Reinforcing a Dangerous Rock Mass Using the Flexible Network Method

CHARACTERISTICS OF A DANGEROUS ROCK MASS AND TYPES OF FAILURE

The dangerous rock mass discussed in this paper is found on Banyan Mountain, Huangshi, Hubei Province. It is mainly dispersed on the top of a threegrade declivity to the north-east. The dangerous rock mass is made up of four separate masses named respectively Ⅰ_w, Ⅱ_w, Ⅲ_w and Ⅳ_w. Figure 1 is a sketch diagram of the structure of the dangerous rock mass. The direction of rock formation is opposite to the dip of the slope. The direction of the rock formation is 150° -158°, and its dip angle is 15° -29°. The rocks are limestones(T₁dy^2-1-T₁dy^3-2), which belong to the second to third lithologic section of the Daye Group. There are over 40 developed fissures in the dangerous area, including three fissure groups, which exist from west-north, east-north and westeast. The fissures are mainly dispersed on the top of the dangerous rock mass slope, and their dip angles are from 80° to vertical. The cliff forelands of the rock masses are dissected by tension cracks or structural fractures, and upright and isolated rock-pillar masses are often seen. Though these rock-pillar masses are different in bulk, they have common characteristics. The low-dip angle of the rock formation inclines to the dome; the slope degree of the rockpillars is large and close to vertical; the fissures are also close to vertical, inclining to the outside of the dome. In this type of rock mass slope, the failure of the rock-pillar masses is mainly collapse due to such forces as earthquake, blasting, or water pressure (Deng et al., 1998; Wuhan University of Technology, 1996).

Figure  1.  Sketch diagram of structure of the dangerous rock mass.

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STABILITY ANALYSIS OF DANGEROUS ROCK MASS

The actions of the self-gravitation of the rock mass, earthquake force and hydraulic pressure are taken into account, and the force analysis of the dangerous rock mass is shown in Fig. 2.

Figure  2.  Force analysis of collapse.

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The anti-collapse stability coefficient of the dangerous rock mass is

where KTis the anti-collapse stability coefficient; M_R is the anti-collapse moment of force; M_S is the collapse moment of force.

According to the collapse force analysis of the dangerous rock mass(Fig. 2), we have

So its anti-collapse stability coefficient is

where T_i is the tension of the cable; B is the width of the collapsible rock mass; θ is the angle of inclination of tension to the horizontal; H_i is the vertical distance from collapse rotary spot to the hydraulic pressure's agent line; K_D is the coefficient of an earthquake; G is the weight of the collapsible rock mass; h_i is the height of the collapsible rock mass; U_i is hydraulic pressure.

Taking section Ⅱ_w of the dangerous rock mass as an example, the anti-collapse stability coefficient is calculated(where T_i= 0)to be K_T= 1.02.

FLEXIBLE REINFORCEMENT MECHANISM OF DANGEROUS ROCK MASS

Because the main type of failure of the dangerous rock mass is collapse, treatment should be focused on controlling a potential collapse. When treating the rock mass, a large disturbance such as blasting should be avoided, as this new damage could cause the collapse of the entire mass. So the self-bearing capacity of the mountain mass must be used to treat the dangerous mass. The flexible network reinforcement method is presented in the paper. It is an anchoring-pulling-grounting network reinforcement system(Fig. 3). Firstly, the vertical pre-stress anchor is used to reinforce the dangerous rock mass. Secondly, all rock-pillar masses are locked by prestressed cables and reinforcing bar nets. Finally, shotcrete is applied to the area so that the rock pillars form one whole. As such the whole dangerous rock mass system changes from a static structure system to a super-static structure system. The system has some flexibility and permits the rock masses to have suitable deformations. When the deformation pressure is near the reinforcement zones, the variation of the stress is harmonized and the stress is released rationally. So plastic areas are not excessively developed, the strength of the rock mass is maintained, and the selfbearing capacity of the rock mass is fully brought into play. The effort of the mountain mass is borne by the rock mass and the reinforcement system.

Figure  3.  Sketch diagram of structure of reinforcement of dangerous rock mass with flexible network method. 1. the vertical pre-stress anchor; 2. pre-stress cable; 3. anchorage stone; 4. bar nets; 5. concrete.

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The flexible network reinforcement method can improve the structure of a dangerous rock mass by tying together several parts to make a whole, strengthening the integrity of the dangerous rock mass, heightening its intensity and rigidity, and providing the self-adaptive ability of deformation(Xie and Xia, 2004a, b; Xia and Zhu, 2000, 1998; Xie and Zhu, 2000; Zhu and Wang, 1992; Vaughan and Iscnbcrg, 1991; Goodman and Tayley, 1968).

DESIGN OF REINFORCEMENT OF DANGEROUS ROCK MASS USING FLEXIBLE NETWORK

Section Ⅱ_w of the dangerous rock mass is taken as an example to illustrate the specific design of the flexible network reinforcement.

Design of Vertical Pre-stress Bolt

The force analysis of the rock bolt is shown in Fig. 4. If the anti-extraction safety coefficient is KB, according to the force decomposition principle, there is

Figure  4.  Force analysis of bolt.

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where P is the anchorage force; θ is the angle of inclination tension to the horizontal formation; T_i is the tension of the cable.

The anti-extraction safety coefficient of the rock bolt in the article is designed to be K_B= 2.5. The total anchorage force of section Ⅱ_w of the dangerous rock mass is 85 500 kN, and the quantity of the total reinforcement is 1 282 500 kN m. A total of 180Ⅳgrade-cold-pulled reinforcing bars(ϕ35) are used, spaced at 3 m×3 m, each 15 m in length, and the internal anchorage is 5 m long.

Design of Pre-stressed Cable

From equation(4), we can obtain

The design value of the anti-collapse safety coefficient of the rock-pillar mass in this paper is K_T= 2.0, so the total tension of section Ⅱ_w of the dangerous rock mass is 14 000 kN, and the number of the 1 000 kN-grade cables adopted is 14, every cable's mean length is 36 m, spacing is 3 m.

Design of Anchorage Stone

Anti-shearing strength design is

Compressive strength design is

where A is the sectional area of the reinforcing bar (m²); Tis the cable tension(kN); θ is the angle of inclination of tension to the horizontal; R_s is the design value of the anti-shearing strength of the reinforcing bar(MPa); σ_c is the compressive strength of the rock mass(MPa); B is the width of the anchorage stone(m); H is the insertion depth into bedrock (m).

After calculating, the anchorage stone is constructed using the No. 300 cast-in-situ reinforced concrete structure. The anchorage stone's geometric dimensions are 1.0 m×1.0 m×2.0 m, and its parameters are shown in Fig. 5.

Figure  5.  Sketch diagram of structure of anchorage stone.

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FINITE ELEMENT ANALYSIS

The two-dimensional finite element method was adopted to calculate the deformations of section Ⅱ_w of the dangerous rock mass(Zhu and Wang, 1992; Vaughan and Iscnbcrg, 1991; Goodman and Tayley, 1968). The calculation model is as shown in Fig. 6, and see Table 1 for the calculation parameters.

Figure  6.  Calculation model of dangerous rock mass.

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Table  1.  Calculation parameters of dangerous rock mass

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The deformations of section Ⅱ_w of the dangerous rock mass before the treatment and after the flexible network reinforcement are calculated using the twodimensional finite element method and the results are shown in Fig. 7.

Figure  7.  Two-dimensional finite element analysis of dangerous rock mass.(a)deformation of pretreatment of dangerous rock mass; (b)deformation of post-treatment of dangerous rock mass.

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The maximum deformation of section Ⅱ_w of the dangerous rock mass is 45.99 mm before treatment and 20.75 mm after the application of the flexible network reinforcement.

CONCLUSIONS

From the results of the finite element analysis in Fig. 7, it can be concluded that the deformation of section Ⅱ_w of the dangerous rock mass is significantly reduced after the application of flexible network reinforcement. This shows that the flexible network reinforcement method used to treat a dangerous rock mass is effective. The method thus provides some scientific basis for the treatment of dangerous rock masses.