*3.2.1 Relationship between the cohesion increment and strength-stress ratio of the surrounding rock*

The 12 points are plotted in **Figure 7** based on the strength-stress ratio and cohesion increment Δ*Cp* of the surrounding rock for the 12 underground plants in **Table 3**. Eq. (6) can be obtained by fitting the least squares curve to the 12 points:

$$\left[\Delta \mathbf{C}\_{\rm p}\right] = \mathbf{0}.7445 \mathbf{K}\_{\sigma}^{-0.2627} \tag{6}$$

As shown in **Figure 7**, the incremental cohesion Δ*Cp* of the surrounding rock provided by the anchor cable decreases with increasing strength-stress ratio. When the strength-stress ratio *Kσ* ≥ 4.0, the weakening rate of the support strength gradually decreased at a certain rate. When *K<sup>σ</sup>* < 4.0, the increase rate of the support strength accelerates.

A comparison of the fitting curves of the anchor bolt in **Figure 5** and the anchor cable in **Figure 7** shows the following differences: (1) There is no obvious transition zone in the fitted curve of the anchor cable; (2) When *K<sup>σ</sup>* < 6.0, the upward trend of the fitted curve of the anchor cable is less than that of the anchor bolt; and (3) when *Kσ* ≥ 6.0, the fitted curve of the anchor cable does not converge to a constant as the anchor bolt fitting curve does but decreases at a certain rate. These differences indicate that anchor cables provide greater support strength than anchor bolts and that the rate of change in anchor cable support strength with strength-stress ratio is less than that of the anchor bolts at *K<sup>σ</sup>* < 4.5.

#### *3.2.2 Relationship among the cohesion increment, strength-stress ratio, and plant span*

The relationship among cohesion increments Δ*Cp*, plant span *B*, and the strengthstress ratio *K<sup>σ</sup>* of the 12 underground plants are plotted in **Figure 8**. The equation can be obtained by least-squares surface fitting:

$$\left[\Delta \text{C}\_{\text{P}}\right] = 0.00262 \left(5.383 + 3 K\_{\sigma} \text{}^{-1} + 4 K\_{\sigma} \text{}^{-2}\right) B \tag{7}$$

As shown in **Figure 8**, the 12 data points are distributed approximately around the fitted curve surface, and the incremental cohesion of the surrounding rock increases with the plant span, which is consistent with engineering practice. The incremental cohesion of the surrounding rock is approximately linearly related to the plant span when the strength-stress ratio is greater than a certain value.

### **3.3 Support strength criteria**

To better reflect the relative relationship between the actual support strength and the empirical formula, the dimensionless anchor support strength index *Ib* is defined as follows:



 *increment reinforced by the anchor cable.*

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

$$I\_{\rm b} = \frac{\Delta C\_{\rm b}}{[\Delta C\_{\rm b}]} \tag{8}$$

where the numerator is the calculated value of the design anchor support strength, which is calculated by Eq. (2); and the denominator is the support strength calculated by empirically fitting Eqs. (4) or (5).


**Table 4.**

*Anchor bolt support index of the underground powerhouse calculated by Eqs. (4) and (5).*

Similarly, the dimensionless anchor cable support strength index *Ip* can be defined as:

$$I\_{\rm p} = \frac{\Delta C\_{\rm p}}{\left[\Delta C\_{\rm p}\right]} \tag{9}$$

where the numerator is the calculated value of the design anchor cable support strength, which is calculated by Eq. (3); and the denominator is the support strength calculated by empirically fitting Eqs. (6) or (7).

The cohesion increment of the anchor cable are calculated by Eqs. (4) and (5) and the anchor cable support strength index calculated by Eq. (8) for each engineering are shown in **Table 4**. **Figure 9** shows the comparison between *Ib* calculated by [Δ*Cb*] of Eq. (4) and *Ib* calculated by [Δ*Cb*] of Eq. (5). It can be seen from **Figure 9** that (1) the anchor bolt support index *Ib* is mostly distributed at approximately 1.0, in which 68.96% of *Ib* calculated by Eq. (5) and 65.51% *Ib* calculated by Eq. (4) are between 0.8 � 1.2; and (2) *Ib* calculated by Eq. (5) is closer to 1 than *Ib* calculated by Eq. (4). This shows that Eq. (5), which considers both the plant span and the strength-stress ratio, can better reflect the support strength of the anchors.

The cohesion increment of the anchor cable calculated from Eqs. (6) and (7) for each engineering project and the anchor cable support index calculated using Eq. (9) for each project are shown in **Table 5**. The comparison between *Ip* calculated by [Δ*Cp*] of Eq. (6) and *Ip* calculated by [Δ*Cp*] of Eq. (7) is shown in **Figure 7**. It can be seen from **Figure 10** that (1) the anchor cable support index *Ip* is mostly distributed at approximately 1.0, in which 58.3% *Ib* is between 0.8 and 1.2; and (2) the support indices calculated by different fitting formulas for the same engineering are similar. This shows that the empirical formula can reflect the strength of the anchor cable support well, and the fitted results of empirical Eqs. (6) and (7) are similar.


#### **Table 5.**

*Anchor cable support strength index of the underground powerhouse calculated by Eqs. (6) and (7).*

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

In summary, combined with the actual engineering and experience formula, the support strength index can be used as a reference basis and judging standard for the actual engineering support design:

