**2. The effect of anchoring measures on the parameters of surrounding rock**

#### **2.1 Effect of anchor on the parameters of the surrounding rock**

At present, numerical calculations generally take the anchor bolt (anchor cable) as the rod element, and the effect of the anchor bolt is reflected by the stiffness of the anchor, which is very small compared to the stiffness of the surrounding rock. Many calculations have shown that this method of simulation does not fully reflect the support effect of the anchor bolts. In fact, the main role of the anchor is to participate in the deformation process of the surrounding rock. The elastic recovery deformation of the anchor has a reverse locking force, which can create an anchoring effect on the surrounding rock. In other words, the deformation and strength parameters of the anchored rock mass can be increased and have been confirmed by laboratory and field tests [5].

For the strength of the surrounding rock after anchoring, the parameters for the shear strength of the surrounding rock after the anchor is applied can be calculated as:

$$\begin{aligned} \mathbf{C}\_1 &= \mathbf{C}\_0 + \eta \frac{\mathbf{r}\_s \mathbf{S}}{ab} \\ \rho\_1 &= \rho\_0 \end{aligned} \tag{1}$$

where *C*<sup>0</sup> and *φ*<sup>0</sup> are the cohesion and angle of internal friction of the surrounding rock before anchoring, respectively; *τ<sup>s</sup>* is the shear strength of the anchor bolt; *S* is the cross-sectional area of the anchor bolt; *a* and *b* are the spacing and row spacing of the anchor arrangement, respectively; and *η* is the anchor group effect factor, which is dimensionless and is related to factors such as the anchor diameter, generally taken as *η* = 2.0 � 5.0. Eq. (1) shows that the improvement of the parameters of the surrounding rock by the anchor is mainly manifested by an increase in cohesion, and the increase in cohesion after the application of the anchor is as follows:

$$
\Delta \mathbf{C}\_b = \eta \frac{\tau\_s \mathbf{S}}{ab} = \eta \tau\_s \frac{\pi d^2}{4ab} \tag{2}
$$

where *d* is the diameter of the anchor.

#### **2.2 Incremental cohesion of the surrounding rock for anchor cable reinforcement**

The traditional anchor reinforcement mechanism considers the reinforcing effect of anchor cables as (1) keeping separated rock masses from falling off and (2) increasing the overall strength by rebounding the damaged rock masses. The anchor cable not only has the above effect but also exerts a positive pressure on the rock in the direction of the anchor. This is equivalent to increasing the lateral pressure of the surrounding rock, which changes the rock near the excavation face from a onedimensional stress state to a three-dimensional stress state and increases the strength of the surrounding rock.

As shown in **Figure 2**, the state of the point on the free surface is one-dimensional pressure, that is, *σ*<sup>1</sup> > 0, and *σ*<sup>3</sup> = 0, corresponding to Mohr's circle **O**. The increase in wall pressure and the decrease in the radius of Mohr's circle after the application of the

*Support Strength Criteria and Intelligent Design of Underground Powerhouses DOI: http://dx.doi.org/10.5772/intechopen.102791*

prestress leads to a decrease in the tangent point of Mohr's circle from A to A<sup>0</sup> , which corresponds to an intercept difference Δ*C* with the *τ*-axis of the shear stress and is taken as the incremental cohesion Δ*Cp* of the surrounding rock provided by the anchor cable.

Assuming that the coefficient of friction *f* = tan*φ* of the rock mass is constant before and after reinforcement, it can be deduced from **Figure 2** that the cohesion of the rock mass can be increased by applying a prestressing force *N* (kN) with spacing *a*(m) and row *b*(m):

$$
\Delta \mathbf{C}\_p = \eta \frac{N \mathbf{f}}{2ab} \left( \mathbf{1} + \frac{\mathbf{1}}{\sin \varrho} \right) \tag{3}
$$

Similar to Eq. (1), the anchor group effect factor *η* = 2.0 � 5.0, where *φ* is the internal friction angle of the surrounding rock before anchoring.

#### **2.3 Comparison of the stability of the surrounding rock with and without support**

Systematic support has a very significant effect on maintaining the stability of the surrounding rock during excavation. Taking the Yebatan hydropower station as an example, the distribution characteristics of the large deformation zones in the surrounding rock with and without system support were compared based on the FLAC3D calculation software. The deformation distribution characteristics of the main powerhouse, main transformer chamber, and tailwater surge chamber under unsupported and systematically supported are shown in **Figures 3**–**10**. The comparison shows that:

1.The maximum local deformation of the roof arch of the main powerhouse is reduced from 70 � 130 mm to 60 � 80 mm and the maximum local deformation of the side walls is reduced from 120 � 180 mm to 100 � 150 mm under systematic support.

**Figure 3.**

*Distribution characteristics of the deformation (black >100 mm) of the main powerhouse under unsupported conditions.*

*Support Strength Criteria and Intelligent Design of Underground Powerhouses DOI: http://dx.doi.org/10.5772/intechopen.102791*

**Figure 5.** *Relationship between cohesion increment of the anchor bolt and strength stress ratio.*

**Figure 6.** *Relationship between cohesion increment reinforced by anchor, strength-stress ratio, and plant span.*

2.The maximum local deformation of the roof arch of the main transformer chamber is reduced from 65 85 mm to 50 60 mm; the maximum local deformation of the side walls is reduced from 90 135 mm to 70 110 under the systematic support.

*Support Strength Criteria and Intelligent Design of Underground Powerhouses DOI: http://dx.doi.org/10.5772/intechopen.102791*

**Figure 7.** *Relationship between cohesion increment reinforces by anchor cables and strength-stress ratio.*

#### **Figure 8.**

*Relationships among cohesion increment reinforce by anchor cable, strength stress ratio, and plant span.*

3.The maximum local deformation of the roof arch of the tailwater surge is reduced from 80 110 mm to 70 105 mm, the maximum local deformation of the side walls is reduced from 100 170 mm to 100 130 mm. under the system support.

**Figure 9.** *Comparison of anchor bolt support index calculated by different fitting formulas.*

#### **Figure 10.**

*Comparison of anchor cable support index calculated by different fitting formulas.*

4.Under system support, the volume of the cavern group surrounding rock deformation greater than 100 mm is reduced from 21.6 to 9.7 thousand cubic meters.

In general, the deformation distribution characteristics of the surrounding rock under system support are similar to those under unsupported, but the extent and magnitude of large deformations at fault-affected areas are substantially reduced under system support.
