, the hydrostatic forces in the exposed crack and in the aquifer underneath the coal seam could both increase under the condition of rainfall, the former increased the driving force, and the latter decreased the resisting force. The compounded results of hydrostatic forces from the crack in the rear of the batter and from the clay layer underlain the batter were pushing the block to slide towards the pit bottom, or batter failure, e.g. the factor of safety was dramatically declined to less than 1.0.
The present article examines the problem related to the axisymmetric torsion of an elastic layer by a circular rigid disc at the symmetry plane. The layer is sandwiched between two similar elastic half-spaces with two penny-shaped cracks symmetrically located at the interfaces between the two bonded dissimilar media. The mixed boundary-value problem is transformed, by means of the Hankel integral transformation, to dual integral equations, that are reduced, to a Fredholm integral equation of the second kind. The numerical methods are used to convert the resulting system to a system of infinite algebraic equations. Some physical quantities such as the stress intensity factor and the moment are calculated and presented numerically according to some relevant parameters. The numerical results show that the discontinuities around the crack and the inclusion cause a large increase in the stresses that decay with distance from the disc-loaded. Furthermore, the dependence of the stress intensity factor on the disc size, the distance between the crack and the disc, and the shear parameter is also observerd. 2b1af7f3a8