investigating toppling failure mechanism of anti-dip

Vol.:(0123456789)1 3

Rock Mechanics and Rock Engineering (2020) 53:5029–5050 https://doi.org/10.1007/s00603-020-02207-y

ORIGINAL PAPER

Investigating Toppling Failure Mechanism of Anti-dip Layered Slope due to Excavation by Physical Modelling

Chun Zhu1,2,3,4 · Manchao He2 · Murat Karakus3 · Xuebin Cui2 · Zhigang Tao2

Received: 15 July 2019 / Accepted: 17 July 2020 / Published online: 25 July 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020

AbstractThe failure mechanism of anti-dip layered slopes is essentially different from that of dip layered slopes. Therefore, it is important to investigate the failure mechanism of anti-dip slopes due to excavations. In this study, slope instability induced by mining excavation at the Changshanhao open-pit mine in Neimenggu province, China, was used as a case study. Based on the similarity ratio theory, a physical model was built to investigate the failure mechanism of the anti-dip layered slope under excavation. The physical model was monitored by various monitoring equipment including static strain data acquisi-tion equipment, infrared thermal camera, and digital speckle displacement field measurement equipment. The evolution characteristics of the multi-physics fields including displacement field, strain field and temperature field of the physical model during the excavation were comprehensively obtained. According to the deformation characteristics of the anti-dip layered slope during excavation test, the failure mechanism can be divided into four stages: initial compression stage, crack generation stage, crack propagation stage and formation of sliding surface stage. The deformation characteristics of the slope at each stage were analyzed and compared with those of the anti-dip slope in the field. The comparison verified the rationality and accuracy of the physical model experiment, and provided a deeper understanding of the failure mechanism of anti-dip layered slope under excavation through the comprehensive monitoring data. The results of this work can be used as a reference for the follow-up reinforcement and treatment of similar anti-dip layered slopes.

Keywords Anti-dip layered slope · Toppling deformation and failure · Physical model · Slope excavation · Monitoring

List of SymbolsCl and Cr Geometric similarity ratio

and unit weight similarity ratio, respectively

C! ,CE,Cc,C" ,C# ,C$ and C! Similarity constants for stress, deformation modu-lus, cohesion, displace-ment, Poisson’s ratio, strain and internal friction angle, respectively

c and φ Cohesion and internal fric-tion angle, respectively

!max Maximum principal strain!x , !u and !y Measured strains in X, U and

Y directions, respectively

* Zhigang Tao [email protected] School of Earth Sciences and Engineering, Hohai University,

Nanjing 210098, China2 State Key Laboratory for Geomechanics and Deep

Underground Engineering, China University of Mining and Technology, Beijing 100083, China

3 School of Civil, Environmental and Mining Engineering, The University of Adelaide, Adelaide, SA 5005, Australia

4 College of Construction Engineering, Jilin University, Changchun 130026, China

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1 Introduction

With increasing construction of engineering structures on slopes, the hazards and economic loss caused by top-pling deformation and sliding failure of anti-dip layered rock slope have become more severe. For example, large-scale toppling landslides occurred in the Jinchuan open-pit nickel mine, the Jinping hydropower station, and the Changshanhao open-pit mine, resulting in large economic losses and many casualties (Qi et al. 2004; Lin et al. 2015).

De Freitas and Watters (1973) first described the com-mon toppling phenomenon and later supplemented it with complete terminology for the toppling failure. Sub-sequently, Goodman and Bray (1976) classified the top-pling deformation of layered slopes into three basic types, namely, flexural toppling, block toppling and block flex-ural toppling. Aydan and Kawamoto (1992) introduced a method for analyzing the stability of slopes and under-ground openings against flexural toppling failure. The reasonability and applicability of the method were proved through model tests conducted in the laboratory. It was found that their proposed method can be used to predict the stability of actual slopes and underground openings in layered rock masses. Through a parametric study of large rock slope using the universal distinct element code, Nichol et al. (2002) proved that certain key parameters of the undeformed rock mass affect the failure behavior in a quantifiable approach. The slope was modeled con-sidering variations of rock mass strength, discontinuity orientation and persistence, and toe over-steepening. Two distinct types of failure behavior were observed, and the two mechanisms showed different patterns of pre-failure stress. After that, many researchers performed systematic investigations of the toppling behavior of rock slopes to explore the failure mechanism and to develop the toppling failure model (Alejano et al. 2010; Tatone and Grasselli 2010; Majdi and Amini 2011; Babiker et al. 2014; Tu et al. 2007).

With the development of computer technology, more scholars are using a combination of analytical methods and numerical simulation to examine the toppling failure mechanism of anti-dip slope (Amini et al. 2018; Lian et al. 2018; Amini and Ardestani 2019; Alzo’ubi et al. 2010). For example, based on the limit equilibrium method, Liu et al. (2008) proposed an approach to analyze the top-pling failure of slope and introduced the influence of inclination βbr of block base on the toppling stability. Garcia-Moya et al. (2019) used field investigations on a mica schist slope to explain the underdip toppling failure mechanism. Moreover, they proposed a numerical method to evaluate the quantitative and qualitative effects of key parameters including the discontinuity strength, in-situ

state of stresses, slope height, and the water table level (WTL). It was found that the WTL had the most significant influence on the underdip toppling failure of the slope. Zhang et al. (2018) analyzed the flexural toppling fail-ure mechanism of slope on the basis of cantilever slab tensile theory and divided the toppling slope into three parts: the stablezone, tensile zone, and shear zone. Then, an innovative stability analysis approach for bending and toppling slope was introduced through the equilibrium theory. Bowa and Xia (2018) introduced an analytical method to determine the angle of toppling failure surface. By incorporating the inclination of toppling weak plane, they modified the conventional model for calculating the slope stability subjected to the toppling mechanism of the rock mass, and the rationality of the modified model was proved by numerical simulation. Moreover, the effects of relative angles of toppling failure surface on the stability of slope were also studied. Gu and Huang (2016) carried out a survey on the Gongjiafang landslide, and performed detailed geomorphological investigations, field and labora-tory experiments to reveal the toppling failure mechanism of the landslide. The conceptual “cantilever beam” model was introduced to explain the failure mechanism of the landslide, and discrete element method (DEM) was used to further study the failure process with a complex mode of toppling failure. The results showed that preventing water erosion at the toe of the slope may be an effective method to prevent landslides in the study area.

Recently, with the development of the similarity ratio theory, many kinds of physical modeling-based experimen-tal systems have emerged. The physical model experiment refers to the experiment on the basis of a certain reduction proportion of the in-situ real situation. Its advantage is that the results are directly obtained during the experiment, and the experimental results are more realistic than those obtained using the numerical model. The physical model test can simulate the complex geological structure comprehen-sively and realistically, and reproduce the deformation and destruction process of the engineering structure intuitively. Thus, it can reveal the influence of controllable influencing factors on the evolution process of engineering disasters, which can provide a basis for establishing new theoretical and mathematical models. Therefore, many scholars are now investigating the toppling deformation mechanisms of slopes by identifying and acquiring information regarding their internal stress and strain fields. For example, Adhi-kary et al. (1997) investigated the toppling failure mecha-nism of jointed rock slopes through a series of centrifuge experiments conducted on models and used a theoretical model based on a limiting equilibrium approach to analyze the experimental data. After the calibration, the built model was found to accurately predict the failure load for all the tests reported in the study. Adhikary and Dyskin (2007)

5031Investigating Toppling Failure Mechanism of Anti-dip Layered Slope due to Excavation by Physical…

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studied the toppling failure mechanisms of slope in foliated rock masses both experimentally by testing a small-scaled centrifuge model and theoretically using a limit equilibrium model and a finite difference model. Two main failure mech-anisms were identified, including instantaneous failure and progressive failure. It was found that the magnitude of the joint friction angle controlled these two mechanisms of slope failure. Huang et al. (2013) conducted large-scale shaking table tests of anti-inclined landslides triggered by an earth-quake and studied the mechanical evolution characteristics of soft and hard slopes under the sinusoidal waves and actual seismic waves. Taking the Wangjiaping toppling landslide induced by an earthquake as an example, Fayou et al. (2012) conducted indoor physical tests under seismic loading, and studied the failure and deformation mechanisms of the anti-dip slope.

According to the above research, when an anti-dip slope becomes unstable, the potential sliding surface is not a sin-gle arc surface or plane, and the sliding track is difficult to predict. The rock mass experiences rotation deformation, and the extent of the slope toppling and bending deformation is large. Its failure mechanism is essentially different from that of the layered slope. The anti-dip layering cuts the rock mass of a slope into slabs, which are similar to cantilever slabs. The internal joints and fissures of the cantilever slabs facilitate the slabs to slide over each other, causing bending and toppling failure to occur in the slope, which eventually results in a landslide.

There are only a few studies on the failure mechanism of anti-dip layered rock slopes under excavation. An unsta-ble slope induced by excavation at the Changshanhao open-pit mine was taken as a case study to construct the physical test model. Various monitoring equipments were employed including static strain data acquisition equipment, infrared thermal camera and digital speckle displacement field measurement equipment. Furthermore, the evolution

characteristics of multi-physics fields including displace-ment field, strain field and temperature field of the anti-dip model slope during excavation were investigated in detail. The model results showed the deformation and failure mech-anism of the anti-dip slope under excavation, which can be used as a reference for the treatment and reinforcement of the anti-dip slope.

2 Geological Conditions of Changshanhao Open-Pit Mine

2.1 Location and Elevation

Changshanhao open-pit mine is located in the Neimenggu province of China. The orefield has a denuded topography of low mountains and hills. Its elevation ranges from 1550 to 1750 m, as shown in Fig. 1. Generally, the east part of the mine is at a higher elevation and the west part is rela-tively low lying. The ore bodies are mainly distributed in the low-lying areas. Within these areas, the rock strata are well exposed, without vegetation cover.

2.2 Geological and Hydrogeological Characteristics

The main lithological components of the Changshanhao open-pit mine include gneiss, andalusite schist, meta-sand-stone, two-mica quartz schist, quartzite, and limestone. The inclination of bedding planes is about 65°–85°. The north side of the mine is dominated by slate and schist, and the south side is dominated by limestone.

The Haoyaoerhudong syncline influenced the develop-ment of the late Variscian granite formation, Halahuogete formation and Bilute formation at Changshanhao open-pit mine. These serve as the deposits of the Hayaoerhudong syncline. The formation comprises steeply dipping, thickly

Fig. 1 Location and landslide failure of Changshanhao open-pit mine

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layered deposits striking NE with an inclination angle of over 60°. Thus, the formation is counter-inclined in the northern slope of the open-pit mine but in the down-dip direction in its southern slope. The main faults are the brit-tle-ductile fracture tectonic zone and the strike-slip faults. The brittle-ductile fracture tectonic zone is located at the left side of the mine pit (Fig. 2), with NE-strike angle of 60°–80°. It consists of several crushing fractured zones and foliation zones. The overall length is 4.5 km along the strike and the width is 200 m. Most of the fractured zones are dis-tributed along the strata strike and a few cutting strata, and their occurrence is consistent with the occurrence of the rock strata. The dip angle of individual sections increases and the strata are cut. The formation time of NW strike-slip faults is later than that of shear zones. Subjected to tectonic control, the mine has a low rock mass integrity, and the stability of the rocks and ores are relatively poor. Therefore, during mining activities, slope failures and deformations are likely to occur.

The mine is within a hilly plateau hydrogeological area, characterized by a dry climate with little precipitation and intense evaporation. Its rainy season is between July and

September. Its annual rainfall is 233.7 mm, and annual evaporation is 2646.2 mm. The groundwater in this area is mainly supplied by atmospheric precipitation, and the runoff discharge is the main mode of groundwater discharge. The groundwater level is deep and the amount of water is small. Thus, the effects of rainfall and groundwater on the mine are minimal.

2.3 Joint Structure Investigation on Changshanhao Mine

A comprehensive engineering geological survey was carried out on the southwest open pit of Changshanhao mine. Three groups of joint sets are present in the southwest pit. Two groups of joint sets (164 < 87 and 345 < 84) which intersect with the long axis of the slope by 45° are the main joint sets. The two groups of discontinuities have the features of the consistent strike and opposite dip. Affected by weathering, stripping and unloading of the open pit, the joint sets on the slope are mostly characterized by slight opening, high joint density, and a smooth and flat surface without filler. The spacing of joints is 0.15–2 m.

Sandy soil Gray andalusite schistˈgarnet schist Granite

Gray sandy mudstone, sandstoneRhyolite porphyryǃTuff

Gray limestone

Slate, quartz sandstone

Quartzite, quartz sandstone

Mixed rock

Aplite

Granitic pegmatite

Quartzite

Quartzite porphyry

Gabbro

Measured unidentified fault

Measured reverse fault

Fig. 2 Structural relations and lithology distributions in Changshanhao open-pit mining region (Tao et al. 2019)


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2.4 Failure Analysis of on-site Slope

With continuous mining of the area, the slope height increases gradually. The scale and frequency of toppling landslides in the mine also increase. In this study, the top-pling failure of the slope on the north side of the southwest pit in the mine was used as a case study (Fig. 3). The angle of the slope was 36°. On April 30, 2017, a toppling failure occurred on the north side of the mine. On both sides of the unstable zones, the total length was 360 m. The length of the main failure zone was 260 m, and the horizontal projected distance was about 230 m. The elevation of the toppling failure zone was between 1534 and 1661 m.

2.5 Geophysical Investigations

According to the field engineering geological conditions, three high-density electrical method profiles and two MASW (Multichannel analysis of surface waves) surface wave profiles were set in the landslide area. Based on the comparison of three high-density electrical method profiles on the landslide mass (Fig. 4), the resistivity of the shallow part in the landslide mass was relatively high and discontinu-ous, which was caused by the landslide. The low resistivity strips on the profiles were speculated to be the faults. The wave velocity in the landslide area was lower than that in the bedrock due to the landslide. The surface wave exploration results are shown in Fig. 5.

By combining the high-density electrical method results and the surface wave exploration results, the characteristics of the sliding surface of field real slope were determined. The sliding surface had concave shape and its depth was about 20–26 m. Two polylines formed the sliding surface. The inclination angle of the upper polyline was about 43° and the inclination angle of the lower polyline was about 20°. All the detection points were used to draw the

three-dimensional shape of the potential sliding surface in the landslide area, as shown in Fig. 6.

3 Physical Model Construction and Experimental Process

3.1 Physical Model Settings

Based on the similarity ratio theory, the physical model experiment of the entire process of failure of the anti-dip layered slope was carried out using the “Physical Model Loading System” (Fig. 7). The experimental device com-prises the main unit, the hydraulic control system, the model transport vehicle, and the console. The device has the char-acteristics of a multi-purpose service. There are six uniform pressure loaders separately set into the four load support beams of the main unit. The top and two sides of the support beams can control each uniform pressure loader separately. Thus, the device can carry out non-linear loadings from the top and from the two sides (Tao et al. 2018; He et al. 2010; Shan and Lai 2020).

3.2 Similarity Ratio Design and Simulated Rocks for the Physical Model Experiment

In this study, a section of the slope in the landslide area was selected. The section was 304 m long from north to south, 76 m wide from east to west, and 275.5 m high. Based on the characteristics of the study area and the size of the test equipment, the geometric similarity ratio Cl of the model was determined, i.e. Cl = 190. According to the field inves-tigation, the horizontal geostress is relatively low and the main factor affecting the stability of this area is the vertical lithostatic stress. Thus, the similarity ratio of the bulk den-sity was considered in the experiment. The physical model can effectively simulate the effects of vertical geostress in

Fig. 3 Location of the failed slope in Changshanhao mine

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a natural state. At the same time, 0.2 MPa horizontal stress was applied to the model to stabilize and compress the slope. The similarity ratio of the bulk density is Cr = 1.5. The natu-ral stress field of the model can be formed during the con-struction process. Based on the similarity ratio theory, the other similarity constants of the simulated rocks are:

where C! , CE , Cc , C! , C! , C! and C! are the similarity constants of stress, modulus of deformation, cohesion, total displacement, Poisson’s ratio, strain, and internal friction angle, respectively.

The rock mass of the research area is mainly andalu-site schist. Thus, the model was composed of materials simulating the properties of andalusite schist. Based on the similarity ratio theory, the main physical and mechanical

(1)C!= CE = Cc = C"= Cr∗ Cl = 285,

(2)C!= C"= C# = 1,

parameters of the rock mass and the pre-calculated simu-lated rocks selected for the model are shown in Table 1.

The physical model was constructed using plates of dif-ferent sizes. The plates were made of barite powder, sand, gypsum powder, and water. The physical and mechani-cal parameters of the plates can be adjusted by changing the proportions of the materials. Through a large num-ber of tests, it was determined that mixing barite pow-der, sand, gypsum powder and water in the mass ratio of 0.504, 0.153, 0.114 and 0.229 was suitable for simulating the andalusite schist rock. Using samples of the simu-lated rocks, Brazilian tests and uniaxial compression tests were carried out (Hu et al. 2020), and the actual physi-cal and mechanical parameters of the plate material were obtained, as shown in Table 1. Due to the complexity of mixing various materials to obtain a model rock, it is dif-ficult to obtain the parameters of the model rock equal to the pre-calculated parameters. Therefore, the physi-cal–mechanical parameters of the model rock are close

Fig. 4 Results of high-density electrical method


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to the pre-calculated values as far as possible, and some error is allowed.

3.3 Construction of the Physical Model of Anti-dip Layered Slope

3.3.1 Geological Model of Anti-dip Layered Slope

The unit plates laid layer-by-layer formed the simulated rock mass structure. This physical model can reproduce the real structure of the rock mass to some extent. Accord-ing to the dip of rock strata in Changshanhao mine, a slope model with 75°-dipping strata was constructed, with a slope angle of 36°. The excavation area was located at the foot of

Fig. 5 Results of MASW surface wave exploration

Fig. 6 Three-dimensional shape of the potential sliding surface in the landslide area

Fig. 7 Physical model loading frame

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the slope and was divided into nine excavation layers. The total length of the excavation area was 0.37 m, the thickness was 0.405 m, and the slope excavation thickness of each layer was 0.045 m (Fig. 8). To better simulate the strati-fication state of the real rock slope, gypsum unit plates of 0.4 m × 0.4 m × 0.02 m and 0.4 m × 0.2 m × 0.02 m were alternately stacked during the model building process. The physical model was 1.6 m long, 0.4 m wide, and 1.45 m high. As the in-situ rock is schist, there is basically no infill-ing in the joint surfaces between schist layers. Thus, the shear strength of the joints delimiting the schist layers can be ignored in the experimental process. Andalusite schist was cut into multilayer structures by rock joints, whereas plates were stacked directly without adding any bonding material between two adjacent plates. A horizontal com-pression stress was applied to the model before the excava-tion. According to the field and experimental conditions, the inclination of the joint was set to 75°. The spacing of field joints was 0.15–2 m. Due to the limitation of plate thickness, the joint spacing of the model slope was set at 0.02 m. Based on the field joint shear strength test, the friction angle of the joint in the model was set to 20°. Therefore, finite element

plates were used to structure the model. The fissures between finite element plates can closely reflect the in-situ character-istics of rock joints.

3.3.2 Layout of Strain Gauges

To obtain information about the strain field during the failure process of the physical model, a total of 40 strain gauges were installed in the model. The monitoring plane of the strain gauges was 200 mm inside the model in the z-direction. Among the strain gauges installed in the physi-cal model, more gauges were installed around the slope excavation area, especially at the foot of the slope.

The layout of the strain gauges is shown in Fig. 8. There were six layers of strain gauges. For each layer, the strain gauges were numbered from right to left. For the first layer of strain gauges, there were eight gauges arranged evenly along the upper slope. For the second to fourth layers, there were six gauges per layer located on the left side of the exca-vation area. For the fifth and sixth layers, there were seven gauges per layer located below the excavation area.

Table 1 Physical and mechanical parameters of field rock, pre-calculated and prepared model rocks

UCS of andalusite schist is the maximum value (load normal to foliation)

Lithology Uniaxial compres-sive strength/MPa

Tensile strength/MPa

Young’s modulus/GPa

Poisson ratio Cohesion c/MPa Internal fric-tion angle φ/°

Density /kg*m−3

Andalusite schist 102.6 11.9 26.9 0.17 9.8 57.4 2810Pre-calculated model rock 0.36 0.042 0.094 0.17 0.034 57.4 1870Prepared model rock 0.35 0.107 0.103 0.16 0.53 21.6 1920

Fig. 8 Layout of strain gauges inside the anti-dip slope model

First excavation layer

Fifth excavation layer

Ninth excavation layer

First strain gauge layer

Second strain gauge layer

Third strain gauge layer

Fourth strain gauge layer Fifth strain gauge layer

Sixth strain gauge layer


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The internal strain of the slope was measured with a three-dimensional 45° strain gauge rosette (Fig. 9a). First, each plate was cut. Then, by digging the side of the plate at the selected location, the strain gauge was installed at that location (Fig. 9b). Thereafter, during the model build-ing process, each plate was placed such that the strain gauge measured the strain at the designed monitoring point (Fig. 9c).

The monitored strains in three directions were processed and analyzed, and the maximum principal strain at each monitoring point was calculated as follows:

where !max is the maximum principal strain; !x , !u and !y are the measured strains in the directions of X, U and Y, respectively (Fig. 9a).

3.3.3 Monitoring Equipment for the Mechanical Field of the Physical Model

The physical model test results can be directly obtained dur-ing the experiment process. However, it is difficult to meas-ure the entire stress and strain evolution inside the model. Placing too many monitoring sensors in the model will affect the initial stability and accuracy of the slope model, so non-contact monitoring equipment is needed for monitoring the model. Therefore, only 40 strain gauges were placed inside

(3)!max =1

2

[

(

!x + !y)

+

√

2

[

(

!x − !u)2

+(

!u − !y)2]

]

,

the model, and the other monitoring equipment were non-contact infrared thermal camera and digital speckle meas-urement system.

The strain data acquisition equipment was a YSV8360 static strain tester, which utilizes an electrical method to measure the slow change in static strain with time. It has a range of ± 20,000 με with a resolution of 5 με and a maxi-mum sampling frequency of 5 Hz. The slope releases energy when it is slowly deformed and the deformation area of the slope is captured by an infrared camera. As the infrared thermal imager does not directly come into contact with the measured object, the impact of contact measurement on experimental model results was avoided. The basic principle of the infrared camera is that the thermal contrast between the measured object and the surrounding environment is markedly different due to the difference in infrared emissiv-ity. This difference is captured by the infrared thermal cam-era. The infrared radiation emitted by the measured object is filtered and signal processed, and finally the infrared thermal image is displayed. The digital speckle measurement system mainly uses a high-speed camera (CCD camera) to capture the image of the object surface, which is then transmitted to the image card for digital processing and stored in the computer (Zhang et al. 2012; Hao et al. 2015). Artificial speckles were added to the model surface so that surface displacement can be captured easily by digital image cor-relation. The digital speckle measurement system is shown in Fig. 10. Assuming that the motion of a point P in the initial state is traced, the characteristic speckle pattern of the

Fig. 9 Three-dimensional 45° strain gauge rosette

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point is first taken from the original image. Then, the target image is matched with the original image by the correlation algorithm. Finally, the sub-pixel matching is obtained by the least square matching method to calculate the displacement of the monitoring object (Valentino et al. 2008).

3.3.4 Building of Physical Model Experimental System

The anti-dip rock slope was built according to the design scheme. During the building process, the gypsum plates were polished to reduce the gaps between the plates. After spraying speckles on the physical model surface, the posi-tions of the speckle displacement field measurement device and the thermal infrared camera were adjusted to capture the deformation characteristics of the slope model, as shown in Fig. 11.

3.4 Physical Model Testing Process

During the construction of the physical model, there were many gaps between the gypsum plates. By pre-pressing the model in the horizontal direction, the gaps between plates were reduced so that the model can reach the tightness level of field condition. During the experiment, the horizontal stress P = 0.2 MPa was first applied on both sides of the model. After loading for 10 min, the horizontal confining stress was kept constant at 0.2 MPa, and the slope was exca-vated layer by layer. Loading process of the physical model experiment is shown in Fig. 12.

After completing the loading process, a shovel was used to excavate the slope layer by layer according to the designed mining operation, until the designed mining boundary of the mine was reached. The excavation time of the adopted method was 3–5 min. The excavation had a certain effect on the crack initiation, which was similar to the influence of field excavation on mine stability. The slope excava-tion thickness of each layer was 0.045 m. After excavating one layer, the layer was maintained for 1 h. After the slope became stable, the next layer was excavated. Since the first

CCD Camera

Speckled surface

Data Processing system

Light

Light

Fig. 10 Principle of digital speckle measurement system

Fig. 11 Main steps in building the physical model experimental system

P=0.2 MPa

First excavation layer

Fifth excavation layer

Ninth excavation layer

P=0.2 MPa

Fig. 12 Loading process during the physical model experiment


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four layers of the slope were 0.09 m high, each layer was divided into two excavation layers. The fifth layer was only 0.045 m, so it was considered as a single excavation layer. There were nine excavation layers in total. The deformation of the surrounding rock during the slope excavation process is shown in Fig. 13.

4 Analysis of Experimental Results

During the initial stage of the slope excavation, the slope deformation increased gradually, and cracks propagated to the deeper part of the slope. When the fifth layer was excavated, V-shaped cracks appeared on the slope, and then potential shallow sliding surfaces also appeared. When the seventh layer was excavated, large-scale toppling failure occurred on the slope. As the excavation proceeded, the scale of the toppling landslide continued to increase until the model was completely broken. During the model excava-tion, the evolution of the displacement field, strain field and temperature field of the slope model were obtained using the static strain data acquisition equipment, infrared thermal

camera and digital speckle displacement field measurement equipment.

4.1 Evolution of the Internal Strain Field of the Slope Model

Figure 14 shows the maximum principal strains of 40 moni-toring points, from which the evolution of the strain field in the anti-dip slope during the excavation can be obtained. It can be seen that the strains of the fifth and sixth strain gauge-layers below the excavation area in the model were relatively small, and their variations were also small. Before the excavation of the fourth layer, the strain curves of each measuring point in fifth strain gauge-layer were similar, and the strain remained around 95 με. The growth rates of each measuring point were different, and the maximum strain dur-ing the excavation was about 501 με. The strain curves of each measuring point in sixth strain gauge-layer were similar before the excavation of the seventh layer, and the strain remained around 120 με. The maximum strain during the excavation was about 404 με. Therefore, the strain curves of each measuring point in these two layers were close to each

Fig. 13 Deformation characteristics of the anti-dip slope during excavation

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other. The strain gauges from the second to the fourth layers were installed horizontally. The strains near the slope face of each layer were significantly affected by the slope excava-tion, while the other internal strains far from the slope sur-face were less affected by the excavation. From the second

strain gauge-layer to the fourth layer, the maximum strains of monitoring points nearest to the excavation area were 1206 με, 1048 με and 830 με, respectively, and the maxi-mum strains of the monitoring points farthest from the exca-vation area were 390 με, 268 με and 229 με, respectively.

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in (µ

ε)

No.6-1 strain No.6-2 strain No.6-3 strain No.6-4 strain No.6-5 strain No.6-6 strain No.6-7 strain

LKJH IGFECB DA

(e) Fifth layer strain gauge (f) Sixth layer strain gauge Experimental working condition: A—Start loading; B—After loading; C—After excavation of first layer;

D—After excavation of second layer; E—After excavation of third layer; F—After excavation of fourth layer; G—After excavation of fifth layer; H—After excavation of sixth layer; I—After excavation of seventh layer ; J—After excavation of eighth layer; K—After excavation of ninth layer; L—Test finish.

Fig. 14 Evolution of internal strains of the slope model


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The first layer of strain gauges was installed along the upper surface of the slope, and the range of the strain variation of each strain gauge was larger than that of the gauges at other layers. The maximum strain of monitoring point nearest to the excavation area was 1394 με, and that of the monitoring point farthest from the excavation area was 511 με. It can be seen that the difference in maximum strain between monitor-ing points in the same layer of strain gauges increased from the fourth layer to the first layer. After the excavation of the seventh layer, the slope collapsed and the landslide occurred. The strains of all the gauges increased sharply at this time. With the further excavation of the slope, the unstable area of the slope continued to expand, and the strain at each layer continued to increase until the end of the test.

4.2 Evolution of Temperature Slope Model

The infrared thermal camera can capture the temperature difference and detect the distribution of invisible infrared energy. The temperature during the entire process of excava-tion in the slope model was measured by the infrared ther-mal camera. The temperature field nephrograms of the slope model are shown in Fig. 15.

After loading the slope model, the temperatures on both sides of the slope model increased, as seen from Fig. 15. The temperature in the lower part of the left side of the slope model reached about 29 °C, while the temperature of the other main part was about 27.32 °C. During the excava-tion, the energy on both sides of the model was continu-ously released, and the temperature gradually decreased to 27.64 °C, which is close to that of the other part of model. With the stratified excavation of the slope, the free surface of the slope was unloaded, which disturbed the original stress balance of the slope. During the process of slope stress adjustment, the rock mass near the excavation area broke, resulting in large deformation. Then, the crack propagated from the bottom to the top. At this time, as shown in Fig. 15, the temperature of the deformation area gradually increased, and finally rose from 27.04 to 28.85 °C. From the tempera-ture diagrams of the slope model, it can be seen that the temperature of the area with large deformation was higher than that of the other stable areas, with a temperature differ-ence of 1.53 °C. These results indicate that the distribution of deformations in the slope can be accurately judged using an infrared thermal camera to monitor the temperature.

4.3 Evolution of Internal Displacements in the Slope Model

The slope model was photographed and recorded by the CCD camera during the whole experiment with the time interval of 1/200 s. Then, the slope shape in each photograph was processed and compared, and the displacement field of

the slope at different times was obtained. The horizontal dis-placement field and vertical displacement field of the slope at each stage are shown in Figs. 16 and 17. After excavat-ing the seventh layer, the slope collapsed and the landslide occurred. With the continuing excavation of the slope, the slope deformation exceeded the measurement range of the digital speckle displacement field measurement device. Thus, the displacements of the slope after excavating the eighth and ninth layer are not available.

The horizontal displacements of the physical model are shown in Fig. 16. In the displacement diagrams, the right displacement is positive and the left displacement is nega-tive. As shown in Fig. 16a, after loading the slope, large horizontal displacements occurred on both sides of the slope model. There was positive displacement on the left side of the slope with the maximum displacement of 14.06 mm, and negative displacement on the right side with the maximum displacement of 12.93 mm. With the stratified excavation of the slope, the rock mass began to crack, leading to the dislo-cation of the rock mass in the upper part of the slope, and the slope deformed towards the free face of the excavation. With the continuing excavation, the shear cracks of the slope grad-ually expanded from the surface of the slope to the deeper part of the slope. This resulted in significant deformation and displacement of the slope, and bending and toppling failures in some areas. From the excavation of the first layer to the excavation of the sixth layer, the maximum horizontal displacements in the deformation area near the excavation were 1.27 mm, 18.46 mm, 24.35 mm, 34.82 mm, 38.31 mm and 43.94 mm, respectively. After excavation of the seventh layer, the slope collapsed and the landslide occurred; the local maximum horizontal displacement reached 55.27 mm. As the excavation proceeded, large-scale toppling failure occurred, as shown in Fig. 13.

The vertical displacements of the physical model are shown in Fig. 17. In the displacement diagrams, the downward displacement is positive and the upward dis-placement is negative. As shown in Fig. 17a, during the loading process, the vertical displacement was caused by the extrusion of both sides of the model. The main displacement of the right side of the slope was directed downward, the main displacement of the left side of the slope was directed upward, and the local maximum verti-cal displacement was 3.83 mm. With the stratified exca-vation of the slope, displacement occurred towards the free surface, coupled with the effects of the self-weight of the rock mass. Consequently, the original ascending movement of the rock mass caused by horizontal compres-sion stress changed to downward movement trend. With the excavation of slope, the unloading of the free surface caused stress redistribution inside the slope. The deforma-tion towards the free surface increased gradually, which led to a gradual increase in the vertical displacement in a

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downward direction. From the excavation of the first layer to the excavation of the sixth layer, the maximum vertical displacements of deformation area near the excavation site were 0.26 mm, 1.74 mm, 6.41 mm, 9.72 mm, 13.09 mm and 21.53 mm, respectively. After the excavation of the seventh layer, some rock masses near the sliding surface broke under the action of shear. Finally, the sliding surface

was completely formed, and the landslide occurred; the local maximum vertical displacement was 30.48 mm.

To better highlight the deformation and failure processes, the displacement vector plots of the model are also shown in Fig. 18. Under the action of loading, both sides of the model were compacted. The left side of the model bottom moved downward to the right, and the right side of the model

(a) After loading (b) After excavation of first layer (c) After excavation of second layer

(d) After excavation of third layer (e) After excavation of fourth layer (f) After excavation of fifth layer

(g) After excavation of sixth layer (h) After excavation of seventh layer (i) After excavation of eighth layer

(j) After excavation of the ninth layer

30.25

24.25

25.75

27.25

28.75

30.26

24.26

25.76

27.26

28.76

30.49

24.49

25.79

27.29

28.79

30.36

24.36

25.86

27.36

28.86

30.46

24.46

25.96

27.46

28.96

30.46

24.46

25.96

27.46

28.96

30.45

24.45

25.95

27.45

28.95

30.32

24.32

25.82

27.32

28.82

30.42

24.42

25.92

27.42

28.92

30.24

24.24

25.74

27.24

28.74

Fig. 15 Infrared temperature distribution in the physical model


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bottom moved downward to the left, while the upper area of the model had a slight upward movement under the extru-sion. Then, under the layer by layer excavation of the slope, as well as the gravity of rock mass, the free face of the slope was unloaded, and the rock mass changed from the initial compression state to the tensile state. Finally, the area above excavation experienced bending failure, which resulted in the deformation of the rock mass to the lower right and the occurrence of a landslide.

5 Analysis of Slope Model Failure and Comparison with the Slope in the Field

5.1 Slope Model Failure Analysis

According to the failure characteristics of the physical model during excavation, the failure process of the slope can be divided into four stages: initial compression stage, crack generation stage, crack propagation stage, and sliding sur-face rupture stage.

5.1.1 Initial Compression Stage

By applying 0.2 MPa horizontal stress on both sides of the slope model, the width of joints between element plates was reduced and the slope model was further compressed. At this stage, there was no large displacement in the slope model,

(a) After loading (b) After excavation of the first layer (c) After excavation of the second layer

(d) After excavation of the third layer (e) After excavation of the fourth layer (f) After excavation of the fifth layer

(g) After excavation of the sixth layer (h) After excavation of the seventh layer

15.87

-15.01

Unit: mm

-7.29

0.43

8.15

20.43

-19.16

-9.26

0.64

10.53

36.77

-32.14

-14.91

2.32

19.54

40.82

-32.13

-13.89

4.35

22.58

42.85

-32.13

-13.39

5.36

24.11

46.88

-32.08

-12.34

7.40

27.14

52.88

-32.09

-10.85

10.40

31.64

62.43

-32.10

-8.47

15.17

38.80

Fig. 16 Horizontal displacement distribution in the physical model

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but some minor deformation and displacement occurred dur-ing the loading process. The temperatures on both sides of the slope increased because of the extrusion, but there was no significant temperature change in the other parts of the slope model. In general, the whole slope was stable.

5.1.2 Crack Generation Stage

With the excavation of the slope, the rock mass unloaded gradually, and the slope changed from the initial compres-sion state to the tensile state. The rock mass began to crack from the slope toe, and dislocation occurred in the upper part of the slope. At this stage, the slope deformed signifi-cantly (Fig. 19). As the excavation area was unloaded, the entire slope moved towards the free surface. Thus, the rock mass partially broke due to tension, and the temperatures of some local areas increased. At this stage, the entire slope was still relatively stable. Only a few tension cracks occurred

at the top of the slope, and a small number of shear cracks appeared around the excavation area.

5.1.3 Crack Propagation Stage

As the excavation of the slope continued, the stress redistri-bution inside the slope led to a gradual propagation of shear cracks, and the shear cracks extended from the surface of the slope to the deeper part of the slope. There was signifi-cant deformation and displacement of the slope, and bending occurred in some areas of the slope. Under the effects of stress redistribution and gravity, the rock mass in the failing area bended and moved downwards. Due to the structure of the anti-dip layered slope, the front rock mass was frac-tured and stacked in an imbricated way, but the back rock mass resisted the shear force. Therefore, V-shaped cracks appeared in the rock mass of the slope, with a flip angle of 10°–15°, and the temperature increased significantly in this




Unit: mm

35.24

-20.63

-6.66

7.31

21.27

24.45

-17.26

-6.83

3.60

14.02

18.30

-15.40

-6.98

1.45

9.88

14.85

-12.91

-5.97

0.97

7.91

10.87

-7.94

-3.24

1.47

6.17

7.90

-7.39

-3.57

0.26

4.08

5.57

-4.74

-2.16

0.42

2.99

4.46

-3.35

-1.40

0.56

2.51

Fig. 17 Vertical displacement distribution in the physical model


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Fig. 18 Plot of displacement vectors of the model at the different excavation stages

Fig. 19 Cracks on the slope model

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area (Fig. 20a). At this stage, the slope deformed signifi-cantly and shear cracks extended to the deeper part of the slope. Moreover, some cracks gradually connected and the potential shallow sliding surface began to appear (Fig. 20b).

5.1.4 Sliding Surface Formation Stage

When the seventh layer was excavated, some rock blocks near the sliding surface broke under the action of shear. Then, the bending zone of the rock mass propagated further to form a multi-stage flexural toppling zone with different depths. The bending zone was gradually formed from the slope toe to the top, and finally the deeper sliding surface was formed. The overall shear failure occurred along the bending zone, and the rock mass underwent a step-like

toppling collapse, with a flip angle of 47°, as shown in Fig. 21. At this stage, the development and formation of the bending zone caused the overall shear failure of the slope along the bending zone. The deeper sliding surface can be divided into two parts, the upper part with an angle of 54° and the lower part with an angle of 37o.

5.2 Comparison of Failure Characteristics Between Physical Model Slope and Field Slope

Through in-situ engineering geological investigation, it was found that the deformation process of the middle part of the slope in the north side of the Changshanhao open-pit mine experienced the following four stages: crack extension, formation of toppling-deformation, imbricated stacking of

Fig. 20 Cracks propagation in the slope model

Fig. 21 Toppling sliding failure in the slope model


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toppling rock mass, and collapse in the lower part of the toppling area. The evolution process of the toppling defor-mation showed unique characteristics, including the devel-opment of imbricated anti-dip steep ridge, wide distribution of dangerous rock mass, the oblique platform, and signifi-cant difference between slope deformations in different sec-tions. The landslide caused the slope in the elevation range of 1620–1604 m to sink by about 6 m (Fig. 22a). The back edge of the landslide was 30 m away from the slope edge at the top of the slope. The crack width at the trailing edge of the slope top was 1.0 m, and the top of the slope was top-pled into an irregular pattern. The volume of the primary landslide was about 1 × 106 m3, and the spreading range was about 0.5 × 106 m3. The displacement of the rock mass in the toppling area also showed significant regularity, which mainly included larger horizontal displacement compared to the settlement. Moreover, the direction of the slope displace-ment was approximately towards the pit base, as shown in Fig. 22.

The toppling deformation failure of the north slope was mainly due to the gravity stress in the rock mass, as well as other secondary causes such as the thrust of the top sliding

body and the excavation of the slope. The evolution process of the toppling failure of the slope in research area showed a complex mechanical mechanism, where shear cracks appeared at the bottom of the slope, and tension cracks appeared at the middle part and top of the slope (Fig. 23). According to deformation mechanism analysis, under certain rock mass structure conditions, the bending failure of the supporting layer at the slope toe constituted a critical fac-tor for the occurrence and development of toppling failure. Therefore, taking measures to increase the strength of the supporting layers at the slope toe can play a significant role in preventing toppling failure. In addition, the slope surface had an original dip angle of 65°, which became − 69° after the toppling deformation of the rock mass. This indicated that the rock formation was inverted over 46° (Fig. 24).

As shown in Fig. 25, under the action of excavation, the flip angle of the rock mass increased gradually to 47° when the toppling failure of the model occurred. The sliding surface was basically the polyline surface and the incli-nation angle of the upper line was larger than that of the lower part. In the field slope, the landslide back wall was erect, the front rock layer experienced toppling failure, and

Fig. 22 Toppling failure characteristics at the real slope in the mine site

Fig. 23 Cracks in the field slope in Changshanhao open-pit mine

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V-shaped cracks occurred at the top of the landslide area. Furthermore, the bending extrusion zone occurred at the bottom of the landslide area. According to the geophysical prospecting results, the depth of sliding surface was about 20–26 m, and two polylines formed the sliding surface. The average inclination angle of the upper polyline was about 43° and the average inclination angle of the lower polyline was about 20°. Overall, the failure characteristics

of the slope model were basically similar to those of the real field slope. Therefore, the physical model test of the anti-dip layered slope reasonably reproduces the toppling failure phenomenon of the field slope in Changshanhao mine. By monitoring the strain field, displacement field and temperature field during the failure process of the slope model, the failure mechanism of the anti-dip slope due to the excavation can be obtained.

Dip of the slope surface before excavation

Dip of the slope surface after excavation

Fig. 24 Geological investigation on the flip angle of rock mass

Fig. 25 Failure characteristics comparison between physical model slope and field slope


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6 Conclusions

A physical model of an anti-dip layered rock slope was built, which was used to investigate the deformation char-acteristics and failure mechanism of the anti-dip rock slope under the action of excavation. The following conclusions can be drawn from the current study:

1. Gypsum plates were constructed according to the designed material proportion scheme, and the physical model was built according to the characteristics of the field anti-dip slope. With the continuous excavation of the slope, the slope model was subjected to a large defor-mation, and the rock mass in the deformed area bended and moved downwards. This was due to the stress redis-tribution in the slope caused by excavation. Due to the structural characteristics of the anti-dip slope, the front rock mass was fractured and stacked in an imbricated way, but the back rock mass was able to resist the shear stresses. Thus, typical V-shaped cracks appeared in the rock mass of the anti-dip layered slope, with a flip angle of 10°–15°. When the seventh layer was excavated, the bending zone of the rock mass expanded further to form a multi-stage flexural toppling zone with different depths, and the bending zone was gradually penetrated from the slope toe to the top. Finally, the deeper sliding surface was formed. Overall shear failure occurred along the bending zone and the rock mass underwent a step-like toppling collapse, with a flip angle of 47°.

2. During the experiment, various measurement equipment was used to record the deformation and failure informa-tion of the model under excavation. Through the moni-toring results, the main deformation area of the slope under excavation was identified, and the horizontal and vertical displacements of the deformation area were measured. The difference in maximum strain between monitoring points in the same layer of strain gauges increased from the deep layer to the shallow layer. Dur-ing the process of slope stress adjustment, the rock mass near the excavation area broke, resulting in large defor-mation. The temperature of the deformation area gradu-ally increased, and finally rose from 27.04 to 28.85 °C, which was higher compared to the other stable areas, with a temperature difference of 1.53 °C. The monitored data can provide a conceptual model for describing the toppling failure mechanism of the slope in the Chang-shanhao mine under excavation. Such a model can help in understanding sliding depth, sliding surface shape and other failure characteristics. Therefore, the instability precursor of anti-dip slope can be obtained. Moreover, the instability location and depth of the slope can be speculated according to the failure characteristics in the

model experiment, and the corresponding reinforcement methods can be adopted to prevent and control the insta-bility of anti-dip slope.

3. According to the deformation characteristics, the anti-dip slope model behavior during the excavation can be divided into four stages: initial compression stage, crack generation stage, crack propagation stage, and forma-tion stage of the sliding surface. The comparison of the deformation characteristics of the model slope at each stage with the failure characteristics of the field slope obtained from engineering geological investigation and geophysical prospecting verified the rationality and accuracy of the physical model experiment. The top-pling failure phenomenon of slope induced by excava-tion in the Changshanhao mine was closely reproduced in the physical model, which can be used as a reliable reference for the follow-up treatment and reinforcement of anti-dip slope.

Acknowledgements This work was supported by the Key Research and Development Project of Zhejiang Province (Grant No: 2019C03104) and the Key Special Project of National Natural Science Foundation of China (No. 41941018).

Compliance with Ethical Standards

Conflict of Interest The authors have no conflict of interest to declare. This manuscript is approved by all authors for publication. I would like to declare on behalf of my co-authors that the work described is original research that has not been published previously.

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