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Support Strength Criteria and Intelligent Design of Underground Powerhouses

Written By

Jianhai Zhang, Tianzhi Yao, Li Qian, Zuguo Mo, Yunpeng Gao, Fujun Xue, Chenggang Liao and Zhong Zhou

Submitted: November 2nd, 2021 Reviewed: January 20th, 2022 Published: March 27th, 2022

DOI: 10.5772/intechopen.102791

IntechOpen
New Approaches in Foundation Engineering Edited by Salih Yilmaz

From the Edited Volume

New Approaches in Foundation Engineering [Working Title]

Associate Prof. Salih Yilmaz

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Abstract

The proper design of underground powerhouse support is the key engineering technique to guarantee the safe construction and operation of underground works. By regression analysis of the surrounding rock support parameters of 29 underground powerhouses with a span of 18.0–34.0 m, the empirical formula of the relationship between the support strength of anchor bar, strength-stress ratio, and plant span and the relationship among the support strength of the anchor cable, strength-stress ratio, and plant span are proposed. Furthermore, an intelligent design model for the anchor support of the underground powerhouse was trained by a BP (back propagation) neural network. Research shows that the support strength index of the anchor bolt and the anchor cable of these 29 plants are all distributed around 1.0. Therefore, a support strength index of 0.8–1.2 can be used as a reference for practical engineering support design. Finally, the reliability of the intelligent design model for the anchor support of the underground powerhouse was verified by comparison with actual engineering and support strength index. This shows that the intelligent design model can provide a reference for engineering design and construction.

Keywords

  • underground powerhouse
  • support strength criteria
  • strength-stress ratio
  • BP neural network
  • intelligent design

1. Introduction

The underground plant of a hydropower station is a large, complex underground building structure, and its stability is affected by factors such as geological structure, carven span, in situ stress, and support strength [1]. As underground plants are located in different stress environments, the lithology and strength of the surrounding rock are different, and the strength of the support to maintain the stability of the surrounding rock varies. Insufficient support strength can lead to local instability, collapse, excessive deformation of the surrounding rock, or even integral damage, while too much support strength can lead to unnecessary waste. Due to the complexity of the surrounding rock, scholars are still unable to fully grasp the deformation characteristics and reinforcement mechanism of the surrounding rock under complex stress conditions, which makes the theory and specification of surrounding rock reinforcement immature, and the support of underground plants still mainly relies on experience for design and construction. At present, the support design of underground plants is commonly based on the engineering analogy method, and there is insufficient knowledge of the deformation characteristics of the surrounding rock in high in situ stress areas. Because of the lack of relevant design experience, it is not sufficient to fully guide the design of the cavern support. The empirical method sometimes leads to safety problems due to inadequate design support strength or waste of resources due to over-support.

On the other hand, many successful examples of underground plants provide valuable data for the design of rock support. Through these data, the reinforcement measures and strength of the surrounding rock can be summarized, and the inherent laws of rock support and a new support design method can be proposed. For underground plants, the commonly used method is the system anchor and anchor cable support method, which can give good play to the strength and its own bearing capacity of the surrounding rock [2]. Through studying research papers and design data, a systematic summarization of sidewall support schemes for 29 underground plants with a span range of 18.0–34.0 m and a strength-stress ratio range of 2.0–14.55 was carried out, and the regression fitting relationships between the strength of the system anchor bolts and cables and the strength-stress ratio of the surrounding rock and the plant span were proposed. Based on the regression fitting relationship, an underground plant support strength index was defined, which can quantitatively evaluate whether the surrounding rock support is reasonable.

Neural network theory is recognized as a method for solving nonlinear problems, and it has been applied in rock mechanics parameter identification and stress analysis, parameter prediction, rock stability, rock deformation prediction, and rock engineering inverse analysis [3, 4]. One of the most popularly used neural network models is BP (back propagation) neural networks, which are multilayer feed-forward neural networks that are widely used in nonlinear modeling, function approximation, logic classification, etc. On this basis, an intelligent design model for the anchor support of the underground powerhouse is proposed based on a BP neural network. The model optimized the design of the system anchor diameter and spacing by inputting the plant span and strength-stress ratio. The different degrees of influence of the plant span and strength-stress ratio on the system anchor support scheme were analyzed according to the weights between the neurons.

1.1 Underground plant and rock surrounds support

1.1.1 Underground plant

According to incomplete statistics, more than 600 underground hydropower plants have been built worldwide, including more than 200 in Norway, which is the largest number of underground hydropower plants, and there are two underground power plants with an installed capacity of more than 1000 MW. As of 2015, the top 10 underground hydropower plants of installed capacity that have been built in the world are shown in Table 1.

NumberNameCountryInstalled capacity/MWSize of underground plant (L*W*H)/mCompletion date
1XiluoduChina13,860439.7*31.9*75.62014
2LongtanChina6300388.5*30.3*74.52009
3NuozhaduChina5850418.0*29.0*79.62014
4La Grande IICanada5280490.0*26.3*47.21980
5Churchill FallsCanada5225300.0*24.5*45.51971
6Jinping IIChina4800352.4*28.3*72.22014
7SanxiaChina4200311.3*32.6*87.32009
8XiaowanChina4200298.4*30.6*79.32012
9LaxiwaChina4200311.7*30.0*73.82011
10Jinping IChina3600277.0*28.9*68.82014

Table 1.

Top 10 installed capacity underground hydropower plants in the world.

The underground plant caverns are generally located in the hills downstream of the dam, mainly consisting of the diversion cavity, underground plant, traffic cavity, transformer room, surge chamber, and tailwater cavity, as shown in Figure 1. When designing the location of the plant, the longitudinal axis of the plant should have a small angle to the direction of the maximum principal stress of the initial ground stress and a large angle to the main structural surface, which is conducive to the stability of the cavern envelope.

Figure 1.

Composition of the underground plant of hydropower station.

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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:

C1=C0+ητsSabφ1=φ0E1

where C0 and φ0 are the cohesion and angle of internal friction of the surrounding rock before anchoring, respectively; τsis the shear strength of the anchor bolt; Sis the cross-sectional area of the anchor bolt; aand bare the spacing and row spacing of the anchor arrangement, respectively; and ηis 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:

ΔCb=ητsSab=ητsπd24abE2

where dis 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 one-dimensional 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, σ1 > 0, and σ3 = 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 prestress leads to a decrease in the tangent point of Mohr’s circle from A to A′, which corresponds to an intercept difference ΔCwith the τ-axis of the shear stress and is taken as the incremental cohesion ΔCpof the surrounding rock provided by the anchor cable.

Figure 2.

Reinforcement mechanism of anchor cable.

Assuming that the coefficient of friction f = tanφof 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):

ΔCp=ηNf2ab1+1sinφE3

Similar to Eq. (1), the anchor group effect factor η = 2.0 ∼ 5.0, where φis 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 310. 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.

  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.

  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.

  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.

Figure 3.

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

Figure 4.

Distribution characteristics of the deformation (black >100 mm) under systematic support conditions.

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.

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.

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.

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.

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3. Relationship among the plant span, strength-stress ratio, and incremental cohesion of the surrounding rock

3.1 Incremental cohesion of the surrounding rock after anchor reinforcement

As shown in Table 2, the physical and mechanical parameters, maximum principal stress, and anchor parameters of the underground plants of 29 hydropower stations, such as Jiangkou, Xiluodu, and Jinping I, are shown [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36]. In Table 2, the maximum principal stress is taken as the maximum value near the main powerhouse. In accordance with the design principle of the “difference between arch and side wall”, generally, the system anchors on the side wall of the main plant are used for statistical data. When the system anchor arrangement for the upstream and downstream side walls varies, the average value is taken as the statistical data. The incremental cohesion of the surrounding rock is calculated by Eq. (2), where η = 3.5, τs = 200 MPa, and the strength-stress ratio in Table 2 is a dimensionless constant.

EngineeringCavern span/mUniaxial compressive strength/MPaMaximum principal stress/MPaStrength-stress ratio KσAnchor diameter D/mmAnchor spacing and row spacing a, b/mCalculated values of cohesion increments ΔCb/MPa
Jiangkou19.2907.4012.225.01.50.153
Tai’an24.516011.014.528.01.50.192
Dazhaoshan26.48511.07.7032.01.50.250
Pubugou32.412023.35.2030.01.50.220
Xiangjiaba31.01008.9011.328.01.50.192
Xiluodu31.912018.06.7032.01.50.250
SanXia32.513011.711.128.01.50.192
Houziyan29.28033.52.4032.01.30.333
Baihetan34.09531.03.1032.01.20.391
Dagangshan30.86022.22.7032.01.50.250
Mengdigou29.18517.05.0028.01.50.192
Gongguoqiao27.87014.04.9925.03.00.038
Zimbabwe23.01008.9011.2425.01.50.153
Yele22.212012.59.6025.01.50.153
Guangxu22.0112.514.08.0425.01.50.153
Laxiwa30.0157.022.876.8628.01.50.192
Wunonglong26.770.010.07.0028.01.50.192
Wudongde32.590.09.709.2832.01.50.250
Changheba30.813824.05.7532.01.50.250
Lubuge18.082.817.04.8725.01.50.153
Shuangjiangkou29.397.329.03.3632.01.50.250
Nuozhadu29.0120.38.2714.5525.03.00.038
Baise20.760.06.0010.0025.03.00.038
Jinping I29.27035.72.0032.01.20.391
Lianghekou28.710018.05.6032.01.50.250
Longtan30.713013.010.030.01.50.220
Huangjinping28.87523.23.2032.01.50.250
Ertan30.720029.56.8028.01.50.192
Baishan25.0108.09.5811.2725.01.50.153

Table 2.

Relevant data of the powerhouse and calculation of the cohesion incrementally reinforced by the anchor bar.

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

The strength-stress ratio and cohesion increment of the 29 underground plants in Table 2 are plotted as 29 data points in Figure 5. These data are fitted by a least-squares curve to obtain Eq. (4).

ΔCb=0.452Kσ2+Kσ4+0.163E4

As shown in Figure 5, most of the 29 data points are distributed near the fitted curve, forming a data band around a certain distance above and below the curve, and the cohesion increment of the surrounding rock increases with a decrease in the strength-stress ratio. The trend of the curve in Figure 5 shows that when the strength-stress ratio Kσ > 6.0, the support strength reflected by the cohesion increment of the surrounding rock gradually tends to be constant. However, when the strength-stress ratio ranges from 3.0 ≤ Kσ < 6.0, the curve gradually rises, indicating that the required support strength of the surrounding rock increases significantly as the strength-stress ratio decreases. When the strength-stress ratio Kσ < 3, the underground plant surrounding rock is in a high-very high-stress state, requiring an even higher support strength, and the cohesion increment ΔCband strength-stress ratio show −2 times nonlinearity. Eq. (4) shows that the smaller the strength of the surrounding rock and the higher the in situ stress of the underground plant are, the greater the support strength required, but the growth rate shows a nonlinear relationship with the strength-stress ratio.

3.1.2 Relationship between the cohesion increment and the strength-stress ratio and plant span

According to the 29 underground plants in Table 2, the cohesion increment ΔCbof the surrounding rock is fitted to the plant span Band the strength-stress ratio Kσby least squares surface fitting, and the equation is as follows:

ΔCb=0.014812Kσ2+0.405BE5

In Figure 6, the cohesion increment provided by the anchor is approximately linearly related to plant span B, which increases with an increase in plant span. In addition, the cohesion increment ΔCband strength-stress ratio still show −2 times nonlinearity.

3.2 Incremental cohesion of the surrounding rock for anchor cable reinforcement

The anchor cable support parameters for 12 large and medium-sized hydropower plants are shown in Table 3, and the cohesion increment in the surrounding rock is calculated by Eq. (3), where η = 3.5.

Engineering projectPlant span/mUniaxial compressive strength/MPaMaximum principal Stress/MPaStrength-stress ratio KσAnchor cable internal force/kNAnchor spacing a/mAnchor row spacing b/mCalculated values of cohesion increments ΔCp/MPa
Shuibuya21.5905.6216.015004.24.50.335
Dazhaoshan26.48511.007.720004.55.20.426
Jinping I29.27035.702.017504.54.50.370
Xiangjiaba31.01008.8511.315005.06.00.239
Xiluodu31.912018.006.717504.54.50.370
Ertan30.720029.546.815003.02.00.544
Huangjinping28.87523.233.217504.04.00.479
Houziyan29.28033.452.425004.04.00.592
Xiaowan31.514025.405.510005.05.00.209
Pubugou32.412023.305.220003.03.00.939
Dagangshan30.86022.902.718004.54.50.845
Mengdigou29.18517.005.020004.54.50.508

Table 3.

Relevant data of each powerhouse and calculations of the cohesion increment reinforced by the anchor cable.

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 ΔCpof 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:

ΔCp=0.7445Kσ0.2627E6

As shown in Figure 7, the incremental cohesion ΔCpof 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 Kσ < 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 Kσ < 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 Kσ < 4.5.

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

The relationship among cohesion increments ΔCp, plant span B, and the strength-stress ratio Kσof the 12 underground plants are plotted in Figure 8. The equation can be obtained by least-squares surface fitting:

ΔCP=0.002625.383+3Kσ1+4Kσ2BE7

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 Ibis defined as follows:

Ib=ΔCbΔCbE8

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).

Similarly, the dimensionless anchor cable support strength index Ipcan be defined as:

Ip=ΔCpΔCpE9

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 Ibcalculated by [ΔCb] of Eq. (4) and Ibcalculated by [ΔCb] of Eq. (5). It can be seen from Figure 9 that (1) the anchor bolt support index Ibis mostly distributed at approximately 1.0, in which 68.96% of Ibcalculated by Eq. (5) and 65.51% Ibcalculated by Eq. (4) are between 0.8 ∼ 1.2; and (2) Ibcalculated by Eq. (5) is closer to 1 than Ibcalculated 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.

EngineeringCalculated cohesion increment ΔCb/MPaValues calculated by Eq. (4)Cb]/MPaValues calculated by [ΔCb] of Eq. (4)IbValues calculated by Eq. (5)Cb]/MPaValues calculated by [ΔCb] of Eq. (5)Ib
Jiangkou0.1530.1690.900.1191.28
Tai’an0.1920.1671.150.1501.27
Dazhaoshan0.2500.1781.400.1721.46
Pubugou0.2200.1971.120.2300.96
Xiangjiaba0.1920.1701.130.1930.99
Xiluodu0.2500.1831.370.2121.18
SanXia0.1920.1701.130.2030.95
Houziyan0.3330.3331.000.3251.02
Baihetan0.3910.2621.490.3091.27
Dagangshan0.2500.2950.850.3100.81
Mengdigou0.1920.2000.960.2090.92
Gongguoqiao0.0380.2000.190.2000.19
Zimbabwe0.1530.1700.900.1431.07
Yele0.1530.1730.880.1401.09
Guangxu0.1530.1770.860.1421.08
Laxiwa0.1920.1821.050.1990.96
Wunonglong0.1920.1821.060.1761.09
Wudongde0.2500.1741.440.2061.21
Changheba0.2500.1911.310.2121.18
Lubuge0.1530.2020.760.1301.17
Shuangjiangkou0.2500.2461.020.2530.99
Nuozhadu0.0380.1670.230.1780.21
Baise0.0380.1720.220.1300.29
Jinping I0.3910.4160.940.3911.00
Lianghekou0.2500.1921.300.1991.26
Longtan0.2200.1721.280.1931.14
Huangjinping0.2500.2550.980.2560.98
Ertan0.1920.1831.050.2040.94
Baishan0.1530.1700.900.1560.98

Table 4.

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

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 Ipcalculated by [ΔCp] of Eq. (6) and Ipcalculated by [ΔCp] of Eq. (7) is shown in Figure 7. It can be seen from Figure 10 that (1) the anchor cable support index Ipis mostly distributed at approximately 1.0, in which 58.3% Ibis 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.

EngineeringCalculated cohesion increment ΔCp/MPaValues calculated by Eq. (6)Cp]/MPaValues calculated by [ΔCp] of Eq. (6)IpValues calculated by Eq. (7)Cp]/MPaValues calculated by [ΔCp] of Eq. (7)Ip
Shuibuya0.3350.3590.930.3151.06
Dazhaoshan0.4260.4350.980.4041.05
Jinping I0.3700.6210.600.6030.61
Xiangjiaba0.2390.3940.610.4610.52
Xiluodu0.3700.4520.820.4950.75
Ertan0.5440.4501.210.4751.14
Huangjinping0.4790.5480.870.5060.95
Houziyan0.5920.5921.000.5611.06
Xiaowan0.2090.4760.440.5000.42
Pubugou0.9390.4831.940.5181.81
Dagangshan0.8450.5741.470.5681.49
Mengdigou0.5080.4881.040.4681.08

Table 5.

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

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:

IPorIb<0.8,LowSupport StrengthIPor0.8<Ib<1.2,Reasonble Support StrengthIPorIb>1.2,High Support StrengthE10
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4. Intelligent design model for the anchor support of the underground powerhouse

4.1 Model design and training logic

4.1.1 Model design

As seen from Parts 2 and 3, the design of the anchor support for the underground powerhouse can be determined by the plant span and strength-stress ratio. There is a certain relationship among the plant span, strength-stress ratio, anchor diameter, anchor spacing, and row spacing. Their mapping relationship can be reflected by a back propagation (BP) neural network. The BP neural network is a multilayer feed-forward neural network that is widely used in nonlinear modeling, function approximation, logic classification, etc. Therefore, an intelligent design model for anchor support of the underground powerhouse was created, which can output diameter D, anchor spacing a, and row spacing bby inputting plant span Band strength-stress ratio Kσ. The model takes advantage of the logical classification of BP neural networks to find the mapping of plant spans and strength-stress ratio to different support schemes. By analyzing the scheme of anchor bolt support of completed underground powerhouses in Table 1, the anchor bolt support schemes are divided into six types, as shown in Table 6.

Scheme numberAnchor diameter D/mmAnchor spacing and row spacing a, b/m
1321.2
2321.5
3301.5
4281.5
5251.5
6253.0

Table 6.

Anchor support schemes.

The model consists of three parts: an input layer, a hidden layer, and an output layer. The structure of the model is shown in Figure 11. The input layer contains the plant span and strength-stress ratio, and the output layer contains the anchor diameter, spacing, and row spacing of the anchor. The hidden layer is used to connect the input and output layers and to pass the weights of the neural network. The number of layers and nodes in the hidden layers affect the prediction results of the model. Theoretically, the greater the number of hidden layers is, the smaller the error of the prediction results, but too many hidden layers will lead to an overly complex network structure and slow computation speed. In this paper, the number of hidden layers is chosen as one layer with reference to a typical BP neural network structure. The number of nodes in the hidden layer is directly related to the number of input and output units, but there is still no perfect analytical formula. Too many nodes in the hidden layer will lead to a long learning time, while too few nodes in the hidden layer will have poor fault tolerance. According to previous experience [37], the number of nodes is designed with reference to Eq. (11).

Figure 11.

The structure of BP neural network.

m=n+l+αE11

where mis the number of nodes in the hidden layer, nis the number of nodes in the input layer, lis the number of nodes in the output layer, and αis a constant between 1 and 10. In this model, the value of αis 7, so the number of hidden layer nodes calculated according to Eq. (11) is 10.

4.1.2 Model training logic

  1. Forward propagation

    The initial training of the model in Step 3 of Section 4.1.2 is achieved by forward propagation of the BP neural network. Suppose the sample set is X, the second layer of the BP neural network (hidden layer) is a2, the third layer (output layer) is a3, Θ(i) is the weight from layer ito layer (i + 1), the initial Θ(i) is set randomly, the model target output value is y, and his the actual output value of the model after training. Forward propagation can be expressed by the following equations:

    a2=sigmoidΘ1×XTE12
    a3=sigmoidΘ2×XTE13
    h=a3E14

    where X, a2, a3, Θ(i), and hare the matrix and sigmoidis the transfer function, as shown in Eq. (15).

    sigmoidx=11+exE15

  2. Cost function

    Because the initial Θ(i) is set randomly, the actual output value hof the initial model has a large error with the target output value y. To evaluate the accuracy of the actual output value h, the cost function J(Θ) is introduced, and the formula is shown in Eq. (16). The smaller the value of J(Θ) is, the closer the actual output value his to the target output value y, representing a better value for the weight Θ.

    JΘ=1mi=1mk=1KxkiloghΘxik+1ykilog1hΘxik+λ2ml=1L1i=1slj=1sl+1Θjil2E16

    where x(i) kis the k-th data in the i-th layer, mis the total number of layers in the BP neural network, Kis the total number of data, λis a constant, L is the total number of layers in the neural network, and slis the number of nodes in the l-th layer.

  3. Back propagation

To continuously obtain a smaller cost function J(Θ), we continuously update the value of the weight Θby back propagation. The error transfer and weight update process are as follows:

δk3=ak3ykE17
δ2=Θ2Tδ3×g'z2E18
g'z2=a2×1a2E19

where δ(l) jis the error of the j-th node in the l-th layer and a(i) kis the k-th data in the i-th layer.

The errors are stored in Δ(l).

Δl=Δl+δl+1alTE20

where Δ(l) is the set of each node in l-th layer. The weight is updated with Δ(l) and calculated by Eq. (20). The intelligent design model is obtained after the optimal weights are calculated.

4.1.3 Model training

The first 23 data points in Table 1 were used as training samples to train the intelligent design model for anchor support of the underground powerhouse. The training process of the model is shown in Figure 12.

  1. Step 1: A neural network structure applicable to the intelligent design model is established, as shown in Figure 11.

  2. Step 2: The weight values of the neural network are initialized.

  3. Step 3: The training set data are input. The initial training model is obtained by forward propagation of the neural network, and the values of the nodes in the neural network are obtained.

  4. Step 4: The output layer errors of the initial training model are calculated and passed to the hidden layer to update the weights between the output layer and hidden layer. Similarly, the errors between the hidden layer and input layer are calculated, and the weights are updated.

  5. Step 5: After the new weights have been calculated, the new model is validated by the validation set, and if it does not meet the requirements of the validation set, then step 4 is repeated. If it does, then the final intelligent support model is obtained.

Figure 12.

The training process of BP neural network.

The validation set for the intelligent design model is shown in Table 7. The test set for the intelligent design model is shown in Table 8.

EngineeringPlant span B/mUniaxial compressive strength Rc/MPaMaximum principal stress/MPaStrength-stress ratio KσAnchor diameter D/mmAnchor spacing and row spacing a, b/m
Jinping I29.27035.72.0032.01.2
Lianghekou28.710018.05.6032.01.5
Longtan30.713013.010.030.01.5

Table 7.

Validation data.

EngineeringPlant span B/mUniaxial compressive strength Rc/MPaMaximum principal stress/MPaStrength-stress ratio KσAnchor diameter D/mmAnchor spacing and row spacing a, b/m
Huangjinping28.87523.23.2032.01.5
Ertan30.720029.56.8028.01.5
Baishan25.0108.09.5811.2725.01.5

Table 8.

Testing data.

4.2 Model implementation

Based on the process in Section 4.1 and the data in Table 1, the intelligent design model was trained. Now, if the plant span and strength-stress ratio are input into the model, then the anchor diameter, spacing, and row spacing can be output. The interaction of the models can be implemented by MATLAB 2019b.

Taking the underground plant of Huangjinping Hydropower Station as an example, by inputting the plant span Band the strength-stress ratio Kσ, the model will automatically output the anchor support scheme, and the results are shown in Figure 13.

Figure 13.

Intelligent model run testing.

4.3 Model test and discussion

The test data are input in Table 8 into the model, in turn, to obtain the support design scheme for the test set, as shown in Table 9.

EngineeringPlant span B/mStrength-stress ratio KσActual scheme of engineeringScheme proposed by intelligent design model
Huangjinping28.83.20Anchor Diameter Φ32,
Spacing and Row Spacing @1.5×1.5
Anchor Diameter Φ32,
Spacing and Row Spacing @1.2×1.2
Ertan30.76.80Anchor Diameter Φ28,
Spacing and Row Spacing @1.5×1.5
Anchor Diameter Φ30,
Spacing and Row Spacing @1.5×1.5
Baishan25.011.27Anchor Diameter Φ25,
Spacing and Row Spacing @1.5×1.5
Anchor Diameter Φ25,
Spacing and Row Spacing @1.5×1.5

Table 9.

Comparison between the actual scheme and the proposed scheme of the intelligent design model.

As seen in Table 9, the scheme proposed by the system anchor design model for the Baishan Hydropower Station is consistent with the scheme used in actual engineering. The proposed scheme for the Ertan Hydropower Station is anchor diameter Φ30, and the anchor spacing and row spacing are @1.5 × 1.5. The proposed scheme for the Huangjinping Hydropower Station is anchor diameter Φ32, and the anchor spacing and row spacing are @1.2 × 1.2. The proposed schemes are safer and more reliable than the scheme used in actual engineering.

The schemes suggested by the intelligent design model are evaluated using the concept of support strength criteria presented in Section 3.3. The comparison of the proposed schemes from the intelligent design model and the actual support schemes are shown in Figure 14.

Figure 14.

Comparison of the support strength index of the actual scheme and the scheme proposed by the intelligent design model.

In high in situ stress areas, the engineering analogy method has fewer projects to provide a reliable reference for support schemes with different plant spans and strength-stress ratios. Therefore, in actual engineering, there may be a situation where the design support strength is low, such as Dagangshan Hydropower Station in Figure 15, which may cause dangerous situations during construction. In low and medium in situ stress areas, the same low strength of system anchor support was observed in Mengdigou, Baise, and Nuozhadu hydropower stations designed by the traditional method. This indicates that the engineering analogy method has difficulty selecting an appropriate system anchor support scheme in situations such as high in situ stress and uncommon plant spans and that the design reliability is low. However, the support strengths suggested by the intelligent design model are generally better than those used in the actual project, and generally, the support index is above 1.0. In relatively complex areas of high in situ stress, such as the Houziyan and Dagangshan hydropower stations, intelligent design models provide safer design schemes than actual engineering. This shows that the intelligent design model can provide a more reliable and economical support scheme than the traditional engineering analogy method and can be used as a reference for the design of system anchors for underground plants in practical engineering.

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5. Influencing factors of support scheme design

5.1 Evaluation methods for neural network weights

The choice of a system anchor support scheme in an underground plant is influenced by several factors, but it is not yet clear which is the main factor. Based on the intelligent design model proposed above, the different degrees of influence of the plant span and strength-stress ratio on the selection of the system anchor support scheme can be further explored by analyzing the weights between the neurons. The relationship can be described with the help of the following indicators [38].

  1. Correlation significance coefficient rij:

    rij=k=1pωki1ex1+exx=ωjkE21

    where iis the input unit of the neural network, i = 1, … …, m; jis the output unit of the neural network, j = 1, … …, n; kis the hidden unit, k = 1, …, p; ωkiis the weight coefficient between neuron iin the input layer and neuron kin the hidden layer, and ωjkis the weight coefficient between neuron jin the output layer and neuron kin the hidden layer.

  2. Correlation index Rij:

    Rij=1ey1+eyy=rijE22

  3. Absolute impact factor Sij:

    Sij=Riji=1mRijE23

The absolute influence coefficient Sijcan be used to evaluate the influence of different input units on the output result, with a higher value of Sijfor an input unit indicating a greater influence on the result.

5.2 Discussion of support scheme impact factors

The weights of the neural network model in Section 4 are shown in Table 10.

Input layer and hidden layer connection weights (ωki)
ω11ω12ω13ω14ω15ω16ω17ω18ω19ω110
0.247−0.263−0.240−0.127−0.282−0.2630.266−0.2320.2840.288
ω21ω22ω23ω24ω25ω26ω27ω28ω29ω210
−0.6620.3050.6640.1730.2410.303−0.3420.665−0.245−0.241
Hidden layer and output layer connection weights (ωjk)
ω11ω12ω13ω14ω15ω16ω17ω18ω19ω110
0.792−0.177−0.807−0.043−0.303−0.1830.131−0.8140.2730.276
ω21ω22ω23ω24ω25ω26ω27ω28ω29ω210
0.355−0.243−0.331−0.059−0.348−0.2460.198−0.3100.3320.335
ω31ω32ω33ω34ω35ω36ω37ω38ω39ω310
−0.495−0.2960.500−0.100−0.328−0.2970.2830.5030.3450.353
ω41ω42ω43ω44ω45ω46ω47ω48ω49ω410
−0.463−0.2590.461−0.150−0.030−0.2550.3190.4560.0810.074
ω51ω52ω53ω54ω55ω56ω57ω58ω59ω510
−0.2670.2360.259−0.3280.5270.245−0.1040.250−0.560−0.520
ω61ω62ω63ω64ω65ω66ω67ω68ω69ω610
−0.1670.3460.1580.4920.4190.143−0.5970.157−0.445−0.442

Table 10.

Neural network weights of the intelligent design model.

The influence weights of the plant span and strength-stress ratio on the 6 system anchor support schemes are shown in Table 11.

Absolute influence coefficient SijScheme 1Scheme 2Scheme 3Scheme 4Scheme 5Scheme 6
Sijof plant span0.3410.3910.2930.0580.4230.444
Sijof strength-stress ratio0.6590.6090.7070.9420.5770.556

Table 11.

Weight of the support scheme for the ratio of span and strength stress.

As seen from Table 11, the weights of the strength-stress ratio on the results in the intelligent support design model are greater than the weights of the plant span. Therefore, when considering only the plant span and the strength-stress ratio, the variation in the strength-stress ratio has a greater influence on the choice of the anchor support scheme for the underground plant.

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6. Conclusion

  1. Anchor bolts or anchor cables can provide additional cohesion increments to the surrounding rock, and the support strength reflected by the anchor shows a certain functional relationship with the strength-stress ratio and plant span. Through the statistical method of least squares fitting, four empirical formulas are proposed for the strength-stress ratio Kσof anchor bolts and anchor cables and the plant span B.

  2. For both anchor cable support and anchor bolt support, there are intervals where the strength of the support increases at a rapid rate. For anchor bolt support, the required support strength increases rapidly when the strength-stress ratio Kσ ≤ 3 and the underground plant rock is in a very high-stress state; for anchor cable support, the required support strength increases significantly when Kσ < 4.

  3. Based on the empirical fitting formula, a dimensionless support strength index Ibis proposed, which can visually characterize the relationship between the designed support strength and the support strength obtained from statistical analysis. The support index can be used as a reference for support design.

  4. Based on the theory of BP neural networks, an intelligent design model for the anchor support of underground plant systems is proposed. Using MATLAB as the development language, the function of obtaining the system anchor support scheme by inputting the plant span and strength-stress ratio of the underground plant is realized.

  5. The Huangjinping, Ertan, and Baishan hydropower stations were selected as engineering cases with high, medium, and low in situ stress conditions to verify the feasibility of the intelligent design model. Compared with actual projects, the intelligent design model provides a safer and more reliable support scheme for Huangjinping and Ertan hydropower stations.

  6. With the help of the support strength index concept, the support strength of the support scheme suggested by the intelligent design model was compared with that of the scheme used in actual engineering. The results show that the support scheme suggested by the intelligent design model is safer and more stable and can still achieve the desired design effect under high in situ stress conditions.

  7. By calculating the absolute influence factor Sij, the weights of the strength-stress ratio and the plant span for the selection of different support schemes were obtained. Based on the calculation results, the strength-stress ratio has a greater influence on the choice of the system anchor support scheme when only the plant span and strength-stress ratio are considered. This method provides a new idea for studying the influence of different factors on the choice of system anchor support scheme.

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Written By

Jianhai Zhang, Tianzhi Yao, Li Qian, Zuguo Mo, Yunpeng Gao, Fujun Xue, Chenggang Liao and Zhong Zhou

Submitted: November 2nd, 2021 Reviewed: January 20th, 2022 Published: March 27th, 2022