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Journal of Rock Mechanics and Geotechnical Engineering. 2011, 3 (4): 352–372

Applications of rock failure process analysis (RFPA) method

Chun’an Tang*, Shibin Tang Institute for Rock Instability and Seismicity Research, Dalian University of Technology, Dalian, 116024, China

Received 29 March 2011; accepted in revised form 1 September 2011; accepted 10 September 2011

Abstract: Brittle failure of rocks is a classical rock mechanical problem. Rock failure not only involves initiation and propagation of single crack, but also is associated with initiation, propagation and coalescence of many cracks. The rock failure process analysis (RFPA) tool has been proposed since 1995. The heterogeneity of rocks at a mesoscopic level is considered by assuming that the material properties follow the Weibull distribution. Elastic damage mechanics is used for describing the constitutive law of the meso-level element. The finite element method (FEM) is employed as the basic stress analysis tool. The maximum tensile strain criterion and the Mohr-Coulomb criterion are utilized as the damage threshold. In order to solve the stability problem related to rock engineering structures, fundamental principles of strength reduction method (SRM) and gravity increase method (GIM) are integrated into the RFPA. And the acoustic emission (AE) event rate is employed as the criterion for rock engineering failure. The prominent feature of the RFPA-SRM and RFPA-GIM for stability analysis of rock engineering is that the factor of safety can be obtained without any presumption for the shape and location of the failure surface. In this paper, several geotechnical engineering applications that use the RFPA method to analyze their stability are presented to provide some references for relevant researches. The principles of the RFPA method in engineering are introduced firstly, and then the stability analysis of tunnel, slope and dam is focused on. The results indicate that the RFPA method is capable of capturing the mechanism of rock engineering stability and has the potential for application in a larger range of geo-engineering. Key words: case studies; rock slopes and foundations; stability analysis; rock failure

1 Introduction

With the development of deep mining of resources, hydropower, underground storage of nuclear waste, underground heat extraction from rocks, underground coal gasification, geological storage of CO2 and other underground engineering projects, studies on rock failure mechanism have attracted more attentions. Brittle failure of rocks is a complex process, which involves initiation and propagation of multi-crack. In fact, rock failure and instability have been difficult problems in solid mechanics. Earlier studies by senior scientists in China indicate that, for researches on solid materials under external loads and environmental conditions, the failure or damage process induced by evolution of defects in material is an interdisciplinary scientific problem, for which scientists in mechanics

Doi: 10.3724/SP.J.1235.2011.00352 Corresponding author. Tel: +86-13840899558; E-mail: [email protected]

Supported by the State Key Development Program for Basic Research of

China (2007CB209400), Projects of International Cooperation and Exchanges

NSFC (50820125405), and the National Natural Science Foundation of China

(51004020)

and material sciences would strive for a very long time [1].

Rock failure is induced by damage evolution of initial defects. The mechanical behaviors of rocks are determined by the internal mesoscopic structures, the mesoscopic damage and its evolution, and the development of cracks. Krajcinovic [2] indicated that the phenomenological model could not effectively deal with the mesoscopic damage process, which could only be overcome by using the mesoscopic mechanical models. Dougill et al. [3–9] and other researchers used damage mechanics to study the failure of rocks from different points of view. Furthermore, many researches established damage mechanics based method to study the behaviors of rocks at mesoscopic level. The relevant results are further extended to general brittle damage problems, and the researches on mesoscopic damage mechanics are continuously enriched.

It is generally recognized that the most important feature of rock material properties is the heterogeneity. Crack initiation and propagation in rocks are different from those in homogeneous media. Even rocks are simplified into homogeneous media (mesoscopic homogeneity) under some circumstances, various

Chun’an Tang et al. / J Rock Mech Geotech Eng. 2011, 3 (4): 352–372 353

macroscopic defects or impurities (macroscopic heterogeneity) in rocks lead to complex laws of crack propagation. With the increase in stress, these defects or impurities become the inducing sources of stress concentration. Crack initiation and propagation lead to increasing crack density and stronger interaction between cracks. The cracks eventually coalesce and result in macroscopic failure. Although the brittleness of rocks determines their failure characteristics, compared to homogeneous materials, such as glass, one of the most important differences is that rocks behave nonlinearly due to their heterogeneity. The brittle characteristics of rocks lead to catastrophic failure. On the other hand, the heterogeneity results in a progressive and evolutionary process before failure. To be more accurate, the failure process of rocks is progressive and catastrophic. The complexity of this process results in the complexity of rock damage mechanics. In view of rock heterogeneity, many researchers considered this feature by statistical distribution. Weibull [10] proposed a statistical theory of strength for brittle materials based on “the weakest-link model” in 1939, i.e. the Weibull distribution, which has been widely applied. At present, a great number of researches on rock damage and failure based on the Weibull distribution have been reported. Since 1995, the authors and their research group have been committed to study the rock failure process analysis (RFPA). Based on the statistical distribution method in rock material properties, mesoscopic damage theory and numerical computation method, a RFPA system was developed and applied to a great number of fundamental researches. The RFPA system is a numerical tool based on the elastic damage model and its theoretical foundation is the academic idea that the authors have been thinking for many years. In 1991, the authors proposed the assumption on the normal distribution of element strength at meso-scale for rocks [11, 12]. The mesoscopic heterogeneity was considered to be the root cause of the macroscopic nonlinearity of quasi-brittle materials. The heterogeneity of rock material and stochastic distribution of defects can be reflected by the statistical constitutive damage model. Thereafter, for the convenience of solution, the Weibull distribution was adopted to reflect the stochastic distribution instead of the normal distribution. The statistical distribution of material properties was integrated into the numerical methods such as finite element method (FEM). Elements that satisfy the given strength criterion were considered to be failed, and thus the numerical simulations of heterogeneous rock

material could be realized. This numerical simulation tool has been applied to numerical studies on the failure process of heterogeneous rocks and their acoustic emission (AE) characteristics [13–15], engineering problems such as movement of rock strata [16], development mode of seismic sources [17], and crack propagation in brittle and heterogeneous materials [18]. The simulation results are in good agreement with the experimental results.

Currently, the RFPA system has been widely used in geotechnical engineering. In this paper, applications of the RFPA system to geotechnical engineering are introduced. 2 Implement of engineering method in

the RFPA

In order to understand the failure mechanism of rock engineering structures, numerical methods, such as the FEM, boundary element method (BEM), and discrete element method (DEM), have been developed, and they have become increasingly popular for the stability analysis of the structures. It has shown that the numerical methods have a number of advantages over the traditional limit equilibrium approaches for stability analysis of rock engineering. Most importantly, the critical failure surface can be found automatically. Nevertheless, the currently widely accepted numerical methods do not take into account the heterogeneity of rock masses at macroscopic levels under complicated geological conditions. The heterogeneity plays an important role in determining the fracture paths and fracture patterns of rock masses. The influence of heterogeneity is pronounced on the progressive failure process [13, 19]. In the RFPA method, the Weibull distribution is used to consider the heterogeneity of rocks.

In order to solve the stability problem related to rock engineering structures, the fundamental principle of strength reduction method (SRM) and gravity increase method (GIM) are introduced into the RFPA. Mathematically, both of these two methods in the RFPA (RFPA-SRM and RFPA-GIM) are completely continuum-based methods, processing nonlinear and discontinuous failure mechanism problems. The code considers the deformation of a heterogeneous material containing randomly distributed micro-fractures. As loads are applied, the fractures will grow, interact and coalesce, resulting in nonlinear rock behavior and formation of macroscopic fractures. The RFPA-SRM and RFPA-GIM not only satisfy the global equilibrium,

354 Chun’an Tang et al. / J Rock Mech Geotech Eng. 2011, 3 (4): 352–372

strain-consistent and nonlinear constitutive relationship of rock and soil materials, but also take into account the heterogeneous characteristics of materials at microscopic and macroscopic levels. A tensile cutoff criterion is also incorporated to model tensile failure. The code has been successfully applied in failure process analysis of rock material.

(1) For the RFPA-SRM, as an alternative approach to the failure analysis problem related to geological or rock engineering, the fundamental principle of strength reduction is incorporated into the constitutive model of the element described above. The shear strength reduction technique [20] is applied to each element. The strength of element, 0f , is linearly degraded as follows:

trial trials 0 0/F f f (1)

where trialsF is the trial factor of safety, and trial

0f is the trial strength of the element. The trial strength trial

0f used in the RFPA-SRM is to investigate the strength of the geological media (in this case, the rock masses).

In this study, rock slope failure is examined. Slope stability simulation in the RFPA-SRM is run with the trial strength trial

0f until the critical failure surface in slopes is determined.

(2) For the RFPA-GIM, the critical failure surface of slopes is obtained by gradually increasing the gravity while keeping material properties constant. In the RFPA-GIM, the gravitation of the elements increases linearly. For each loading step, there is a corresponding trial gravitational acceleration trial

0g (m/s2). Referring to the definition of factor of safety in the finite element strength reduction technique [21, 22], the safety repertory factor trial

sF is defined as the ratio of the element gravitation in the failure state to the initial element gravitation, which can be written as

trial trials 0 0/F g g (2)

where 0g is the initial gravitational acceleration (m/s2). In the RFPA-GIM, slope stability analysis is run

with the trial gravitational acceleration trial0g until the

critical failure surface in the slope is determined. Several possible techniques can be used to define

slope failure, including the formation of critical failure surface, non-convergence of the finite element solution, etc. In the RFPA-SRM, the maximum AE event rate is used as the criterion of slope failure. Slope failure is commonly accompanied by a dramatic increase in the nodal displacement within the elements. Accordingly, there is a dramatic increase in the number of damaged elements. Monitoring AE event rates seems to be a good way of identifying the initiation and propagation of cracks and fractures in rocks. In quasi-brittle materials, such as rocks, AE is predominantly related to

the release of elastic energy. Therefore, as an approximation, it is reasonable to assume that the AE counts are proportional to the number of damaged elements and that all the strain energy released by damaged elements is in the form of AEs [14].

In the RFPA-SRM model, the AE counts are determined by the number of damaged elements and the energy release is calculated from the strain energy released by the damaged elements. Based on the above assumptions, the cumulative AE counts and the cumulative AE energy release can be realistically simulated using the RFPA-SRM model. Provided that the AE event rate reaches the maximum value, a macroscopic failure surface forms and slope failure occurs. Simultaneously, the corresponding trial

sF is the factor of safety, Fs, of the slope.

In the following sections, we present some engineering applications of the RFPA method to show the convenience of this method to analyze the stability of rock engineering.

3 Variation of deformation and stress at key places in the Baziling tunnel

3.1 Overview of geology and numerical model

The Baziling tunnel is located in Changyang County of Yichang City and Badong County of Enshi Tujia and Miao Autonomous Prefecture. The tunnel entrance is at Baziling Village, Langping Town, Changyang County, and the exit is at the east bank of the Sidu River, Liziyuan Village, Yesanguan Town, Badong County. The tunnel is designed as a forked tunnel. The entrance is designed as two separated tunnels and connected with the west end of the Baziling extra-long bridge. The exit is a twin-arch tunnel, only 20–30 m away from the bridge abutment of the Sidu extra-long bridge. The tunnel extends along WE in plan. As the stability in the forked section is of great importance, the RFPA is adopted to simulate the variations of deformation and stress at key places and the failure mechanism of the surrounding rocks in the Baziling tunnel.

In consideration of computational precision during numerical simulations, hexahedral elements are adopted in the model. The mesh is refined near the tunnel and is coarser at some distance away from the tunnel. In other words, the mesh is denser and smaller near the tunnel and coarser and larger at some distance away from the tunnel, which can better satisfy the computational precision. The forked tunnel is simulated by four models according to the stepwise excavation. The total number of elements in each model is about one million.


Figure 1(a) shows the model mesh after excavation and Fig.1(b) shows the local elastic modulus.

(a) Model mesh after excavation.

(b) Local elastic modulus (unit: MPa).

Fig.1 3D numerical models after tunnel excavation.

The surrounding rocks of the tunnel are of classes IV and V. It is relatively intact and contains no fault or fracture. The homogeneity index of rock masses is 8.0, which indicates relatively homogeneous distribution. As the model size is small, if the tunnel is excavated according to the actual excavation steps, the model excavation and installation of rock bolts are hardly implemented. Hence, the excavation steps are further simplified, and the numerical simulation is performed with four excavation steps. In the first step, half of the left tunnel is excavated (the 1st section); in the second step, half of the right tunnel is excavated (the 2nd section); in the third step, the other half of the left tunnel is excavated (the 3rd section); in the fourth step, the other half of the right tunnel is excavated (the 4th section). Excavation is then completed. 3.2 Simulation results and analysis

Figure 2 shows the distribution of the maximum principal stress during tunnel excavation obtained by

(a) The first excavation step. (b) The second excavation step.

(c) The third excavation step. (d) The fourth excavation step.

Fig.2 Distribution of the maximum principal stresses during tunnel excavation (unit: MPa).

the RFPA. Under the action of gravity, it can be observed that:

(1) Due to stress release after excavation, the surrounding rocks generally deform towards the tunnel. After certain computation steps, the floor rebounds due to stress release in the floor. The deformation is upwards due to squeezing in the vertical direction.

(2) The deformation is larger in the upper pillar between two tunnels and smaller at the bottom of the pillar. This shows that the pillar is subjected to high compressive stresses.

(3) The maximum principal stress is mainly concentrated on the bottom of the pillar. It can be seen from the distribution of failure zones at the four excavation steps that the subsidence at the fourth step is smallest, which indicates that the tunnel at the first step is the weakest in stability and likely to fail or collapse, and it is relatively stable at the fourth step.

Figure 3 shows the variation of crown displacement in the surrounding rocks with excavation steps. It can be seen that:

(1) After tunnel excavation, due to stress release around the tunnel, the surrounding rocks deform towards the tunnel. As the design load is mainly gravity, the tunnel deformation is predominantly the subsidence of tunnel crown. The vertical downward displacement of the tunnel crown is much larger than the horizontal displacement at the sidewall of the tunnel.

(2) The maximum displacement is 8 mm in the surrounding rocks after excavation, which occurs at the right arch of the twin-arch tunnel at the 1st section. The magnitude of tunnel deformation is generally small and satisfies the safety requirement of tunnel construction.

(3) The displacement at each section increases with the advance of tunnel excavation. When the tunnel is excavated to a certain section, the displacement at this section increases obviously. As the excavation face further advances, the displacement at this section still increases, however, by a smaller magnitude. (4) During excavation of the forked tunnel, obvious interaction between the left and right tunnels is


(a) Variation of displacement at the crown of the left tunnel.

(b) Variation of displacement at the crown of the right tunnel.

(c) Variation of displacement at the left sidewall of the left tunnel.

(d) Variation of displacement at the right sidewall of the right tunnel.

Fig.3 Variations of displacement in the surrounding rocks of the forked tunnel with excavation steps. observed. For instance, when the excavation of the left tunnel stops at a certain section and the excavation continues for the right tunnel, the deformation of the left tunnel still increases. Similarly, when the excavation of the right tunnel stops at a certain section and the excavation continues for the left tunnel, the deformation of the right tunnel increases as well. Therefore, the distance between the excavation faces of the left and right tunnels shall be controlled properly so as to reduce the effect of interaction between the left and right tunnels due to alternative excavation.

(5) The displacement at the twin-arch tunnel sections (i.e. the 1st and 2nd sections) is generally larger than that in the separated tunnel sections (i.e. the 3rd and 4th sections). As the left and right portions of the twin-arch tunnel are separated by a thin layer of concrete partition wall, the transversal distance between the left and right portions is relatively small. Therefore, the interaction

between the two portions is prominent. At the separated tunnel sections, the left and right tunnels are separated by thick rock wall and the transversal distance between the left and right tunnels is large. Hence, the interaction between them is weak. Therefore, the displacement at the twin-arch tunnel sections is greater than that at the separated tunnel sections. This shows that during tunnel design and excavation, the thickness of the wall between the left and right tunnels shall be optimized and ensured. The wall cannot be either too thick or too thin. The wall should be thick enough to effectively reduce the interaction between the two tunnels. However, it can not be too thick, which will result in much higher construction cost.

(6) With the advance of excavation, the tunnel deformation gradually becomes smaller from the twin-arch section to the separated tunnel section. The reason is that the interaction between the left and right tunnels becomes weaker as the thickness of the wall in the forked tunnel increases.

According to the above simulation results, in combination with the distribution and development of stress, displacement and AEs, the factors of safety after each excavation step are shown in Table 1. As seen from the simulation results, the factor of safety after the 1st excavation step is the highest, which indicates that the excavation of the half left tunnel has no significant effect on the stability of the surrounding rock. The factor of safety drops from 50 after the 1st excavation step to 10 after the 2nd excavation step, which indicates lower stability. The factors of safety after the 3rd and 4th excavation steps are close to that after the 2nd step.

Table 1 Factors of safety of the tunnel.

Excavation step Factor of safety

1 50

2 10

3 7.69

4 6.67

The calculation results indicate that: (1) Due to unloading after tunnel excavation, the

surrounding rocks deform towards the tunnel. Under the action of gravity, the deformation is predominantly the subsidence of the crown and heave of the floor. The vertical deformation is larger than the horizontal deformation. The displacement of the tunnel wall is relatively small after excavation, with the maximum deformation less than 10 mm. The overall deformation satisfies the safety requirement of tunnel construction.

(2) The large arch section of the forked tunnel is excavated in upper and lower benches. The twin-arch

7 Cro

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section (including the section with integrated partition wall and the section with sandwiched partition wall) is excavated by alternative half-section excavation of the left and right tunnels with central heading, and the separated tunnels are excavated by alternative excavation of the left and right tunnels. Adoption of various excavation methods leads to higher excavation efficiency, less repeated disturbances to the surrounding rocks, and enhanced overall stability of the surrounding rocks.

(3) With tunnel excavation, the radial stress in the surrounding rocks is released and the shear stress increases. The stress in the surrounding rocks is predominantly compressive stress. The maximum compressive stress is far less than the compressive strength of the rock mass. At the same time, due to excavation unloading, stress concentration occurs at the arch corners and crown, and the shoulder of the partition wall. However, the magnitude of stress concentration is small.

(4) During excavation of the forked tunnel, the interaction between the left and right tunnels is obvious, i.e. excavation of the left tunnel affects the right tunnel and vice versa. Therefore, the distance between the excavation faces of the left and right tunnels shall be properly controlled so as to reduce the interaction between the left and right tunnels during alternative excavation.

(5) With advance of the excavation face, the tunnel deformation gradually becomes smaller from the twin-arch section to the separated tunnel section. The reason is that the interaction between the left and right tunnels becomes weaker as the thickness of the partition wall or the rock pillar in the forked tunnel increases.

(6) By analyzing the variation of deformation and stress in the surrounding rocks and the failure mechanism of the overloaded tunnel, the designed factor of safety of the Baziling forked tunnel is 4.0 and the ultimate factor of safety is 7.0. It is shown that the design of the Baziling tunnel is safe and reliable and the surrounding rocks are overall stable.

4 Analysis of the minimum rock cover depth for the Jiaozhou Bay tunnel in Qingdao

4.1 Overview of geology and numerical model The Jiaozhou Bay tunnel in Qingdao is a major

channel connecting Qingdao City and its auxiliary cities. On the south is Xuejia Island and on the north is Tuan Island. The tunnel runs below the Jiaozhou Bay

mouth. The Jiaozhou Bay tunnel is an express road tunnel with six lanes in two directions and the design vehicle velocity is 80 km/h. Completion of the tunnel can fundamentally solve the temporary shortage, improve the investment environment in the west, speed up the development of new economic zone, realize the complementary advantages of the new and old port districts, and enhance the overall efficiency. It is a major engineering measure to provide strong support for Qingdao City to develop into a modern international city.

The RFPA system is employed to analyze the minimum rock cover depth for the Qingdao Jiaozhou Bay tunnel. Relevant theoretical and numerical studies are carried out to study the minimum rock cover depth for the Qingdao Jiaozhou Bay tunnel. The studies are performed according to the variation of geological strata along the longitudinal profile, especially those of some weak strata and structural zones. The minimum cover depth under different combinations of engineering geology, hydrogeology and construction method is proposed and the measures to reduce the minimum cover depth are suggested, which can provide some references for the tunnel alignment and design.

The plane strain model is adopted. In the model, the x-axis is perpendicular to the tunnel axis in the horizontal plane and the y-axis is along the vertical direction. The range of x-coordinate is 60 m < x < 60 m, the bottom boundary is 50 m below the tunnel floor, and the top is covered by the overburden layer. During RFPA simulations, the displacement at the tunnel crown is monitored with emphasis. 4.2 Simulation results and analysis

One of the key problems in stability analysis is how to judge whether the engineering structure is stable according to the calculation results. At present, there are mainly two types of criteria for instability:

(1) During modeling by the FEM, non-convergence of stress and displacement is used as the criterion for instability.

(2) The coalescence of plastic strain or damage zone is taken as the criterion for instability.

The structural instability is usually accompanied by large displacement. In modeling by the FEM, the number of failure elements inevitably increases. When the centrifugal loading method is adopted in the RFPA to find the factor of safety of the tunnel, the increment of displacement and the number of failure elements at the crown are taken as the joined criterion, which is simple and effective. Section ZK5+915 is taken as an example for illustration. Figure 4 shows the increment of displacement and the number of failure elements with


Fig.4 Increment of displacement and number of failure elements at the crown at section ZK5+915. the loading step during the failure process under centrifugal loading. It can be seen that at the 72nd step, a drastic change is observed in both the increment of displacement and the number of failure elements, which indicates that the global structural failure of the tunnel occurs at this step. At this moment, the factor of safety is 9.0.

Figure 5 shows the relationship between the rock cover depth and the factor of safety and crown displacement at some sections. It can be seen that the distributions of the calculated factor of safety and the crown displacement at each section generally exhibit the above-mentioned trend, with individual section having different trends.

Figure 6 illustrates the rock failure process of the tunnel with different cover depths by RFPA simulation.

(a) At section ZK4+919.

(b) At section ZK5+607.

(c) At section YK4+843.

(d) At section YK5+823.

(e) At section YK6+833.

Fig.5 Relationship between the rock cover depth and the factor of safety and crown displacement.

The minimum rock cover depth of the left and right

tunnels obtained by numerical simulations is listed in Table 2.

(a) Rock cover depth of 7 m.

(b) Rock cover depth of 13 m.

(c) Rock cover depth of 19 m.

0 1 2 3 4 5 6 7 8 9

10

5 10 15 20 25 30 351.01.1 1.21.31.41.51.61.71.8

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5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.09.5

10.0

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(d) Rock cover depth of 23 m.

Fig.6 The rock failure process of tunnel with different cover depths by the RFPA.

Table 2 The minimum rock cover depth of left and right tunnels determined by numerical method.

Tunnel No. Stratum Section Depth of

water (m)

Minimum rock

cover depth (m)

1 f2-3 ZK4+919 32.6 23

2 Intact rock ZK5+271 38.1 15

3 f3-1 ZK5+607 43.6 23


5 f4-1 ZK6+297 37.7 20


Left

tunnel

7 f4-3 ZK6+785 33.8 31

1 f2-3 YK4+843 27.2 29

2 Intact rock YK5+218 36.2 13


4 f3-2 YK5+953 43.2 33

5 f4-1 YK6+249 40.8 25


Right

tunnel

7 f4-3 YK6+833 32.1 29

With simulation and analysis of ten cross-sections (148 working conditions) by the centrifugal loading method incorporated in the RFPA system, the minimum rock cover depth at the controlling sections of the Jiaozhou Bay tunnel is suggested. In the numerical simulations, the increment of displacement and number of failure elements at the crown are taken as the joined criterion. The modeling results indicate that, for any cross-section of the subsea tunnel, the crown displacement first decreases and then increases with increasing rock cover depth. Hence, there is a minimum value for the crown displacement. In addition, the factor of safety obtained by numerical simulation features obvious regularity: for any cross- section of the subsea tunnel, the factor of safety first increases and then decreases with increasing rock cover depth. Hence, there is a maximum value for the factor of safety. The distribution trends of the factor of safety and crown displacement correspond to each other.

Therefore, it is reasonable and effective to determine the minimum rock cover depth corresponding to the maximum factor of safety and the minimum crown displacement. The minimum rock cover depth obtained by the RFPA can be a valuable reference for planning of tunnel vertical profile.

5 Stability analysis for enlargement excavation and undercut of west section of the headrace tunnels of Jinping II hydropower station in chlorite schist

5.1 Overview of geology and numerical model

The chlorite schist revealed at the west section of the headrace tunnels #1 and #2 of Jinping II hydropower station is of predominantly class IV surrounding rock. It has low strength and becomes softer in the presence of water. Hence, the tunnel deformation is large and the tunnel diameter becomes smaller than the designed size. A marble stratum exists between the two groups of chlorite schist, which irregularly distributes between the chlorite schist and sandstone. It exists in strips or lentoid shape and is of relatively good quality. This stratum is mainly of class III, with local class IV surrounding rock.

During tunnel construction in chlorite schist, due to the effect of high in-situ stresses and the inherent properties of chlorite schist, continuous deformation, damage in support structures and large-scale collapses occurred. Four large-scale collapses took place in the tunnel section during construction in chlorite schist, namely, once at stakes No.(1) 1+759 and (1) 1+941 in the headrace tunnel #1, and twice at stake No.(2) 1+643 in the headrace tunnel #2. The volume of collapsed rock in each event was 500–1 000 m3. A photo taken at the collapse site is shown in Fig.7.

Fig.7 Collapse in the west section of the headrace tunnels in chlorite schist.

After the deformation in some tunnel sections became

convergent and stable, it was measured. The results


indicated that large deformation occurred in chlorite schist, which led to the reduction in tunnel diameter. The deformation generally varied in the range of 20–60 cm, with some local deformation more than 1 m. The large deformation occupied the space of tunnel effective diameter. Secondary enlargement excavation was required so that the tunnel size could meet the design requirement. During the enlargement excavation, further disturbance led to damage and failure in the surrounding rocks. The stability was deteriorated and further large deformation or failure might occur. According to the magnitude of the maximum deformation towards the tunnel lining, the tunnel sections were divided into four classes, namely, the section with deformation less than 20 cm, 20–40 cm, 40–60 cm and greater than 60 cm. The RFPA system was then adopted to analyze the scheme for enlargement excavation and undercut of the tunnel in chlorite schist, which could provide some theoretical basis for construction design.

According to engineering practices and relevant theoretical analysis, excavation only influences the stress and strain in the surrounding rocks of a underground cavern within 3 to 5 times of excavation span (height) away from the center of the cavern. In the numerical simulation, the model boundaries are determined based on the following principles: (1) in the horizontal direction, the tunnel length at both sides is more than 5 times of the tunnel diameter; (2) in the vertical direction, the distances between the tunnel axis and the model top and bottom boundaries are more than 5 times of the tunnel diameter. The overburden rock layer is represented by an equivalent load on the top boundary. Therefore, the numerical model is square. The tunnel diameter is 14.3 m. Hence, the model dimension is calculated as 14.3 5 2 + 14.3 = 157.3 m, and an integral of 150 m is finally taken. The boundary conditions include a confining pressure of 29.8 MPa applied on the left and right boundaries, a vertical pressure of 39.51 MPa on the top boundary, and the shear stress is taken as 1.79 MPa. 5.2 Back analysis of parameters of the surrounding rocks

The disturbance from excavation of the upper bench in chlorite schist and the deformation of soft rock in the later stage lead to the softening of rock mechanical properties. Water used during construction and atmospheric humidity sometimes may result in argillitization of chlorite schist. Therefore, shotcrete was sprayed immediately after excavation of the upper bench so that the surrounding rocks could be isolated

from the external environments. No sufficient data on the rock mass parameters for the tunnel section in chlorite schist were collected, such as statistics on geological structures. The physico-mechanical properties of the tunnel in chlorite schist can hardly be determined during the theoretical and numerical analyses. In this study, back analysis is conducted to calculate the mechanical parameters of various deformed tunnel sections by the RFPA system in combination with the field monitoring data of displacements and the data of the loose zones. The simulation of enlargement excavation and undercut of tunnel is then performed.

According to the measured depth of loose zones, the range of loose zones is large for tunnel sections in class IV chlorite schist, which is generally 3–6 m, while that for tunnel sections in class IV intercalated chlorite schist and marble is relatively small, generally 2.5–4.0 m. For better safety during operation of tunnel sections in chlorite schist, the depth of loose zones is assumed uniform and has a value of 5 m in all tunnel sections under study. Due to the complex geological structure in engineered rock masses, the physico-mechanical properties distribute nonuniformly. Hence, the loose zones measured are not regular. However, in numerical simulations, the complex structures in rock mass cannot be considered individually and an average value of 5 m is taken. In addition, it can be seen from the monitoring data of deformation that the deformation in most tunnel sections becomes convergent within about 2 months.

Different maximum deformations towards the tunnel can be obtained by adjusting the initial deformation modulus of rock masses. Figure 8 show the relationship between the maximum deformation towards the tunnel and the initial deformation modulus of rock masses.

Fig.8 Relationship between the maximum deformation towards the tunnel and the initial deformation modulus of rock masses.

Figure 9 shows the designed tunnel cross-sections and

those after large deformation due to excavation under various initial deformation moduli. It can be seen from

1 2 3 4 5 6 7

Initial deformation modulus (GPa)

Max

imum

def

orm

atio

n (m

m)

0

100

200

300

400

500

600

700

Fitting line


Horizontal coordinate of the tunnel (m)

(a) Initial deformation modulus is 1.5 GPa, and the maximum deformation is

641 mm.


(b) Initial deformation modulus is 1.9 GPa, and the maximum deformation is

494 mm.


(c) Initial deformation modulus is 2.25 GPa, and the maximum deformation is

408 mm.

Fig.9 The deigned tunnel cross-sections and those after large deformation due to excavation under different initial deformation moduli.

the calculation results that, when the initial deformation modulus is 1.5 GPa, the maximum deformation towards the tunnel is more than 60 cm; when the initial deformation modulus is 6 GPa, the maximum deformation is less than 20 cm. Comparing the simulated deformation with the measured deformation

at site, the following deformation modului are taken for analysis of enlargement excavation and undercut: 1.5 GPa for sections with deformation more than 60 cm, 1.9 GPa for sections with deformation of 50–60 cm, 2.25 GPa for sections with deformation of 30–50 cm, 4.5 GPa for sections with deformation within 20–30 cm, and 6 GPa for sections with deformation in the range of 0–20 cm.

Figures 10 and 11 shows the evolutionary processes of deformation modulus and stress field during formation of loose zones in the tunnel sections with the final deformation towards the tunnel more than 60 cm (the initial deformation modulus is 1.5 GPa). As seen from the stress field evolution, the loose zones develop from the tunnel periphery to deeper rock masses. The stress in the support system gradually increases. The support system plays an effective role in protecting the tunnel from further deformation and reduces the time to deformation convergence. The change of deformation modulus in Fig.10 reflects the formation process of loose zones. As chlorite schist is a kind of soft rock, the formation of loose zones partially attributes to the excavation disturbance to the stress field and also the deterioration of material properties due to the rheological effect of chlorite schist.

Fig.10 Softening of deformation modulus during formation of loose zones.

Fig.11 Variation of shear stress in surrounding rocks and support system during formation of loose zones. 5.3 Stability analysis of tunnel undercut

The tunnel sections at the west of Jinping II hydropower station in chlorite schist were excavated in the upper and lower benches, i.e. the upper bench (8.5–9.3 m) was excavated and then the lower bench (4.5–5.3 m) was excavated. For the tunnel undercut, the deformation

14

0

2

4

6

8

10

0 2 4 6 8 10 12

Designed tunnel cross-section

Tunnel cross-section after

large deformation

Ver

tical

coo

rdin

ate

of th

e tu

nnel

(m

)

14

0

2

4

6

8

10

0 2 4 6 8 10 12


Tunnel cross-section

after large deformation

Ver

tical

coo

rdin

ate

of th

e tu

nnel

(m

)

0

2

4

6

8

10

0 2 4 6 8 10 12 14


Tunnel cross-section after

large deformation

Ver

tical

coo

rdin

ate

of th

e tu

nnel

(m

)


and stress in the surrounding rocks during the left and right half-width excavation are analyzed.

Figure 12 shows the maximum deformation at cross- sections with various deformation moduli due to the left and right half-width undercut. Figure 13 exhibits the model evolutionary process during undercut. It can be seen that the maximum deformation caused by undercut and the deformation modulus have a negative exponential relationship. The maximum deformation due to the left half-width excavation is greater than that caused by the right half-width excavation. This is because that the support installed after the left half-

(a) The maximum deformation due to the left half-width undercut.

(b) The maximum deformation due to the right half-width undercut.

Fig.12 The maximum deformation due to the left and right half-width undercut at cross-sections with different deformation moduli.

Fig.13 Model evolutionary process during the left and right half-width undercut.

width excavation restricts the deformation during the right half-width excavation. This shows that the current support scheme for the left half portion has played an effective and reliable role in restricting the deformation. At the section with the maximum inward deformation more than 60 cm, the maximum deformation caused by the left half-width undercut reaches about 160 cm. However, when the upper bench and left half portion are supported, the maximum deformation caused by the undercut of the right half portion is reduced to about 80 cm. With the left and right half-width excavation method, the maximum deformation occurs at the left and right sidewalls of the undercut portion. During the left half-width portion excavation, relatively large deformation occurs at the left sidewall of the undercut portion. During the right half-width excavation, the deformation is relatively small as the left sidewall has been supported and the maximum deformation occurs at the right sidewall.

It can be seen from the above analysis that, as the left half portion is supported timely after excavation, the support and the lining for the upper bench form an integral support system, thus the deformation in the surrounding rocks is controlled. Meanwhile, it ensures the safety of the undercut of the right half portion. Therefore, the left and right half-width excavation method is favorable for controlling deformation in the surrounding rock and enhancing the tunnel safety. However, it should be noted that, as the construction procedures are relatively complex with the left and right half-width excavation, the construction space is relatively narrow, and the excavation speed is restricted. After the stepwise excavation, the support system shall be installed in steps as well. The support system shall be connected effectively after the left and right half-width excavation. As the support is installed timely after undercut, further deformation is restricted. Especially, the shotcrete sprayed after undercut has effectively prevented the deterioration of the surrounding rock due to the effect of air humidity and water used during construction. When the left and right half-width excavation scheme is adopted, the proportion of the left and right parts can be adjusted properly to increase the operation space, improve the construction speed, and ensure the construction quality. 6 Stability analysis of open-pit slope in Jinfeng gold mine 6.1 Geological survey and model introduction

At present, Guizhou Jinfeng Mining Co., Ltd. mainly depends on the open-pit production. With the increase

0

20

40

60

80

0 1 2 3 4 5 6 7

Deformation modulus (GPa)

Max

imum

def

orm

atio

n (m

m)

Max

imum

def

orm

atio

n (m

m)

0

40

80

120

160

200

0 1 2 3 4 5 6 7Deformation modulus (GPa)

Fitting line

Fitting line


of open-pit mining for upper ore body, intensive landslide damages occur continuously in the three mining benches of slopes in the north of the open-pit, which poses a great safe threat to the lower ore body and negatively affects the production schedule of open-pit mine. Therefore, reasonable controlling measures should be proposed through site investigation, scientific computation and analytical research.

In this part, detailed analysis of the ultimate strength of slope with 14 standard benches is conducted to eliminate the dependence of strength parameters on project computational scale, which makes the safety assessment focus on different sections’ profile. The geometrical size of computational model is designed according to the original parameters of open-pit slope, while the specific bench is not concerned in this group of model. The three-bench height model is taken for case study.

The ore body and surrounding rock in deposits of Jinfeng gold mine mainly consist of sandstone and clay. According to the experimental data from geological material, the physico-mechanical parameters are shown in Table 3. 6.2 Stability analysis of slopes

This section builds a two-dimensional (2D) model for stability analysis of slopes in Jinfeng open-pit gold mine, makes numerical computation and gives a full and integrated assessment on the original design parameters. Based on the evaluated results, the parametric optimization has been made and the secondary calculation and analysis have been performed to check rationality and validity of parametric optimization, which offers a scientific foundation for safe design of slopes in mining area.

The geological profile of Jinfeng mining area is shown in Fig.14. The calculation and analysis in this section mainly concern 13 profiles: 1560, 1600, 1640, 1680, 1720, 1760, 1800, 1840 and 1920 along the west-east direction, 1200 and 1250 along the north-south direction, and S-N-1 and S-N-2 along the supplemental direction. In every profile, analysis will be made according to the real elevation and slope angle.

The safety coefficients of these sections are shown in Table 4. The failure processes of section mg-sec1a- 1560-west, mg-sec1a-1680-east and mg-sec1a-1200-north are shown in Fig.15(a)–(c), respectively. 6.3 Conclusions and suggestions

This study has built up mechanical models for open-pit slopes through site investigation and analyses of existing geology and mining material, and made an assessment on the stability of the open-pit slopes. The following suggestions and plans for the design parameters of the open-pit slope are put forward.

(1) The ultimate height of the slope in open-pit mining area is more than 300 m, which belongs to the medium or high slope. But the present slope angle seems to be chosen conservatively. Increasing the overall slope angle in eastern, southern and western areas is advised. Numerical results are shown in Table 5.

(2) The reasons of three benches’ falling in the northern area are mainly the weathering of geological structure and earth surface. After three benches falling from elevation 700 to 750 m, the second bench falling will not happen in two months, so it has little influence on the slope’s overall stability and the bench wall angle can keep its original state. The recommended bench wall angle is 60–65.

(3) During the open-pit mining, it shows that the width of bench can affect not only the angle but also the stability of slope, so it is advised to be adjusted by level based on the original design parameters. The recommended width of bench at depth of 560 m from the ground is 11–12 m, while that at the position deeper than 560 m is 8 m. 7 Stability analysis of the left slope of Jinping I hydropower station 7.1 Overview of geology and numerical model

Jinping I hydropower station is located in Yanyuan County and Muli County of Liangshan Yi Autonomous Prefecture, Sichuan Province. It is the controlling reservoir cascade in the development and plan of hydropower on the middle and lower reaches of the Yalong River, and plays an important role of “connecting

Table 3 Physico-mechanical parameters of rocks.

Strength (MPa) Rock

Dry Saturated

Density

(kg/m3) Cohesion (MPa) Friction angle

Secant modulus

(GPa)

Poisson’s

ratio Remark

Sandstone 26.49–59.92 18.18–40.41 2 799 10.09–19.98 26°39–38°56 1.08–10.8 0.13–0.25

Sandston 59.92 40.41 2 776 16.64–12.59 37°31–38°56 10.8 0.16 Ore

Clay 21.09 11.51 2 842 3.78–5.31 38°31–40°55 15.04 0.28

Clay 21.09–37.21 3.46–11.51 2 834 3.69–5.71 29°04–40°55 10.27–17.87 0.14–0.28

Saturated-dry


Fig.14 Space diagram of ground drilling profile.

Table 4 Safety coefficients of selected sections.

Section Model size

(m m) Slope angle

() Safety

coefficient

mg-sec1a-1560-east 240 80 31.03 1.92

mg-sec1a-1560-east 230 139 47.81 1.22

mg-sec1a-1560-west 49 286 44.70 1.33

mg-sec1a-1600-east 220 80 36.78 1.67

mg-sec1a-1600-east 230 150 49.09 1.18

mg-sec1a-1600-west 492 280 38.13 1.79

mg-sec1a-1640-east 184 70 33.94 1.72

mg-sec1a-1640-east 219 150 51.57 1.15

mg-sec1a-1640-weat 476 250 42.20 1.47

mg-sec1a-1680-east 200 80 37.04 1.43

mg-sec1a-1680 east 216 140 50.36 1.2

mg-sec1a-1680-west 478 220 38.36 1.54

mg-sec1a-1720-east 240 100 35.54 1.7

mg-sec1a-1720-east 186 100 48.33 1.52

mg-sec1a-1720-west 352 160 38.52 1.53

mg-sec1a-1760-east 150 60 33.69 1.56

mg-sec1a-1760-east 249 120 37.22 1.59

mg-sec1a-1760-west 304 124 30.68 1.82

mg-sec1a-1800-east 356 180 35.11 2.08

mg-sec1a-1800-west 290 108 32.28 1.75

mg-sec1a-1840-east 156 80 37.04 2.7

mg-sec1a-1840-west 104 40 36.53 3.45

mg-sec1a-1920-east 121 40 29.4 4.55

mg-sec1a-1200-south 207 150 43.69 1.41

mg-sec1a-1200-west 262 160 44.64 1.61

mg-sec1a-1200-north 115 67 45.87 1.32

mg-sec1b-1250-south 110 71 49.80 1.12

mg-sec1b-1250-south 120 89 51.42 1.08

mg-sec1b-1250-north 270 154 42.17 1.61

hydropower on the middle and lower reaches of the Yalong River, and plays an important role of “connecting link” during the rolling development of cascade reservoir along the Yalong River. The mainstream of the Yalong River from Xiayi Temple to the estuary is 1 386 km long and the natural elevation drop is 3 180 m. 21 cascade hydropower stations are preliminarily designed on the mainstream, among which the Lianghekou cascade hydropower station is the leading reservoir and has the capacity of multi-year regulation. Jinping I hydropower station is the controlling reservoir

Displacement vector Stress evolutionary process

(a) Computational results of section mg-sec1a-1560-west.

Displacement vector Stress evolutionary process

(b) Computational results of section mg-sec1a-1680-east.

Displacement contour map Stress evolutionary process

(c) Computational results of section mg-sec1a-1200-north. Fig.15 Failure processes of sections mg-sec1a-1560-west, mg-sec1a-1680-east and mg-sec1a-1200-north.


Table 5 Recommended slope angles.

Slope zone Location Slope angle (°) Above 560 m 45

North Below 560 m 49.6

North of ore body East

South of ore body 45

South and west 45

in the lower reach of the Yalong River. It has the capacity of one-year regulation and can provide good compensation for its downstream cascade hydropower stations. Jinping I hydropower station is located in a typical deep-cut V-shaped valley. The relative elevation drop of the two banks reaches 1 500–1 700 m. The geological structure is an overturned syncline. The attitude of the rock strata is N15–60E/SE35–45 and the strike is approximately consistent with the direction of the river. The bedrock is mainly upper and middle Triassic metamorphic rock of Zagunao group (T2-3Z), namely, chlorite schist (T2-3Z1), marble (T2-3Z2) and sandy slate (T2-3Z3). The slope on the left bank is an inversed slope, consisting of marble below elevations of 1 820–1 900 m with slope angles of 55–70, and sandy slate above 1 820–1 900 m with slope angles of 40–50. The slope features micro-topography of ridge and shallow gully.

The RFPA system is adopted to preliminarily investigate the stability and possible instable regions in the natural slope and reinforced slope on the left bank. The regions requiring support and particular reinforce-ment are identified. The stability of the slope and reinforcement measures are analyzed for two cross- sections. The 2D RFPA finite element models for cross-section 1-1 in the left slope are shown in Fig.16, considering two working conditions, namely, natural slope and reinforced slope. The models are 480 m long (from the center line of the riverbed to the left bank) in the horizontal direction perpendicular to the river and 320 m wide in the vertical direction (elevations from 1 610 to 1 930 m). The unloading, weathering boundaries, interfaces between different rocks, rock dikes and faults such as f2, f5 and X, and fractures are simulated in details in the RFPA models. The models

(a) Model for natural slope.

(b) Model for reinforced slope.

Fig.16 RFPA finite element models for cross-section 1-1 in the left slope.

are divided into 480 × 320 = 153 600 elements.

Figure 17 shows the 2D RFPA finite element models for cross-section 2-2 in the left slope, including natural slope and reinforced slope. The models cover 550 m (from the center line of the riverbed to the left bank) in the horizontal direction perpendicular to the river and 330 m in the vertical direction (elevations from 1 610 to 1 940 m). The unloading, weathering boundaries, interfaces between different rocks, rock dikes and faults such as f2, f5 and X, and fractures are also simulated in details in the RFPA models. The models are divided into 550 × 330 = 181 500 elements.

(a) Model for natural slope.

(b) Model for reinforced slope.

Fig.17 RFPA finite element models for cross-section 2-2 in the left slope in the atomization area.

7.2 Simulation results and analysis 7.2.1 Cross-section 1-1 in the left slope

Figure 18 shows the evolutionary process of shear stress in the cross-section 1-1 in the left slope obtained

Dike X

Fault f2

Boundary Fault f5

f

AnchorsFault f2

Fault f5

Dike X

Boundary

X dike Dike X

Fault f2

Boundary

Fault f5

Anchors

Fault f2

Fault f5

Dike X

Boundary


Fig.18 Simulation results for cross-section 1-1 in natural slope by the RFPA.

by the RFPA. The results indicate that:

(1) Generally, the horizontal deformation in cross- section 1-1 is towards the river valley and the vertical deformation is downwards. By the SRM, the natural slope becomes unstable at the step 36 and the corresponding factor of safety is 1.562 5. It shows that the left slope is safe and stable under natural condition.

(2) In combination with the distribution of failure zones and shear stresses from numerical simulations, especially the AEs captured by the special function of the RFPA, it can be seen that, when the slope strength is further reduced, a large amount of shear failure occurs in the porphyry dike X, accompanied with some tensile failure. This shows that local small deformation would occur in the faults and slightly weathered zones such as f5, f8 and X even before excavation and affects the stability of the natural slope.

(3) The slope instability evolves and develops along large faults and weak zones. Therefore, the faults and weak zones in rock slopes are important for the slope stability analysis.

Figure 19 shows the shear stress distribution in

Fig.19 Simulation results for cross-section 1-1 in reinforced slope by the RFPA.

cross-section 1-1 in the reinforced left slope obtained by the RFPA. As the slope excavation is not considered, the effect of excavation on slope instability is not introduced here. This paper aims at studying the instability mechanism of typical cross-sections in the left slope in the atomization area. By comparison with the spatial characteristics of the microseismic monitoring results, the stability of the left slope can be evaluated preliminarily. The simulation results indicate that:

(1) Generally, the horizontal deformation in cross- section 1-1 in the reinforced slope is still towards the river valley and the vertical deformation is downwards. By the SRM, global failure occurs in the reinforced slope at the step 45 and the corresponding factor of safety is 1.818. It can be seen that the factor of safety increases by 0.255 5 after reinforcement. It shows that current reinforcement scheme with anchor cables is feasible and can improve the local and global stability of the slope, and enhance the safety reserve of the slope in the atomization area.

(2) As seen from the failed model, the instability still develops along the fault f5. At 25 steps after the step 45, the model is fractured along the interface between the rock strata. This shows that the faults and the interfaces between weak rock strata have great influences on stress and strain of the slope in the atomization area. Meanwhile, it can be found that, except that two long anchor cables near the bottom of the dam platform at the elevation 1 885 m pass through the fault f5 and can effectively reinforce the slope during failure process, almost all the anchor cables are outside the potential slip surface. Hence, they cannot effectively prevent the whole slope from slip. Therefore, it is suggested to extend the anchor cables in the slope in the atomization area below the elevation 1 885 m appropriately (especially those above the elevation 1 810 m) to pass through the fault f5 so as to ensure the safety of the slope.

(3) As the hanging walls of the fault f5 and the dike X are on the large platform at the elevation 1 885 m, if no anchorage is applied or the safety reserve is low after reinforcement, the faults f5 and f2 and the interfaces between weak rock strata can form a potential slip body, which will become a potential threat to the slope stability in the atomization area. 7.2.2 Comparison between the microseismic monitoring data and RFPA simulation results in terms of spatial distribution

The size effect of seismic sources on the cross-section 1-1 in the left slope in the atomization area obtained by the microseismic monitoring is shown in Fig.20. Figure 21 shows the apparent seismic deformation region, and Fig.22 shows the energy loss density nephogram


Fig.20 The size effect of seismic sources on the cross-section 1-1 in the left slope in the atomization area obtained by the microseismic monitoring.

Fig.21 Apparent seismic deformation region of microseismic events in the slope in the atomization area.

Fig.22 Energy loss density nephogram and distribution region of microseismic events in the slope.

and spatial distribution. Figure 21 indicates that the apparent seismic deformation region in the cross-section 1-1 mainly distributes at the elevation 1 580–1 785 m and along the faults f5, f8 and dike X. Large deformation concentrates at the position 80 m away from the slope surface at the elevation 1 650–1 730 m. Figure 22 shows that the large micro-fracturing energy loss density due to unloading also concentrates near the elevation 1 730 m and the dam foundation. It can be seen that most microseismic events due to unloading-induced compressive and shear failure occur between the elevation 1 785 m and the dam foundation.

As seen from Fig.23, at the cross-section 1-1 in the left slope in the atomization area, the potential slip surface based on the SRM and the spatial distribution of AEs in hard rock slope are consistent with the spatial distribution characteristics of microseismic events captured by the microseismic monitoring technique. Tensile failure takes place at the slope top and shear failure occurs at the slope toe. The dense AE region induced by shear failure in the slope modeled by the RFPA system is consistent with microseismic events with high energy release and large magnitude concentrating within the elevation 1 600–1 785 m in terms of spatial distribution. The microseismic events evolve and develop continuously along the footwalls of faults f5 and f8 and dike X. However, at present, the apparent seismic deformation and energy loss due to micro-fracturing are relatively small, and the potential microseismic events distributing in strips along the dam abutment trench will not threat the overall stability of the slope.

Fig.23 Comparison of spatial distribution of microseismic events and potential slip surface obtained by the RFPA for the slope in the atomization area.

Microseismic events distribution along the dam

Surface of left slope

Potential slip surface obtained by the RFPA

Microseismic events distribution obtained by the RFPA


7.2.3 Cross-section 2-2 in the left bank

Figure 24 shows the shear stress distribution in cross-section 2-2 in the natural left slope. From the simulation results, it can be seen that:

Fig.24 Simulated shear stress distribution in cross-section 2-2 in natural slope.

(1) Generally, the horizontal deformation in the cross-section 2-2 is still towards the river valley and the vertical deformation is downwards. During RFPA simulation with the SRM, macroscopic failure occurs in the slope at the step 40. The corresponding factor of safety is 1.667. It shows that the cross-section 2-2 in the natural slope in the atomization area is safe and stable without human disturbances.

(2) As seen from the failure mode of the model, the potential slip surface initiates, propagates and coalesces downwards along the fault f5. At the interface between the fault f5 and the weak rock stratum near the elevation 1 710 m, the slip surface extends to the rock dike X. Then, it gradually develops along the interface between rock strata until the fault f2 at the slope toe at the elevation 1 700 m. Finally, a huge potential slip block, delimited by the fault f5 as the hanging wall and the interface between rock strata and the fault f2 as the footwall, is formed.

Figure 25 shows the shear stress distribution in the

Fig.25 Simulated shear stress distribution in cross-section 2-2 in reinforced slope.

cross-section 2-2 in the reinforced left slope. It can be seen that:

(1) Generally, the horizontal deformation in the cross- section 2-2 in the reinforced slope is still towards the river valley and the vertical deformation is downwards. During RFPA simulation with the SRM, the potential slip surface coalesces and macroscopic failure occurs in the slope at the step 48. The corresponding factor of safety is 1.923, which increases by 0.256 after slope reinforcement. It shows that the current reinforcement scheme with anchor cables is feasible and can improve the local and global stability of the slope, and enhance the safety reserve of the slope in the atomization area.

(2) As can be seen from the failed model, the slope instability still develops along the fault f5. At 20 steps after the step 48, the model fractures along the interfaces between the rock strata. This shows that the faults and the interfaces between weak rock strata have great influences on the stress and strain of the slope in the atomization area. With further strength reduction, due to the effect of the fault f2 at the elevation 1 700 m, at 21 and 23 steps after the step 48, a huge potential slip block, delimited by the fault f5 as the hanging wall and the interfaces between shallow weak rock strata and the fault f2 as the footwall, is formed in the cross-section 2-2.

(3) After the cross-section 2-2 is reinforced with anchor cables, the anchor cables basically pass through the fault f5, which induces the potential slip surface obtained by the SRM in the RFPA and can provide effective anchorage for the fault f5. The simulation results also indicate that the factor of safety is increased drastically after slope reinforcement. However, it can be seen that the anchor cables are too short to pass through the fault f5 below the elevation 1 835 m, and the anchorage effect is not perfect. During validation of stability evaluation in the later stage, if the factor of safety cannot meet the operation requirement, more longer anchor cables shall be arranged appropriately in the slope above the elevation 1 835 m so as to enhance the safety reserve of the slope.

8 Simulation and analysis of Xiluodu arch dam with refined model

8.1 Overview of geology and numerical model Xiluodu hydropower station is located on the Xiluodu

Gorge between Leibo County of Sichuan Province and Yongshan County of Yunnan Province. It is the third cascade hydropower station developed on the Jinsha River. Its superstructure is a double-curvature arch dam (the azimuth of the center line of the arch is N48.2W). The elevations of crest and foundation are 610 and


332 m, respectively, and the maximum dam height is 278 m. It can sustain thrust force by about 1.3108 kN water, which requires the foundation to have the corresponding bearing capacity. The normal water level is 600 m and the dead water level is 540 m. The total reservoir capacity is 11.57109 m3 and the regulating storage is 641.6109 m3. It is an incomplete annual regulating reservoir. The total installed capacity is 12.6 GW. The station is designed as a huge hydropower station to provide power generation, control sediment and flooding, and improve navigation downstream.

A 3D model is employed in this study. Taking the dam axis as the center, the computation range is about one dam height towards the upstream direction, about 2.5 times of the dam height towards the downstream direction, and about 2 times of the dam height towards the left and right river banks, respectively. The depth of the foundation is taken about one time of the dam height. The model meshes are generated according to the horizontal profile provided by HydroChina Chengdu Engineering Corporation. Eight-node hexahedral elements are employed in the model. The total number of elements is 3 316 704 and the total number of nodes is 3 578 648. The number of elements for the dam is 1 601 192. The model meshes are shown in Fig.26.

Fig.26 Model meshes used for numerical simulations.

8.2 Loading conditions The following loads are considered in the simulation: (1) In-situ stresses. Only gravity is considered. (2) Deadweight of the dam. The bulk density of

concrete is 2 400 kg/m3, the elastic modulus is 24 GPa, and the Poisson’s ratio is 0.17.

(3) Water pressure. The upstream normal water level is 600 m and the corresponding downstream water level is 378 m (381 m when 18 power generation units are in operation). The dead water level is 540 m and the corresponding downstream water head is 378 m. The upstream check flood level is 607 m and the corresponding downstream water level is 414.61 m.

The upstream design flood level is 600.7 m and the corresponding downstream water level is 409.78 m.

(4) Sediment load. The elevation of upstream sediment is 490 m, the buoyant density of sediments is 500 kg/m3, and the internal friction angle is 0º. 8.3 Simulation results and analysis

The RFPA3D is employed to simulate normal and special loading combinations. It can be seen from Fig.27 that, under normal loading condition I (in-situ stresses + deadweight of the dam + upstream normal water level + corresponding downstream water level + sediment load), the maximum deformation of the dam crest is 132.5 mm along the river direction, occurring at the elevation 610 m; the maximum deformation of the left arch is 27.7 mm towards the river direction, appearing at the downstream side at the elevation 340 m; the maximum deformation of the right arch is 25.5 mm towards the river direction, appearing at the downstream side at the elevation 450 m.

(a) The displacement of downstream dam crest.

(b) The displacement of upstream dam crest.

Fig.27 Displacement of downstream and upstream dam crests of the Xiluodu arch dam along the river direction under normal loading condition I.

As seen from Fig.28, under the normal loading condition II (in-situ stresses + deadweight of the dam + upstream dead water level + downstream minimum tail water level + sediment load), the maximum deformation at the dam crest is 85.92 mm along the river direction, occurring at the elevation 450 m; the maximum deformation of the left arch is 16.8 mm towards the river direction, appearing at the downstream side at the elevation 360 m; the maximum deformation of the right arch is 18.2 mm towards the river direction, appearing at the downstream side at the elevation 360 m.


(a) The displacement of downstream dam crest.

(b) The displacement of upstream dam crest.

Fig.28 Displacement of downstream and upstream dam crests of the Xiluodu arch dam along the river direction under normal loading condition II.

The deformation in the direction perpendicular to

the river under special loading conditions is listed in Table 6.

Table 6 The deformation in the direction perpendicular to the river under special loading conditions.

The maximum deformation Special loading condition

Location Value (mm) Location

Left abutment 10.5 The elevation 560 m,

downstream face

Arch crown 5.6 The elevation 500 m,

upstream face I

Right abutment 9.9 The elevation 520 m,

downstream face


downstream face


upstream face II


downstream face


downstream face


upstream face III


upstream face

The simulation results indicate that: (1) Under the normal loading conditions, the

displacement of the arch dam distributes evenly and symmetrically. The maximum displacement of the dam crest in the river direction is 132.5 mm at the elevation 610 m. The maximum deformation of the left arch is 27.7 mm towards the river direction, appearing at the downstream side at the elevation 340 m. The maximum deformation of the right arch is 25.5 mm towards the river direction, appearing at the downstream side at the

elevation 450 m. The maximum deformation in the arch foundation is 25.5 mm, appearing in the right arch at the elevation 440 m. The relative displacement in the shear zones is small. The normal loading condition I is the controlling loading condition in various combinations of basic loadings.

(2) Under special loading condition II (in-situ stress + deadweight of the dam + upstream check flood water level + corresponding downstream water level + sediment load), the maximum deformation at the dam crest is 149.7 mm along the river direction; the maximum deformation of the left and right arch is 25.1 and 271 mm, respectively, towards the river direction. This loading condition is the controlling loading condition among various special loading conditions.

(3) During pouring of concrete at the elevation 410–440 m, the dam crest moves towards the upstream direction with the maximum value of 2.6 mm. The displacement is towards the downstream direction in other stages. 9 Numerical study of unloading-induced strainburst 9.1 General description

Rockburst is defined as damage to an excavation that occurs in a sudden or violent manner and is associated with a seismic event [23]. It is observed that a rockburst often occurs in brittle hard rock subjected to high in-situ and/or mining-induced stresses, and is associated with a sudden release of strain energy accumulated in the rock as a result of rock failure. The occurrence of rockburst depends on many factors, such as geology, mining conditions (including geometry of underground openings, excavation method and sequence, etc.), and stress condition. It is generally recognized that geology and stress are the two major factors that dictate the occurrence of a rockburst.

Due to the complexity of the rock and the unloading-induced rock failure process, there is little knowledge about the strainburst process, from micro-cracking to impending unstable rock failure and associated energy release. In this paper, the RFPA is firstly adopted to conduct numerical tests on square granite samples under uniaxial compressive loading, followed by unloading tests under biaxial loading. In addition, the mechanism of strainburst induced by unloading during tunnel excavation in layered rock masses is investigated. A better understanding of the rock failure process under unloading is important for rockburst prediction and prevention in underground construction.


9.2 Modeling results of strainburst under unloading from high confining pressure

The mechanical behavior of rock mass under unloading condition is of great importance for underground construction at depth. It has been recognized by many researchers that a rockburst, in terms of its mechanism, results from catastrophic tensile or shear/tensile failure due to a sudden release of a large amount of elastic strain energy stored in the failed rock itself and the surrounding rocks during excavation and unloading, or stress change due to nearby mining. In this study, the mechanism due to sudden unloading is studied using the RFPA.

In the simulation model, an initial confining pressure is applied to the specimen by displacement-controlled loading through the steel frame surrounding the specimen. Then, the horizontal displacement is maintained and the vertical displacement is increased until a pre-defined stress state is reached, and then the vertical displacement is maintained. The steel plate between the specimen and the steel frame is removed suddenly and the right-hand side of the specimen becomes a free surface. In this way, the rock can fail in a brittle manner and strainburst due to sudden unloading is simulated.

The loading curves for the surface of the sample are presented in Fig.29. It can be seen that when the initial stresses are applied, the maximum and minor principal stresses are 83 and 73 MPa, respectively. When the maximum and minor principal stresses reach 996 and 479 MPa, respectively, unloading starts and the maximum and minor drop immediately. Compared with the results under uniaxial compression, it can be observed that there is no platform in the loading curves and no transition from brittle to ductile behaviors. The drop from peak to residual load is abrupt, showing a very brittle post-peak behavior. Thus, unloading is more likely to induce unstable rock failure and release a large amount of strain energy.

Fig.29 Loading curves at the lateral surface of the specimen under unloading test.

As seen from the failure plot presented in Fig.30,

almost no failure occurs before unloading. When the

Fig.30 Failure process of specimen SII due to unloading.

confining pressure is removed suddenly, intensive cracking occurs on the free surface. Compressive failure dominates inside the specimen, accompanied by tensile failure in some areas. The figure clearly shows that there is a stress concentration near the free surface, indicating that irregular stress distribution is generated in the specimen due to unloading. 9.3 Concluding remarks

Using the RFPA method, the mechanism of unloading-induced strainburst was investigated using rock specimen. It is found that rock failure due to abrupt unloading exhibits a distinct brittle failure behavior and is associated with large dilation in the unloading direction. There is no brittle to ductile transition during the failure process. Rock failure is sudden and the failed rock is highly fragmented.

Furthermore, under the biaxial unloading, AE events and energy release are rapid and can only be seen or monitored immediately after unloading. This often leads to instantaneous strainburst. The energy release rate in biaxial unloading is much higher than that in uniaxial compressive loading.

The simulation results agree well with the physical test results on unloading-induced strainburst, demonstrating that numerical simulation is useful for study of the strainburst mechanism. Insights from such investigations are important for safe and cost-effective underground construction at depth. 10 Conclusions

Rock brittle failure is a complex process, involving not only the initiation and propagation of single crack, but also the initiation, propagation and coalescence of many cracks. In fact, rock failure and instability have been difficult problems in solid mechanics. Rock failure is the accumulative result of damage evolution including the initial defects. The mechanical behaviors


of rocks are determined by the internal mesoscopic structures and controlled by the mesoscopic damage and its evolution and development.

Since 1995, the authors and their research group have been committed to study the RFPA method. Based on the statistical distribution method in rock material properties, mesoscopic damage theory and numerical computation method, a RFPA system has been developed and applied in a great number of fundamental researches. The RFPA system has been widely applied to the analysis of the heterogeneous rock failure process. In this paper, the engineering applications of the RFPA are introduced with emphasis. The simulation results indicate that satisfactory results can be obtained by the RFPA in geotechnical engineering, such as coal mining, coal bump, tunnel stability, high slope stability and dams for hydropower stations. References [1] Chinese Society of Mechanics. Introduction to the rheology of bodies

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