GUO Jin-xing, GRAEBER Peter-Wolfgang

1 Center of Hydrogeology and Environmental Geology, China Geological Survey, Baoding 071051, China.2 Institute of Groundwater Management, Technical University of Dresden, Dresden 01062, Germany.

Abstract: There are concerns about the safety issues of dump slope in the open-cast mining pit because of the risk of catastrophic destruction caused by slope failures that are related to several factors, such as atmospheric conditions (especially precipitation), vegetation and some others. The aim of this study is to investigate the hydrological regime in a dump slope and the influence of the saturation degree on the stability of dump slopes with consideration of precipitation and vegetation using the program of PCSiWaPro®. Based on the hydrological simulation conducted through PCSiWaPro®, the calculation of the Factor of Safety (Fs) in the dump slope using Geo-slope Software was improved with further consideration of soil-water weight in the unsaturated dump slope and the influence of water content on the variation of soil property parameters (e.g. cohesion).

Keywords: Open mining pit; Water saturation; Hydrological simulation; Landslides; Stability analysis; Factor of safety

Introduction

Mining activities are necessary for minerals production and thus for modern society development. Serious environmental and ecological problems, however, are caused by these activities and among which dump slope failure in open mining pits raised big concerns. Some frequently happened has, for example, heavy rainfall events and variation of ground water levels,have significant influence on the dump slope instability. The heavy or prolonged rainfall has been found as the main trigger of slope instability,which can be explained by the fact that the rainfall raised the pore water pressure within the soil. A long period of rainfall can saturate, soften, and erode soils. Water enters into existing cracks and may weaken underlying soil layers, leading to failures, for example, mud slides. In addition, in some cases when the rainfall event is heavy and prolonged enough, the increasing groundwater flow can provide additional contribution on the slope as a result of a hydraulic push to the soil block, which further decreases the slop stability(Caine N, 1980; Corominas J and Moya J, 1999;Oikos-team, 2007).

Surface erosion (surface runoff) and water saturation increase in dump slopes are two main direct causes of slope instability (Bonelli G, 2013).There was an early assumption that the landslides phenomenon arose only in fully saturated soil areas;Aigner D (2004) concluded from a physical experiment (Fig. 1), however, that the slope failure also happened in partially saturated soil areas.While surface erosion is relatively easy to be detected and avoided, increased risk of higher soil water content cannot be easily identified inside the unsaturated slopes. Therefore, the dump slope is more dangerous due to increase of soil water saturation in unsaturated zones (Bonelli G, 2013).

In unsaturated slope areas, various factors have influence on water balance and then the slope stability: Soil materials, geometry, atmospheric conditions (e.g. precipitation), and even vegetation(WU T H, 2013) (Fig. 2). Precipitation has direct influence on the change of water content by means of infiltrating water into the unsaturated slope and thus changing the groundwater movement regime(especially in an extreme rainfall event). The significant influence of vegetation on slope stability is essentially contributed to two major aspects: water movement via the soil-plantatmosphere continuum (SPAC) (Coppin N J et al.1990) and soil reinforcement by the root system(Gray D H, 1995). As a major component of SPAC,vegetation is responsible for the suction force of water against gravity, then water absorbed from soil is removed through the transpiration process.Ultimately, this water cycle system leaves a less saturated and more stable slope. Vegetation also contributes to mass stability by increasing the shear strength of soil through root reinforcement(Gray D H, 1995). The frequency of slope failures tends to increase when vegetation has been cut down and vegetation roots decay (Abe K, 1997).

Fig. 1 A physical model slope with slides on the air side (Aigner D, 2004)

1 General description of the study area

Our study site locates between Leipzig and Bitterfeld with the City of Delitzsch in the center which has been shaped by lignite mining activities for more than one century.

A dump slope has been selected from this mining area and the simplified structure of this dump slope was shown in Fig. 2 and circled by a red line. The study structure is totally 300 m wide and 94 m high with horizontally layered dump soils (e.g. 20 m depth of clay layer in the middle)and sandy slope. Fig. 3 shows the detailed distribution of different soil layers in this dump slope. Additional basic data, like soil hydraulic conductivities and porosities, have been obtained from the local agency and the consulting company IBGW Leipzig; a constant groundwater level was measured with a value of 88 m (above the sea level).

2 The hydrological program PCSiWaPro®

The hydrological process in the dump slope can be simulated by the Program PCSiWaPro®(developed at the Technical University Dresden,Institute of Waste Management and Contaminated Site Treatment) which calculates water saturation distribution under both steady and transient boundary conditions (Graeber P W et al. 2006).With PCSiWaPro®a 2D model of the dump slope was built, incorporating information of slope structure geometry, soil properties, climate parameters, geohydraulic and time-dependent boundary conditions.

Fig. 2 A simplified structure of the dump site

Fig. 3 Distribution of soil layers with different hydraulic conductivities in the dump slope

2.1 Mathematical background

PCSiWaPro®is based on solving the Richards equation (equation 1) in two spatial plus time dimensions using the finite element combined with the Galerkin-method (Hasan et al. 2012).

Where θ is volumetric water content; h is pressure head; xiis spatial coordinates (x1= x and x2= z for vertically-plane simulation); t is time;and KijAare components of the dimensionless tensor of anisotropy K. S means a source/sink term,which expresses the volume of water that is removed from the soil by plant root systems. The effects described by this strongly nonlinear partial differential equation are due to hysteresis,especially the relationship between water content and pressure head (Hasan I et al. 2012). This relationship has been described by the Van-Genuchten-Luckner as equation (2).

Where Ф is the porosity of the soil; θr,wis residual water content; θr,lis residual air content;hccharacterizes the pressure head difference between the wetting (water) and non-wetting phase(air); α (scale factor) and n (slope) are empirical Van-Genuchten parameters (Kemmesies, 1995).

2.2 Advantage of the Program PCSiWaPro®

Although there have been several programs available for the hydrological process simulation,for example, Hydrus, Feflow, program PCSiWaPro®has two distinctive advantages compared with them.

On the one hand, PCSiWaPro®is paired with a weather generator whose data basis is the German Weather Service (DWD). Based on the statistical Markov chain analysis, this generator calculates transient infiltration fronts with respect to different atmospheric conditions and removal of water by plant roots (Graeber O, 2014); the potential evapotranspiration on the site is easily calculated by the method of Turc-wendling with input of different site parameters like top surface soil types,site inclination and orientation, land-use forms,and vegetation covers; furthermore, it is applicable for all unknown locations on the basis of the spatial interpolation method and the inverse distance method with the recorded data collected from surrounding climate stations (Fig. 4). This advantage allows for a much better resolution of the hydrological process simulation that can be achieved in the dump slope either during a dry season or under a rainfall event. However, when applying this program to such countries as Poland,China and Japan, the DWD data in this weather generator is no longer suitable for other local hydrological simulation works; the local weather data of other countries, therefore, need to be input into PCSiWaPro®in order to get better resolution(Guo J et al. 2015; Graeber P W, 2014).

Fig. 4 Application of the weather generator for an example in Germany

In addition, PCSiWaPro®provides a strong calibration system between the observation values and calculated results; based on the observation data from all defined points in the study field, this program conducts detailed calculation for different kinds of values (e.g. pressure head, water content,water saturation, solute concentration) according to simulation schedule (Guo J et al. 2015).

With PCSiWaPro®, a 2D model of a Chinese earth dam can be built based on the information of geometry, soil properties, climate parameters,geohydraulic and time-dependent boundary conditions.

3 Stability analysis model

Slope stability problems of dump slopes are some of the most commonly encountered problems in geotechnical engineering. Numerous scientists conducted a large amount of researches in this field and several numerical methods were developed for the slope stability analysis. Limit equilibrium models, for example, Bishop’s Model and Ordinary Method of Slices (Hammond C et al.1992; Biondi G et al. 2000) are typical methods that are used to forecast the circle slip landslide in a deeper layer of a dump slope (Gover S and Hammah R, 2013). The objective of this analysis is to estimate the probability of a dump slope failure using the conventional factor of safety (Fs) which is defined as the ratio of shear strength to shear stress under both saturated and unsaturated conditions (Griffiths D V et al. 2011; Duncan J M and Wright S G, 2005; Hammond C et al. 1992);Equation 3 and 4 below show one type of the limit equilibrium models, the Bishop’s Model.

Although the Bishop’s Model has been proved to be highly applicable for deep slip landslide forecasting, it is too complicate for hand calculation; to solve this problem, various computerbased geotechnical software have been developed for slope stability analysis based on the Bishop’s Model. Among those softwares, the Geo-slope Software is one of the most efficient software and has been applied worldwide in landslide forecasting (Krahn J, 2004); the position and the Fs(factor of safety) value of critical slip surface (the surface with the highest possibility of landslide) in a dump slope can be easily and quickly calculated(Krahn J, 2004); nevertheless, it does have two limitations in the geo-engineering practice:

(1) The soil parameters (e.g. cohesion) have always been considered as constant in stability analysis. When an earth body has been passed through by a seepage line or when water saturation in an earth slope has been changed greatly by water infiltration during a heavy rainfall event, in anticipation, the pre-input of unsaturated soil property values may lead to inaccuracy of stability analysis in the Geo-slope. For example, in Fig. 5 the value of unsaturated soil parameters that is available for the stability analysis for the 1stto 6thslope slices are above the seepage line, with other slices under the seepage line, the unsaturated soil parameters’ values can result in the overestimation of the Fs value of the critical slip surface.

Fig. 5 An earth slope body being passed through by a seepage line from the Geo-slope Software

(2) In addition, the weight of the infiltrated rainfall water in the unsaturated slope has been neglected and only dry earth slope has been considered in this software, which can also lead to inaccurate stability analysis.

In these cases, the Fs value of the critical slip surface from the Geo-slope can be improved with additional consideration of soil-water weight in the unsaturated slope and the variation of soil parameters (e.g. cohesion) caused by water content change.

4 Results and discussion

4.1 Hydrological simulation results

The van Genuchten parameter values (α and n)of different soils in the dump slope have been estimated in the program PCSiWaPro®. Detailed values of soil parameters applied in the hydrological simulation are shown in Table 1.

Table 1 Soil parameters for the hydrological simulation in the Program PCSiWaPro®

After setup of the model in the program PCSiWaPro®, a simulation period of five years from January 2000 to December 2004 was selected.On the dump slope, atmospheric boundary condition was defined, which meant this slope received input of rainfall water; after the formation of this dump slope, a constant groundwater level of 88 m was detected during this simulation period,which helped to determine the boundary condition of constant potential head on the left side of this model.

In order to better investigate the contribution of precipitation to the increase of water saturation in the slope and groundwater table, a simulation without the input of rainfall water is shown beforehand on Fig. 6 which displays the saturation condition in this slope for the day of August 28th,2003. In the zoomed-in figure, the rigid decrease of groundwater surface can be explained by the fact that slope sand has smaller permeability than the soil material on the left side of the slope.Accordingly, on Fig. 7, different shades of blue below the groundwater surface indicate different saturated water content of different dump materials;due to its highest porosity, the clay material with the darkest blue colour has the highest saturated water content (0.52); the sand slope has the lowest water content (0.4). In addition, in PCSiWaPro®the implemented mesh generator for calculation depends on the finite element method; in this simulation the structure of the model has been discretized with medium finer (0.5 m) meshes,through which the model better represents the water content distribution. However, the serrated lines between the layers of different water content and water saturation can be even more smoothed with finer model structure meshes (e.g. 0.1 m).

Fig. 6 Water saturation simulation without input of precipitation on August 28th, 2003

Fig. 7 Water content simulation results without input of precipitation on August 28th, 2003

Fig. 8 exhibits the precipitation data conducted from the weather generator in PCSiWaPro®for a typical year in the region of Leipzig. As what can be seen in this graph, the rainfall events mainly occurred between June and September, especially in mid-June, early July and early September. In addition, although the rainfall season came every year from mid-June, the groundwater level experienced no change between the year of 2000 and 2004, which happened mainly because of human operation of pumping discharge from the groundwater during the mining activities in order to prevent the possible overload in groundwater storage especially in rainfall seasons and to prevent the possible geological and environmental disasters.

Fig. 8 Typical precipitation data for one year in the study area from the weather generator in PCSiWaPro®

With the help of weather generator, the effect of rain water was added into the simulation process for the sandy slope which had the atmospheric boundary condition. The result of water saturation distribution thatis illustrated in Fig. 9 represents the simulation for August 28th, 2003 with a heavy rainfall event. Rainfall water provided an additional flow into some part of the top and the right sand slope embankment, thereby increasing the water content in this unsaturated slope. The highest water saturation was found to be 70%; in addition, the rainfall water reaching the groundwater table in the slope complemented the groundwater recharge. Furthermore, the interspaces between two light green layers were mainly resulted from the discontinuous rainfall events before August 28th, 2003. From this simulation, the dynamic influence of rainfall water on the variation of water saturation in the unsaturated slope is exhibited clearly and therefore can be easily understood.

Fig. 9 Simulation of water saturation distribution with input of precipitation on August 28th, 2003

Due to the constant groundwater table (88 m above the sea level) after the year 2000, a stable value of 84.74 m was measured for water level from an observation well in this dump slope. A comparison between the measured and simulated water level is shown on Fig. 10. The equivalence of the measured and the computed values using the program PCSiWaPro®was good for our study area.Although a small deviation (0.3 m) found in the comparison can be explained by the fact that our simulation was mainly based on the average values of those different dump soil parameters (e.g.average porosity, hydraulic conductivity); the accuracy of the simulation, however, can be improved with more field and laboratory investigation for soil parameters from different dump slope soils.

Fig. 10 Comparison between the simulation data and the measurement data in the observation well

Table 2 Soil parameters for the stability analysis in the Geo-slope Software (Watts P J et al. 2001;Swiss Standard SN 670 010b; Minnesota Department of Transportation, 2007)

4.2 Stability analysis results

Water saturation in the dump slope on a wet-weather day (August 28th, 2003) was simulated by PCSiWaPro®and expressed on Fig. 9,which is the previous work of later stability analysis by the Geo-slope Software. In stability analysis, the Geo-slope was implemented to determine the position of the critical slip surface(the surface with the highest possibility of landslide or with the minimum factor of safety, Fs).After inputting different soil properties’ data(Table 2) and the seepage line position simulated by the Program PCSiWaPro®, 60×60 grid net and 50 tangent lines have been setup to determine various slip surfaces; then totally 152 561 slip surfaces were analyzed for the Fs values; and the result expressed on Fig. 11 is the image for the critical slip surface and informs us that this air side slope was in great stability when the minimum Fs value is 4.70 conducted from the Bishop’s Model with reference to the safety value of an earth slope shown in the Table 3.

Table 3 Typical values of customary safety factors (Fs) as presented by Bowels J. E (1988)

Fig. 11 Critical slip surface analysis for the sandy dump slope by the Geo-slope depending on the simulation result of the seepage line position (the blue line) from the program PCSiWaPro®

However, the Fs value of 4.70 has been proved to be overestimated; in order to overcome this disadvantage and achieve a more accurate figure of Fs value, an improved analysis of Fs concerning soil water weight and the influence of water content on soil parameters (e.g. cohesion) is applied in the force analysis of each slice above the critical slip surface (Fig. 12). In the Bishop’s Model, the slope above the critical slip surface has been divided into several slices for the force analysis, and the determination of the slice increment number for stability analysis depends on the precision required. In this study case 30 slices in the slope (shown in Fig. 12) have been selected for the improved stability analysis above the slip surface. In addition, for the 5thto 30thslices below the groundwater table the saturated soil property parameters (cohesion c=0 kPa, internal friction angle=30°) would be applied in the improved Fs calculation (Watts P J et al. 2001; Swiss Standard SN 670010b, 1999; Minnesota Department of Transportation, 2007). Finally, an improved Fs value can be achieved as a safe value of 3.05, a much smaller factor compared with the Fs value of 4.70 without the consideration of water content in the slope shown on Fig. 10. Due to the influence of water content on the variation of the soil parameters and also the weight of rainfall water,the slope was with much less safety.

Fig. 12 Analysis of slices above the critical slip with the consideration of soil water in the dump slope

5 Conclusions

(1) By the Program PCSiWaPro®, water content and saturation distribution in the dump slope could be simulated and predicted dynamically within the whole study period, which was the preliminary work for stability analysis.

(2) This study has also tested the applicability of PCSiWaPro®in calculating the groundwater level in an observation well within a continuous period.

(3) There was a nice correspondence between the measured groundwater level and the computed one using the program PCSiWaPro®; however a little deviation (0.3 m difference) between these two values was caused by inadequately estimated soil parameters (e.g. porosity, hydraulic conductivity). In order to achieve a closer result, more investigation work for these soil parameters both in the field and laboratory is needed.

(4) The slope stability was carried out by the Bishop’s Model which is applied specifically for circle slip surface analysis in the deeper slope layer although with a complicated calculation process. In order to overcome the inconvenience of complicate calculation, the Geo-slope Software has been introduced into the Fs (factor of safety) calculation process.

(5) The Fs analysis by the Geo-slope Software has been proved to be overestimated because of the omission of the soil-water weight in the unsaturated dump slope and the influence of water content on the variation of soil property parameters(e.g. cohesion). An improved version of stability analysis clearly indicated the negative influence from water content on the dump slope stability.

Acknowledgements

This research has been greatly supported by the grant from the Graduate Academy at the Technical University Dresden, Germany. This research was conducted at the Institute of Groundwater Management and the Institute of Waste Management and Circular Economy at the Technical University Dresden.