The paper presents a numerical simulation of the development of a catastrophic landslide in a sandstone quarry and methods of reconstructing the quarry to its previous condition from before the landslide. The important objective of the paper is to present the capabilities of the numerical method used in the analysis of the landslide process, namely the Distinct El- ement Method (DEM). This method is poorly known, though it is capable of solving impor- tant geotechnical problems in which massive displacements are modelled. The features of the method are presented on the basis of a case study. Therefore a numerical analysis is carried out to show the performance of DEM in generating a displacement of several dozen meters in the example of a catastrophic landslide that occurred some years ago in a sandstone quarry. This engineering problem makes it possible to describe and analyse the mechanisms, causes and consequences of the landslide. Key words: Distinct Element Method, sandstone quarry, landslide 1. Introduction The paper presents a numerical simulation of the development of a catastrophic land- slide in a sandstone quarry and methods of reconstructing the quarry to its previous condition. In the process, the paper also presents the capabilities of the Distinct El- ement Method (DEM). This method is poorly known, though it is capable of solv- ing important geotechnical problems in which massive displacements are modelled. (Itasca 2004). The quarry is located about 70 km south of Cracow in the Polish Carpathians, the rock mass is built of a ﬂysch formation, composed mainly of sandstone and clay shale in diﬀerent proportions (Zabuski 2019, Bober et al 1997, Bober and Zabuski 1993, Zabuski et al 2009). In the surroundings of the quarry, thick-bedded muscovite sandstone dominates (Fig. 1), which is exploited and used for construction of roads. © 2020 Institute of Hydro-Engineering of the Polish Academy of Sciences. This is an open access article licensed under the Creative Commons Attribution-NonCommercial-NoDerivs License (http://creativecommons.org/licenses/by-nc-nd/4.0/). 4 L. Zabuski, J. Mierczyński Fig. 1. Geology of the neighbourhood of the quarry (after Borysławski et al 1981; supplemented and modiﬁed) The extraction of the sandstone is performed by the standard method, in which explo- sives are used. In the uppermost part of the quarry, the sandstone deposit is covered by a few-meter-thick Quaternary overburden composed of sand and gravel. In early September 2007, rainfalls were extremely intensive in the south of Poland, triggering ﬂoods and landslides. At the same time, the Quaternary soil cover slid down, together with the underlying sandstone blocks. The mining was stopped, and the following questions were raised: How serious is the loosening of sandstone below the moving overburden? Is further mining possible, and can it be safe? What countermeasures should be taken to avoid further damage? Distinct Element Simulation of a Landslide Process 5 The main objective of this paper is to answer the above questions. For this pur- pose, a numerical analysis was carried out to simulate the phenomena that are visible on the surface or occur in the sandstone under the sliding cover. The inﬂuence of water was also considered in the simulation. The numerical code UDEC 2D (Itasca 2004) based on the distinct element method (Starﬁeld and Cundall 1988, Giani 1992, Zabuski and Marcato 2014, Cundall and Hart 1993) was used in the analysis, which makes it possible to simulate the process of deformation of discontinuous media. The rock mass was modelled as a set of solid rock blocks interacting along discontinuities. It has to be underlined that discontinuities play a fundamental role in the development of deformation processes in rock masses (Hoek and Bray 1981). Discontinuous mod- elling is appropriate, above all, in the case of hard rocks (Marcato et al 2005, 2007, Zabuski and Marcato 2014). However, in the present example, the soil mass was also divided into blocks. It can be assumed that in this approach such an approximation is suﬃciently accurate provided that the soil blocks are small. The geotechnical pa- rameters of the rock and soil layers were unknown, so they were determined using the back analysis procedure. 2. Causes of the Landslide Development 2.1. General Remarks The landslide developed on September 6, 2007, during a period of extremely high rainfall, equal to about 230 mm, which caused a signiﬁcant saturation of the soil over- burden covering the sandstone deposit (Fig. 2). The mean annual precipitation in this Fig. 2. Level of precipitation at the time of the landslide; measured at a meteorological station ca 10 km from the quarry 6 L. Zabuski, J. Mierczyński Fig. 3. Region of the landslide main scarp. An inﬂow of water from a spring into the landslide area can be seen region is about 900 mm, which means that almost 25% of this amount fell during only 5 days. The soil was additionally saturated by springs originating in the upper part of the slope, above the quarry (Fig. 3). These two factors had a strong eﬀect on the deterioration of the soil quality, i.e. its weakening and probably scouring. The soil practically lost its strength, turning into ﬂuid. It is also probable that a continu- ous ground water table (GWT) was created, generating high hydrostatic pressure in fractures between the sandstone blocks that underlie the soil cover. The above-mentioned premises are the starting point for the numerical analysis, which aims to simulate the slide and reconstruct phenomena occurring in the sand- stone. 2.2. Numerical Simulation of the Landslide Computer program and numerical model The UDEC code is based on the distinct element method which makes it possible to simulate a displacement in a two-dimensional model composed of continuous rock or soil blocks, touching one another along the so-called “interfaces”, which imitate nat- ural or artiﬁcial fractures. The principles of the method were elaborated by P. Cundall (1971). The properties of the method make it especially useful in the analysis of dis- continuous media. It is possible to take into account the heterogeneities of the medium (rock mass), complex conﬁgurations of the discontinuities, non-linear behaviour of both the intact rock and discontinuities, and water ﬂow through discontinuities. Distinct Element Simulation of a Landslide Process 7 Fig. 4. Schematic map of the quarry (on May 20, 2007, i.e. before landslide) with the cross-section “A” The location of the analysed cross-section “A” is shown on the map of the quarry in Fig. 4. The geomechanical model for the cross-section “A” with divisions of the analysed space into layers of diﬀerent kind and quality is presented in Fig. 5. This division was carried out on the base of the observation of the disintegration of the rock 8 L. Zabuski, J. Mierczyński Fig. 5. Model of the slope with two curves marking the position of the Ground Water Table (GWT) mass composing the whole slope. Two curves of GWT are drawn in the ﬁgure. One of them, marked by dotted line, represents relatively favourable, “average” hydrological conditions, whereas the other (continuous line) shows the water table at the time of the landslide. As already mentioned, GWT suddenly rose during the heavy rainfall period, and the soil became fully saturated, which was the principal cause of the landslide development. Figure 6 presents a numerical model composed of continuous blocks. The di- mensions of sandstone block are 2 2 m (i.e. 4 sq.m). The soil body was artiﬁcially divided into small blocks with dimensions of 0:5 0:5 m (i.e. 0.25 sq.m). Thanks to this division, it can be assumed that the soil is imitated properly as an assemblage of blocks. In the present case, the blocks are non-deformable (rigid). Therefore the de- formation processes, both sliding and widening triggered by tension, can occur only in the interfaces between them. The geomechanical parameters of the interfaces are shown in Table 1. In fact, these parameters were unknown, so they were determined using a back analysis procedure. The correctness of parameters was checked by a trial and error procedure – the parameters were changed iteratively until the initiation of the landslide and its continuous movement occurred. 2.3. Results of Numerical Simulation The slope is stable in the case of the lower (“S”) GWT (see Fig. 5), and an equilibrium is reached after small displacements (Fig. 7). However, it is supposed that the water ﬂuctuated in the past, and some signs of failure, such as open cracks, were visible even earlier. Thus, the analysed landslide can be considered as an ultimate stage of failure. Distinct Element Simulation of a Landslide Process 9 Fig. 6. The mass split into continuous blocks Table 1. Geomechanical parameters of interfaces Shear Normal Cohesion Angle of Tension Layer stiﬀness stiﬀness friction strength [kN/m] [kN/m] [kPa] [ ] [kPa] Bedrock 2.5E+7 2.5E+7 500 45 Intact sandstone 2.5E+7 2.5E+7 100 40 Disturbed sandstone 2.5E+6 3.0E+6 25 35 0.0 Sliding soil 5.0E+4 5.0E+4 0 5 Soil above the landslide 2.5E+6 2.5E+6 20 30 A rise in the GWT during the ﬁrst days of September caused sudden deforma- tions, and the ﬁnal eﬀect was an extensive slide. As a roof of loosened sandstone was uncovered by the sliding soil, water inﬁltrated easily into this mass, and the GWT dropped rapidly. In consequence, the situation after the landslide became stable. In the next period and the calculation trial, the GWT rose to the level shown by the continuous line in Fig. 5. The soil started to move from its initial position, and large displacements occurred. Two states of failure are shown in Fig. 8: the intermediate and the ﬁnal one. It should be underlined that the latter state is very similar to the appearance of the sandstone walls. With regard to the possibility of sandstone mining in the future, an important problem was the unknown quality and condition of this deposit. It is highly proba- ble that the rock blocks were separated due to water pressure, and the entire mass was signiﬁcantly loosened. Moreover, moving soil fell into empty spaces and ﬁlled opened fractures between sandstone blocks, which is shown in Fig. 9. This problem cannot be evaluated reliably, as the parameters of the interfaces can be only approx- 10 L. Zabuski, J. Mierczyński Fig. 7. Displacement vectors – the model under dry conditions, a low ground water table and a stable state of the slope Fig. 8. Two states of the landslide process; (a) intermediate state, (b) ﬁnal state imated, and even a small decrease in their values results in a signiﬁcant opening of the fractures and loosening of the sandstone. Such a situation is shown in Fig. 10 for a decrease in normal stiﬀness of the disturbed sandstone to 2.5E+6 kN/m (instead of Distinct Element Simulation of a Landslide Process 11 3.0E+6 kN/m – see Table 1). The fracture is wide open, and loosening is very inten- sive. It can thus be said that the numerical simulation indicates certain mechanisms only qualitatively. Fig. 9. Separation and slide along fractures in the sandstone mass Fig. 10. Probable opening of fractures in the sandstone mass 12 L. Zabuski, J. Mierczyński 3. Proposals for Stabilisation and Reconstruction Regulation of water conditions Since the main or even the only cause of the landslide development was water action, it was ﬁrst necessary to stop water inﬂow into the quarry. A system of superﬁcial and underground draining ditches was proposed to stop the inﬂow of water from springs and to limit the run-oﬀ from rainfall. A designed system is presented in Fig. 11. The superﬁcial drains are lined with concrete forms. The underground drainage, shown in Fig. 12, is built in a typical way,. The drain is composed of perforated pipe surrounded by granular soil, and the ditch is inlayed with geotextile. In addition, and very impor- tantly, open cracks are sealed with impermeable soil, e.g. clay or loam, which prevents the penetration of water through the cracks into the sandstone mass. Fig. 11. Scheme of water inﬂow and drainage works around the quarry Distinct Element Simulation of a Landslide Process 13 Fig. 12. Underground drain Change of the inclination of the landslide main scarp The steep inclination of the main scarp wall (see Fig. 3) causes a retrogressive fail- ure of the slope above the main scarp of the landslide. It was therefore suggested that this inclination be decreased (Fig. 13). No sophisticated structures are necessary; only grass should be sown on the slightly inclined surface. The soil from the area below the scarp will also be removed, which will have the positive eﬀect of unloading the sandstone deposit. All earth works should be started at the uppermost place and proceed downwards. Numerical simulation of the behaviour of the model after introduction of countermeasures The numerical simulation was repeated after the introduction of above modiﬁcations into the model. The results, in the form of displacement vectors, are presented in Fig. 14. Some displacement in the direction opposite to the open space was generated, which proves that the formerly open cracks were closed. The model reached equilib- rium within a short time. 4. Final Remarks Three questions were formulated in the introduction to this paper, and the results obtained provide the answers. It was proven that sandstone below the soil slide is loosened due to the opening of fractures. Further mining of the rock in the quarry was still possible, although special attention has to be paid during exploitation as the 14 L. Zabuski, J. Mierczyński Fig. 13. Proposed earth works in the region of the main scarp of the landslide Fig. 14. Displacement vectors in the quarry after repair and stabilisation works Distinct Element Simulation of a Landslide Process 15 loosened blocks may fall, causing danger. The suggested countermeasures are not so- phisticated. Since the main cause of the landslide was water inﬂow, closing the path of this inﬂow and decreasing the amount of water will be beneﬁcial. It can be said that it will help prevent further instability under the condition that the drainage system works properly, without any disturbances. This paper also shows a possible method of solving rock and soil mass deforma- tion problems by modelling the medium as discontinuous, especially by the Distinct Element Method. This approach can undoubtedly be correctly applied in cases of hard rocks divided into solid blocks, such as sandstone or similar. It is problematic in the case of soil, but the results of the present analysis show that the approximation of the soil mass as a set of blocks is suﬃciently accurate and satisfactory provided that the blocks are small. Discontinuous modelling makes it possible to simulate very large displacements, and it could be considered as one of main advantages of this approach. References Bober L., Zabuski L. (1993) Flysch Slope Classiﬁcation from Viewpoint of the Landslide Predic- tion, Proc. Int. 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(2014) Analysis of Deformation Processes of Slopes with Taking into Account Discontinuous Character of the Rock Mass (in Polish with an English summary), Przegląd Geo- logiczny, 62, 308–316. 16 L. Zabuski, J. Mierczyński Zabuski L. (2019) Three-Dimensional Analysis of a Landslide Process on a Slope in Carpathian Flysch, Archives of Hydro-Engineering and Environmental Mechanics, 66 (1–2), 27–45. Zabuski L., Wójcik A., Gil E., Mrozek T., Rączkowski W. (2009) Landslide Process in a Flysch Mas- sif – Case Study of the Kawiory Landslide, Beskid Niski Mts. (Carpathians, Poland), Geological Quarterly, 53 (3), PGI, Warsaw, 317–332.
Archives of Hydro-Engineering and Environmental Mechanics – de Gruyter
Published: Dec 1, 2020