Stability Assessment and Optimization Design of Lakeside Open-Pit Slope considering Fluid-Solid Coupling Effect

Chengmenshan copper mine, located at Jiujiang city in the Jiangxi Province, is a rarely lakeside open-pit mine in China. Since the open-pit is very close to Sai Lake, the seasonally changed water level and the distance between lake and slope have great influence to the stability of open-pit slope. Based on the drill data and geological sections, a numerical model of the slope is built. With the fluid-mechanical interaction associated, the stability of the slopes is numerically analyzed, in which different lake water levels and lake-slope distances are taken into consideration. The comparative analysis shows that a larger lake-slope distance can promise better slope stability and weaken the sensitivity of slope stability to water. The stability of slopes with different heights is analyzed to find that the stability weakens and the sensitivity is enhanced with the height increasing. To the most serious situation, the slope height and the lake water level being 238m and 17.2m, respectively, the F s value equals 1.18945 which is extremely closed to the allowable safety factor of 1.20 for slope design. According to the minimum F s for slope design, the minimum distance between lake and open-pit slope is found to be 60m.


Introduction
According to a large number of engineering practices, landslides of natural and artificial slopes often happen after the heavy rain or continuous rainfall.The failure of reservoir bank slopes occurs in sharp decline of water level, long-term immersion, and hydrological cycle.It shows that the seepage of ground water in the slope makes great difference to the stability of slope.
Theoretical study and practical experience show that open-pit slopes usually experience four stages from excavation completion to collapse: the elastic stage, the nonlinear deformation stage, creep deformation stage, and the collapse stage.According to the Mohr-Coulomb criteria, the shear strength of rock decreases greatly when encountering with water.To rock slopes, this means a great reduction of stability.With the development of the numerical calculation, many modules in kinds of numerical software have been developed to realize the hydromechanical coupling in fractured rock mass [1][2][3][4].The Itasca software FLAC 3D based on fast Lagrangian method can be used to simulate the flow of fluid through a permeable solid [5], and the pore pressure of the fluid will change in response to the change of mechanical volume.
A lot of studies have been done to learn the coupling mechanism of water pressure and rock mass stress [6][7][8][9][10][11][12].Rutqvist and Stephansson [13] and Wang [14] recognized two types of hydromechanical coupling: direct and indirect.Direct coupling occurs through deformation and pore fluid interactions.Indirect coupling is where changes in the mechanical or hydraulic processes affect each other through changes in mechanical and hydraulic properties.The deformation of pit slope, which is largely inelastic with creep and slip on structures, causes irreversible changes in the rock mass and hydraulic properties of the mass and is largely indirect coupling.
The stability of mine slopes depends on the designs.Implicitness or explicitness in this design process is an acceptance of some instability or a certain percentage of failure [15,16].Usually the deformations after excavation and critical factors that may cause landslides are taken into consideration in the mine slope design process.A lot of preanalyses are made to make sure that the mine slope attains a certain safety coefficient.In some sense, the slope we designed is an acceptance of some instability or a certain percentage of failure [17].In fact, the groundwater seepage has serious influence on the stability of mine slope.The deformation of slope rock mass will result in the change of cracks and porosity and then the change of seepage effect.Sartori et al. [18] described that the Randa landslide was a devastating rock landslide along with high pressure infiltration water injection.Cappa et al. [19] found that the infiltration of seasonal rainfall accelerated the process of Clapière landslide.
Many methods have been carried out to study the influence of seepage on slope stability.Saada et al. [20] adopted the limit analysis method to evaluate the slope stability under seepage.Lv et al. [21] established the mathematical model of rock mass damage under the influence of seepage.The mathematical model was used to analyze the stability of coal mining open-pit slope, and the result indicated that the reduction of effective stress caused the failure of the slope.Chu-Agor et al. [22] performed a series of experiments of the slope instability under the action of water pressure, and the results were applied to the mountain slope stability analysis.Srivastava et al. [23] adopted FLAC5.0 to analyze the influence of groundwater seepage on the stability of slopes with different slope conditions and material properties.
Numerical modeling is an efficient method in the analysis of slope stability under the action of seepage.The Itasca software FLAC 3D has been widely used in the analysis of underground tunnels, open-pit mining, and underground mining complicating gravity, groundwater, and other factors.But there are some difficulties in the construction of a complex numerical model by employing FLAC 3D alone.Some researchers constructed the model by the way of integrating SURPAC and FLAC 3D [24][25][26][27][28].In this study, DIMINE, a 3D geological model construction software, is adopted to construct the geologic model of a lakeside open-pit copper mine.Then the model is imported into FLAC 3D with the assistance of Midas-GTS.The open-pit slope stability is finally assessed numerically by FLAC 3D associated with the lake water.Comparing the safety factors of slope under different heights of water level, a reasonable distance between lake and open-pit slope is determined.

Engineering Background
Chengmenshan copper mine is an open-pit mining located at suburb of Jiujiang city, Jiangxi Province, China.It is in the middle-lower reaches of the Yangtze river region.The terrain slopes gently.Ruichang River flows from the west of the openpit (Figure 1), across the Sai Lake in the north and east of the open-pit, and then ends at Yangtze river.The open-pit is just beside the Sai Lake (Figure 2).
In the preanalysis area of the open-pit, stratum in the mining area belongs to upper Pleistocene series mostly.The metal ore exits in the magmatic rock in the middle area of the mining area.The bed rocks of Sai Lake are the Triassic and Permian limestone of Carboniferous.The limestone is the main aquifer of the mining area.Due to the long-term immersing of the ground water, there exist lots of karst caves, Sai Lake

Ruichang River
Analysis area Open-pit But as time goes on, the mining area will extend with the mining depth increasing and the open-pit will get closer to Sai Lake.The water surface acreage of Sai Lake is about 970 km 2 .Ruichang River is the main water resource of Sai Lake.When the rainy season comes, the water level of Ruichang River will rise and result in the rise of water level of Sai Lake.Furthermore, the water of Yangzi River that is not far from Sai Lake will influence the water level of Sai Lake.On the contrary, the water level will fall after rise in dry season.Historical hydrological survey data show that the highest water level of Sai Lake is +25.2 m and the lowest is +10.4 m.
Chengmenshan copper mine is currently in the continuous stage of the second phase and third phase.Ore body of copper in Chengmenshan distributes from the shallow strata to the deep, and there are lots of copper exits below −300 m.In order to protect the environment surrounding the lake and ensure safety production, in the end of third phase the open-pit mining will be changed into underground mining.The main mission at present is to make a decision about the ultimate size, the depth of open-pit, and the distance between lake and the open-pit to make sure of a safe and reasonable environment for underground mining in the future.The preanalysis of the open-pit slope stability under the influence of a changeable level of lake water becomes a difficult but most important task.The lithology of every strata from ground surface to the bottom is: Quaternary upper Pleistocene Series ( 3 ), Triassic Daye limestone (T1d), Permian Changxing limestone (P2c), Permian Longtan limestone (P2l), Permian Maokou limestone (P1m), Permian Qixia limestone (P1q), Permian Liangshan limestone (P1l), and Yanshanian granodioriteporphyry ().

Numerical Model and Boundary Conditions
In the section the slope steps are not taken into account (Figure 4(c)).The whole slope is divided into two stages by the weathering line: the weathered stage above the weathering line and the unweathered stage below that.Learning from the section, the elevation of the slope top is +38 m and the bottom is −238 m, so the height of the whole slope is 276 m.The elevation of weathering line in this area is about −100 m.According to the slope design, the overall dip angles of the weathered stage, the unweathered stage, and the whole open-pit slope are 41 ∘ , 48 ∘ , and 44 ∘ , respectively.The lake is at the top-right corner of the model.The elevation of lakebed is +8 m.
Considering that the 3D seepage calculation based on complicated geological model is very difficult, the plane strain mode in FLAC 3D numerical model is used in this study, and this methodology has previously been applied by many researchers [29][30][31][32][33].The geological section model cannot be imported to FLAC 3D directly, so with the help of Midas-GTS, the model is got meshed.Then the grid points and elements data are exported into FLAC 3D from Midas-GTS and the plane strain numerical model is established (Figure 5).The infiltration faces of the lake water are the lake bottom and the lake bank, and the outflow faces are the slope surface and the slope bottom face (Figure 4).The pore water pressure of the outflow faces is fixed 0 MPa.The right boundary, the bottom boundary, and the left boundary are impermeable boundaries set by default in FLAC 3D .The lake water is considered as a seepage force and a gravity load to the lake bottom and bank.The influence of the lake water seepage under different heights of water level is considered.

Boundary Conditions and Calculation
The mechanical parameters of the lithologies are listed in Table 1.All the mechanical parameters are acquired from laboratory tests, and the permeability is tested by pumping experiment in situ.Other parameters such as bulk and shear modulus that will be used in numerical modeling can be

Numerical Modeling and Analysis
4.1.Failure Criteria and Calculation Method.The strength reduction method (SRM) is adopted for the slope stability analysis associated with fluid flow.The SRM is based on the Mohr-Coulomb failure criterion.In the SRM, the definition of factor of safety is the ratio between the actual shear strength and the reduced shear strength at failure (1).Let the original strength parameters  0 and  0 be divided by a strength reduction factor , increasing or decreasing the value of  until the critical failure state of slope.If strength parameters under critical failure state are  cr and  cr , then  cr = 1, and the corresponding factor of safety is   as follows: The fluid-mechanical interaction function of FLAC 3D [29] is adopted in the slope stability analysis, which can calculate the safety factor of the slope associating with fluid flow.In this function, rock mass is treated as a permeable solid and the flow modeling is independent of mechanical calculation.The fluid-mechanical interaction in FLAC 3D behaves in two mechanical effects.First, changes in pore pressure cause changes in effective stress and affect the response of the solid.Second, the fluid in a zone reacts to mechanical volume changes by a change in pore pressure.Fluid flow in the porous media is based on Darcy's law, processing Biot equation to describe fluid-solid interaction.Changes in the variation of fluid content are related to changes in pore pressure, , saturation, , mechanical volumetric strains, , and temperature, . the response equation for the pore fluid is formulated as follows: where  is Biot modulus,  is the porosity,  is Biot coefficient, and  is the undrained thermal coefficient.The fluid mass balance can be expressed as follows: where  V is the volumetric fluid source intensity,  is the variation of fluid content, and − , is the fluid seepage

Role of Lake Water Level on Slope Stability.
The contour of shear strain increment after   solution in FLAC 3D of the slope in the condition of  = 20 m, ℎ  = 2 m is shown in Figure 7.The slip surface of the slope is marked out in dotted lines.Because the slope is divided into two stages, the weathered stage and the unweathered stage, the failure surface behaves in two stages as well.The two failure surface stages connect with each other at the weathering line.The slip surface can be shown by the contour of shear strain increment [29].Through connecting the mutation point of the shear strain increment, the slip surface is shown approximately, Figure 7.In follows of the passage, the slip failure surface of slope is shown in the form of dotted line as Figure 7.
Contour of shear strain increment Magfac = 0.000e + 000 Gradient calculation −9.7568e − 004 to 0.0000e + 000 0.0000e + 000 to 2.5000e − 003 It can be learned from the comparison of different slope failure modes that variable heights of lake water level have different influence on the slope failure modes.But as the same result the higher the lake water level, the larger the failure region that also means a greater destructive catastrophe.Once the slope slipped, immeasurable water would flow into the open-pit and it would be a disaster to the mine.Above all, a safe distance between lake and open-pit has significant meaning to Chengmenshan copper mine.

Determination of Minimum
Lake-Slope Distance.The safety factor (  ) of slopes under different distances is numerically calculated by SRM in FLAC 3D ; the results are listed in Table 2.The   values of slopes without the influence of lake water exceed 1.41 which is far larger than   of slopes under the seepage of lake water.Dry slope of  = 80 has the best The   variation trend of slopes under the influence of different heights of lake water is shown in Figure 9.The   values of slopes under the seepage of lake water are all lower than 1.30.The maximum   value of 1.29492 belongs to the slope of ℎ  = 0 m,  = 80 m, and the minimum   value corresponds to the slope of ℎ  = 17.2 m,  = 20 m.Under the condition of the same lake-slope distance, the   value decreases with the lake water level rising.To every lake-slope distance,   value reaches the minimum when the water level rises to 17.2 m.
By comparing the   values of slopes under the same lake water level but different lake-slope distances, it can be noted that the larger the lake-slope distances, the better the slope stability.This indicates that the lake-slope distance has some influence in the weakening effect of the lake water on openpit slopes.
The variation range of   values of different lake-slope distances increases with the decreasing of lake-slope distance.In order to analyze the sensitivity of slope stability to the lake water level, the parameter Δ is defined as the weakening degree of the slope   under the seepage of lake water, expressed as (4).  represents   of dry slope and   represents   of slope containing lake water.A larger Δ means the slope stability is more susceptible to the height of lake water level.The Δ values of slopes under every condition are shown in Figure 10.To the slope of  = 20 m, the minimum and maximum Δ values are 11.6% and 23.3%, respectively.To the slope of  = 80 m, the minimum and maximum Δ values are 9.8% and 13.4%, respectively.The varying trend is evident that Δ gets smaller as the lake-lope distance gets larger.The weakening degree of   gets lower when the slope locates further from the Sai Lake.This indicates that with the slope getting closer to Sai Lake, the slope is more sensitive to the lake water.Thus, a reasonable lake-slope distance is needed to make sure a safe environment of underground mining and keep the slope insensitive to the lake water: In the design plan of Chengmenshan open-pit slope,   = 1.20 is adopted as the allowable safety factor for slope design.According to Figure 9, as for the slope of  = 60 m,   of the most dangerous condition is 1.18945 which is close to 1.20, and when the water level gets lower than 17.2 m, the safety factor increases to larger than 1.20.With respect to the slope of  = 80 m, the   of slope under every height of water level is much larger than 1.20.The larger   value means a greater diminution of the open-pit area.Furthermore, the condition of  = 20 m and  = 40 m cannot ensure every   value larger than 1.20.In conclusion,  = 60 is determined as the minimum lake-slope distance.

Conclusions
Based on the drill data and geological sections of exploration line, a 3-dimensional geological model of the lakeside openpit slope is established by DIMINE.Through a flow of DIMINE → MIDAS → FLAC 3D , the numerical model of the slope is built.The seasonally changed water level of Sai Lake and the distance between lake and open-pit slope have been considered in the numerical analysis.The numerical analysis results show that the lake water near the open-pit has great influence on the slope stability.With the water level rising, the   value of the slope decreases, and when the water level rises to the historically recorded highest of 17.2 m, the slope will get to the most dangerous situation.The stabilities of slopes under different lake-slope distance ( = 20 m, 40 m, 60 m, and 80 m) are compared.The distance plays some role in the weakening effect of the lake water on open-pit slope; that is, the larger the distance, the better the slope stability.The weakening degree coefficient Δ is defined to evaluate the sensitivity of slope   to water under different lake-slope distance.The larger the distance is, the weaker the effect of lake water seepage on the slope stability performs.The stabilities of slopes of different heights are analyzed, and it is discovered that, with the height increasing, the slope stability reduces greatly, and the saturation effect on slope stability is enhanced.To the highest slope of  = 238 m under a lake water level of 17.2 m, the   value is 1.18945, which is extremely closed to 1.20.According to the allowable safety factor for slope design, the minimum distance between lake and open-pit slope is found to be 60 m.
Parameters.In the numerical modeling, the displacement boundary conditions of the model include (a) fixed displacements in -, -, and -direction at the bottom boundary of the model; (b) fixed displacements in -direction at the left and right boundaries; (c) fixed displacement in -direction of the total model; (d) free boundary at the slope top, slope surface, slope bottom face, and the faces in lake area.
Connect the boundary lines of every lithology through boolean operation and construct the 3D geologic model of mining area in DIMINE Extract the slope model from DIMINE Acquire the safety factor of the slope Import the lines into MIDAS-GTS, meshing, and generate the numerical model of slope them, assign the mechanical parameters to the groups, and define the boundary Read the extracted file and acquire the boundary line of every lithology and the weather line Import the geologic section maps which are constructed based on bore histogram into DIMINE and distinguish lithologies from the maps Import the numerical model into FLAC 3D , set every lithology a group and name

Figure 3 :
Figure 3: Flow of model development and calculation.

Figure 5 :Figure 6 :
Figure 5: Numerical model of the slope in FLAC 3D .

Figure 7 :
Figure 7: The contour of shear strain increment in the failure slope.

Table 1 :
Mechanical parameters of the rock formations contained in numerical model.
velocity.In FLAC 3D numerical approach, the flow domain is discretized into brick-shaped zones defined by eight nodes.Both pore pressure and saturation are assumed to be nodal variables.The contour of original pore pressure of the slope is shown in Figure6.4.2.Modeling Conditions.According to historical hydrology data, the lowest water level of Sai Lake corresponds to a depth of 2.4 m, and the highest level corresponds to a depth of 17.2 m.In order to estimate the influence of different depth of water to slope stability, five kinds of water levels of Sai Lake

Table 2 :
Safety factor of slope under different  and ℎ  .