# Study on the Mechanical Behavior of Double Primary Support of Soft Rock Tunnel under High Ground Stresses and Large Deformation

Authors: Zhe Liu
Journal: Advances in Civil Engineering
 (2020)

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## Abstract

Double primary support structures could effectively solve the problem of large deformation of surrounding rock for soft rock tunnels. However, the mechanical behavior of this new support structure is still incomplete, and the design method should be revised. Based on the theory of energy conversion, this paper analyzes the support characteristic curve of double primary support and puts forward the dynamic design method of double primary support. Considering that the secondary lining can be set after monitoring the deformation amount and deformation rate of the first primary support, its support parameters can be dynamically adjusted according to the actual situation. By applying the double primary support design method in the Maoxian tunnel of Chenglan Railway, the field monitoring results show that the double primary support has a significant effect on the energy release of surrounding rocks, greatly reducing the load acting on the secondary lining and ensuring the safety and reliability of the tunnel structure.


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## Body

## 1. Introduction

The research on the theory of tunnel support has made significant progress through continuous development. In the early 20th century, the cave-arch theory represented by Terzaghi and Platts theory achieved a theoretical breakthrough in tunnel support design [1, 2]. In the 1960s, the theory of elastic-plastic mechanics [3] and the new Austrian tunneling construction method [4] gradually became the leading theory, design, and construction methods of tunnel support. In recent years, abundant achievements have been made in the application and practice of energy support theory [5], strain control theory [6], and effective stability theory [7].With the rapid development of railway construction in western China, plateau railway construction represented by Sichuan-Tibet Railway and Yunnan-Tibet Railway has become one of the highlands of railway construction technology. The plateau railway construction will inevitably build a large number of ultralong and deep buried tunnels. Due to the compression of Qinghai-Tibet Plate, Yangtze Plate, North China plate, and Tarim plate, the western plateau and its marginal areas are prone to form high ground stress zones and often cause rockburst, large deformation, and other related geological disasters, which bring significant challenges to the construction of the tunnel. The traditional support theory of “timely support and strong support” is often unable to effectively solve the problem, and the deformation and support failure of surrounding rocks can always be controlled only after experiencing multiple cycles of support, failure, and replacement [8].To solve the above technical problems, the concept of “yield control” support has been gradually developed to make the support structure deform along with surrounding rock before failure. This method mainly includes the filling of compressible primary behind rigid support applicable for TBM tunnels and the combination of sliding steel frame, telescopic bolt, and shotcrete applicable for drilling and blasting methods [9–14]. However, the steel frame is difficult to retract after spraying concrete, and the sudden sliding is easy to occur under surrounding rock pressure, which leads to sudden extrusion of rock mass, and the cost is too high. The double primary support structure, which is widely used in China, also applies the above support concept [15, 16]. The design of double primary support makes use of the characteristics of flexible support of the first-layer support and combines the concept of “yielding control” to allow the surrounding rock and the first-layer support to deform together to release controllable energy. At the same time, the design parameters of the second-layer support can be adjusted timely in the construction process, which could make the design more cost-effective and safer. This paper analyzes the characteristic curve of the surrounding rock and support based on the theory of energy support and puts forward the design method of the double lining support under high ground stresses and large deformation. The traditional double primary support method is mainly a static design method, and the timing of the installation of second layer is difficult to determine. Based on the real-time monitoring results of the first layer, the dynamic design method of the double primary support could ensure the accurate design of the timing and parameters of the first and second layers of primary support.


## 2. Analysis on the Characteristics of Double Primary Support

### 2.1. Energy Conversion in Support Process

The large deformation of surrounding rock is a kind of mechanical behavior of surrounding rock under the environmental conditions such as ground stress and groundwater activity. Its essence is the loss or partial loss of self-supporting ability of surrounding rock, the lack of effective constraints on deformation, and the plastic deformation of surrounding rock, which leads to the failure of surrounding rock support to different degrees. The large deformation of surrounding rock caused by tunnel excavation will be accompanied by the release of rock energy. To make the surrounding rock reach the stable state as far as possible after tunnel excavation and support, the energy value of reaccumulated energy of surrounding rock must be reduced. According to the energy conservation theory, the energy conversion relationship between tunnel excavation and support is as follows:(1)Wc+Um=Uc+Wr+Wn+Wf,where Wc is the work done by the internal stress of rock mass due to tunnel excavation, Um is the strain energy released during the rock mass excavated from the tunnel, Uc is the reassembled elastic energy in the surrounding rock, Wr is the elastic energy lost in the process of excavation, Wn is the inelastic strain energy lost in the surrounding rock, and Wf is the energy absorbed by the support structure.After tunnel excavation, the rock mass has viscous, plastic, and brittle fracture behavior, leading to local failure of surrounding rock. Surrounding rock will lose energyWr and Wn and regain part of energy Uc. Support will absorb part of energy Wf. Since the nature of surrounding rock is an inherent property, Wc, Um, and Wr can be approximately considered as unchanged after the tunnel form is determined. It can be seen that(2)Uc+Wn+Wf≈const.Based on the energy transformation of the surrounding rock in (2), the supporting structure of the tunnel can be designed in a reasonable way. By appropriately increasing the inelastic strain energy Wn lost in the surrounding rock and energy Wf absorbed by the supporting structure, the reaccumulation of energy Uc in the surrounding rock can be reduced and the stability of surrounding rock can be maintained as far as possible.However,Wn is the inelastic loss of work, and the large deformation of surrounding rock will cause excessive loose pressure, so the increase of Wn should be limited within a certain range. Therefore, lowering Uc should consider primarily raising Wf.When the surrounding rock pressure works on the support structure,Wf converted to the support structure can be divided into(3)Wf=We+Wp,where We is the elastic energy stored in the support and Wp is the energy consumed by plastic deformation of support.


### 2.2. Support Characteristic Curve of Double Primary Support

Figure1(a) shows the single primary support structure, and its support characteristic curve is shown in Figure 2(a). AB is the stress characteristic curve of single primary support. Support stores and consumes energy through elastic-plastic deformation. The energy conversion amount is low, which can be expressed as follows:(4)Wfs=Wes+Wps,where Wfs is the total energy absorbed by single primary support structure and Wes and Wps are the elastic and plastic energy absorbed by the single primary support structure, respectively.Figure 1
Support structure drawing. (a) Single primary support structure. (b) Double primary support structure.
(a)(b)Figure 2
Support characteristic curve. (a) Single primary support structure. (b) Double primary support structure.
(a)(b)Figure1(b) shows the double primary support structure, and its support characteristic curve is shown in Figure 2(b), where AB is the stress characteristic curve of single primary support and ACF is the stress characteristic curve of double primary support. The double primary support structure is first applied to the first primary support, and its stress characteristic curve is AC. In order to absorb more deformation energy of the surrounding rock, Uc>Ub, when the deformation of the first primary reaches Uc, the second primary support is applied. The first primary support stiffness K1 (AC) of the second primary support is less than that of the single primary support stiffness Ks (AB). It is assumed that the overall equivalent stiffness Kd (CF) of the second primary support is equal to that of the single primary support Ks, point F coincides with point D and CF||AB. Normally, point F is within the interval DE. If the deformation of first-layer primary support exceeds the design value significantly, Point F can move towards DB. The overall equivalent stiffness Kd of the double primary support can be expressed as(5)Kd=λ1K1+λ2K2,where λ1 and λ2 are the double primary support structure parameters, respectively.The surrounding rock deformation energy absorbed by the double primary support structure can be expressed as(6)Wfd=Wfd1+Wfd2=We1+Wp1+We2+Wp2,where Wf1 and Wf2 are the energy absorbed by the support structure of the first primary and the second primary supports, respectively, and We1 and We2 are the elastic energy absorbed by the supporting structure of the first primary and the second primary supports, respectively. Wp1 and Wp2 are the plastic energy absorbed by the first primary and the second primary support structures.Because the double primary support allows the surrounding rock to do work on the support structure by allowing greater deformation, compared with the single primary support, the surrounding rock deformation energy absorbed by the support structure is increased.For example, whenKD=Ks, point F coincides with point D and Uf=Ud>Ub; then, We1+We2>Wes and Wp1+Wp2>Wps, so Wfd>Wfs.The support parameters of the second primary can be dynamically adjusted with the support effect of the first primary. Generally speaking, under the condition that single primary support can stabilize surrounding rocks, the equivalent stiffnessKD of double primary support can be less than that of single primary support and greater than that of the first primary support, K1<KD<Ks. Therefore, point F is in the DE interval of the surrounding rock characteristic curve.


### 2.3. Dynamic Design Method of Double Primary Support

To cope with the impact of large deformation in soft rock on tunnel structure, railway tunnels built in western China, such as Yu-Lan line tunnel, adopt secondary lining with a thickness of 1.5∼2.1 m to solve large extrusion deformation of the surrounding rock in high in situ stress-broken phyllite rocks. The secondary lining is a formwork concrete structure with high stiffness and easy to be crushed and broken, which affects the operation safety and service life of railway tunnels. At the same time, the construction cost has been greatly increased. Therefore, the dynamic design method of double primary support is put forward. Considering that the secondary lining can be set after monitoring the deformation amount and deformation rate of the first primary support, its support parameters can be dynamically adjusted according to the actual situation. The dynamic design method of double primary support is shown in Figure3. Its design idea is as follows:(1)
The double primary support structure is designed based on geological prospecting data, and the initial values of the support parameters of the first primary and the second primary are determined. The equivalent flexural stiffness of the double primary support isKd=λ1K1+λ2K2.(2)
Construct the first primary support according to the design parameters, and monitor the deformation of the first primary in real time.(3)
Draw the relation curve between support deformationUc and time t, get the function of Uc=ft, and calculate deformation acceleration dUc2/dt2.(4)
After the timeT (the deformation time of the first support design under the compression of surrounding rocks), the dynamic support design scheme of the second primary is determined by comparing the deformation limit value UsU1<Us<U2 of the first support with the initial design and the deformation acceleration dUc2/dt2. The deformation limit value of the first-layer primary support Us is an empirical parameter in the range of 20∼50 cm, which is equal to the reserved deformation between two primary supports.(5)
WhenUc>Us, the deformation of the first primary support exceeds the deformation limit value Us, and it is necessary to remove and replace the first primary support or take other treatment measures, such as temporary or permanent enhancement of the first-layer primary support, to improve the stiffness of the first primary support. In particular cases, the deformation of the first-layer primary support can be adjusted to exceed the deformation limit value Us with the evaluation and approval of experts, and the parameters of the second-layer primary support can be further evaluated and modified.(6)
WhenUc=Us and dUc2/dt2≥0, the deformation of the first primary support Uc reaches the deformation limit value Us, and the deformation rate is still increasing. However, as the deformation of the first primary support does not exceed the deformation limit Us within the design time T, considering the setting of double primary support, the stiffness of the second primary of support (K2′) should be higher than the design value K2. After the construction of the second primary support, continue to monitor the deformation Ud and calculate dUd/dt. According to the in situ test, combined with relevant experience and the regulation of the Code for Tunneling in Squeezing Rocks, if Vda<1mm for the small- and medium-span tunnels or Vda<2mm for the large-span tunnel [17], where Vda is the deformation rate of average for 7 d, Vda=∑m=17dUdm/7dt, and dUdm is for the m days, when the second primary support is finished. Otherwise, it is necessary to change a support structure or take other measures.(7)
WhenUc<Us and dUc2/dt2≥0, the supporting deformation Uc of the first primary does not reach the deformation limit value Us, but the deformation rate is still increasing. Measures can be taken to delay further release of surrounding rock deformation to make the supporting deformation Uc reach the deformation limit value Us, and then, the deformation rate can be calculated. If dUc2/dt2≥0, it indicates that the deformation of the surrounding rock has slowed down, and the second primary of support can be set without further increasing the support stiffness, that is, K2′=K2. If dUc2/dt2≥0, it indicates that the deformation of the surrounding rock is still not obviously controlled. The second primary support should be set as soon as possible, and the supporting stiffness should be improved, that is, K2′>K2. After the construction of the second primary support is completed, continue to monitor the deformation Ud, and calculate dUd/dt. The next step is the same with Step (6).(8)
WhenUc<Us and dUc2/dt2<0, the deformation of the first support primary Uc does not reach the deformation limit value Us, and the deformation rate also slows down, indicating that the deformation of the surrounding rock is well controlled after the first support primary. By calculating Vda, if it meets the requirements lining timing of [17], the second primary support cannot be applied. Otherwise, it is still necessary to apply the second primary support to ensure the safety of the structure.Figure 3
Dynamic design method of double primary support.


### 2.4. Application of the Proposed Method

The Chenglan Railway is a plateau railway over 3,000 meters above the sea level, rising from the Chengdu Plain at 500 meters above the sea level to the eastern edge of the Qinghai–Tibet Plateau at 3,400 meters above the sea level. There are a large proportion of bridges and tunnels in this project. The Maoxian tunnel is located in Guangming Town, Maoxian County, Sichuan Province. The tunnel runs through the core of the active fault zone in the back mountain of Longmen Mountain, with a total length of 9,913 meters. It is a key and difficult project in the whole line. The Maoxian tunnel will pass through three faults, two anticlines, and one synclinal fault zone with a maximum depth of about 1650 m. The strata are mainly carbonaceous phyllite, argillaceous limestone, sericite, and sandstone. The strength of the soft surrounding rock is extremely low, and its own stability is extremely poor. Figure4 shows the support failure caused by the large deformation of the tunnel.Figure 4
Support failure caused by the large deformation of the tunnel. (a) Shotcrete squeezed off. (b) Failure and deformation of steel frames.
(a)(b)According to a large number of engineering practices, it is likely to have large deformation of the surrounding rock in the construction of phyllite tunnel in western China. To study the deformation mechanism of phyllite tunnels, Chen et al. [18] statistically analyzed the buried depth, maximum ground stress, rock compressive strength, and other data of 93 phyllite tunnels in western China. To describe the high in situ stress caused by the release of strain energy in soft rock, the strength-stress ratio of rock mass is defined as the indicator to anticipate the extrusion deformation according to Hoek E [19], as shown in Table 1, where σcm is the uniaxial compressive strength and P0 is the initial ground stress.Table 1
Compressibility classification of the soft surrounding rock.
Classificationσcm/P0Strainε (%)Deformation descriptionI>0.4<1LowII0.4∼0.21∼2.5MediumIII0.2∼0.152.5∼5SevereIV0.15∼0.15∼10Very severeV<0.110∼15Extremely severeAccording to the Hoek E classification method, the statistical data of Chen et al. [18] and other scholars are classified as shown in Figure 5. The proportion of tunnels with severe large deformation exceeds 20%, and the proportion of tunnels with medium grade and above large deformation exceeds 60%. Thus, it can be seen that there is a high probability of large deformation in the excavation process of phyllite tunnel in western China, so it is necessary to focus on the analysis of the mechanical properties of surrounding rocks in the investigation and design stage and determine the classification of compressible surrounding rocks according to the intensity stress ratio of surrounding rocks.Figure 5
Schematic diagram of the intensity stress ratio classification of phyllite tunnel in western China.To further understand the mechanical properties of surrounding rocks of Maoxian tunnel and determine the level of surrounding rocks that can be compressed, uniaxial compression tests were conducted on the samples of surrounding rocks of No. 1 inclined well of Maoxian tunnel. The rock specimens at XJ1K0 + 350 and XJ1K0 + 270 points are shown in Figures6 and 7.Figure 6
Rock specimens at XJ1K0 + 350. (a) Surrounding rock. (b) Rock specimens.
(a)(b)Figure 7
Rock specimens at XJ1K0 + 270. (a) Surrounding rock. (b) Rock specimens.
(a)(b)Multiple test results show that the uniaxial compressive strength of the rock is 1.95∼2.38MPa, which belongs to the category of extremely soft rock according to the standard in [20]. In the test section, the ground stress of the surrounding rock is 20–25 MPa, and its intensity stress ratio is lower than 0.1. According to the conclusion in Table 1, it is likely to encounter large compressive deformation in the process of tunnel excavation.According to the above research results, the dynamic design method of double primary support is adopted in the large deformation section of the Maoxian tunnel. Satisfactory engineering results have been obtained through field application. The design of double primary support is shown in Figure8, and the design of double primary support and secondary lining is shown in Figure 9.Figure 8
Large deformation support design of the Maoxian tunnel.Figure 9
Schematic diagram of double primary support and secondary lining.HW175 and C30 high-strength concrete, ∅8 steel net, resin bolt, and automatic bolt are all used for the steel frames of double primary support. The specific support parameters are shown in Table2.Table 2
Parameters of double primary support.
Double primary supportDeformation allowanceGunite concreteReinforcing meshBoltLocationGap (mm)LocationThickness (mm)LocationSpace (cm)LocationTypeLength (m)Space (m)Resin4Primary 1Arch wall25Whole ring245Whole ring20∗20ArchAutomatic101.0∗1.2Side wallAutomatic101.0∗1.2Primary 2Arch wall15Whole ring230Arch wall20∗20————The compressive stress values between surrounding rocks and the first primary support, between the first primary support and the second primary support, and between the second primary support and the secondary lining are measured, respectively. After the tested values are stable, the compressive stress values at the arch roof, arch waist, and side wall are read, as shown in Figure10. The red line represents the compressive stress between the surrounding rock and the first primary support, the yellow line represents the compressive stress between the first primary support and the second primary support, and the green line represents the compressive stress between the second primary support and the secondary lining. The results show that the stress values of the second primary support and the secondary lining at the vault decreased by 30.5% and 42.1%, respectively, compared with that of the first primary support. The stress values of the second primary support and the secondary lining at the arch waist decreased by 22.1% and 44.6%, respectively, compared with the first primary support. The stress values of the second primary support and the secondary lining at the side wall decreased by 23.7% and 54.1%, respectively, compared with the first primary support. The double primary support has a significant effect on the energy release of the surrounding rock and significantly reduces the load on the secondary lining.Figure 10
Schematic diagram of double primary support and secondary lining.


## 2.1. Energy Conversion in Support Process

The large deformation of surrounding rock is a kind of mechanical behavior of surrounding rock under the environmental conditions such as ground stress and groundwater activity. Its essence is the loss or partial loss of self-supporting ability of surrounding rock, the lack of effective constraints on deformation, and the plastic deformation of surrounding rock, which leads to the failure of surrounding rock support to different degrees. The large deformation of surrounding rock caused by tunnel excavation will be accompanied by the release of rock energy. To make the surrounding rock reach the stable state as far as possible after tunnel excavation and support, the energy value of reaccumulated energy of surrounding rock must be reduced. According to the energy conservation theory, the energy conversion relationship between tunnel excavation and support is as follows:(1)Wc+Um=Uc+Wr+Wn+Wf,where Wc is the work done by the internal stress of rock mass due to tunnel excavation, Um is the strain energy released during the rock mass excavated from the tunnel, Uc is the reassembled elastic energy in the surrounding rock, Wr is the elastic energy lost in the process of excavation, Wn is the inelastic strain energy lost in the surrounding rock, and Wf is the energy absorbed by the support structure.After tunnel excavation, the rock mass has viscous, plastic, and brittle fracture behavior, leading to local failure of surrounding rock. Surrounding rock will lose energyWr and Wn and regain part of energy Uc. Support will absorb part of energy Wf. Since the nature of surrounding rock is an inherent property, Wc, Um, and Wr can be approximately considered as unchanged after the tunnel form is determined. It can be seen that(2)Uc+Wn+Wf≈const.Based on the energy transformation of the surrounding rock in (2), the supporting structure of the tunnel can be designed in a reasonable way. By appropriately increasing the inelastic strain energy Wn lost in the surrounding rock and energy Wf absorbed by the supporting structure, the reaccumulation of energy Uc in the surrounding rock can be reduced and the stability of surrounding rock can be maintained as far as possible.However,Wn is the inelastic loss of work, and the large deformation of surrounding rock will cause excessive loose pressure, so the increase of Wn should be limited within a certain range. Therefore, lowering Uc should consider primarily raising Wf.When the surrounding rock pressure works on the support structure,Wf converted to the support structure can be divided into(3)Wf=We+Wp,where We is the elastic energy stored in the support and Wp is the energy consumed by plastic deformation of support.


## 2.2. Support Characteristic Curve of Double Primary Support

Figure1(a) shows the single primary support structure, and its support characteristic curve is shown in Figure 2(a). AB is the stress characteristic curve of single primary support. Support stores and consumes energy through elastic-plastic deformation. The energy conversion amount is low, which can be expressed as follows:(4)Wfs=Wes+Wps,where Wfs is the total energy absorbed by single primary support structure and Wes and Wps are the elastic and plastic energy absorbed by the single primary support structure, respectively.Figure 1
Support structure drawing. (a) Single primary support structure. (b) Double primary support structure.
(a)(b)Figure 2
Support characteristic curve. (a) Single primary support structure. (b) Double primary support structure.
(a)(b)Figure1(b) shows the double primary support structure, and its support characteristic curve is shown in Figure 2(b), where AB is the stress characteristic curve of single primary support and ACF is the stress characteristic curve of double primary support. The double primary support structure is first applied to the first primary support, and its stress characteristic curve is AC. In order to absorb more deformation energy of the surrounding rock, Uc>Ub, when the deformation of the first primary reaches Uc, the second primary support is applied. The first primary support stiffness K1 (AC) of the second primary support is less than that of the single primary support stiffness Ks (AB). It is assumed that the overall equivalent stiffness Kd (CF) of the second primary support is equal to that of the single primary support Ks, point F coincides with point D and CF||AB. Normally, point F is within the interval DE. If the deformation of first-layer primary support exceeds the design value significantly, Point F can move towards DB. The overall equivalent stiffness Kd of the double primary support can be expressed as(5)Kd=λ1K1+λ2K2,where λ1 and λ2 are the double primary support structure parameters, respectively.The surrounding rock deformation energy absorbed by the double primary support structure can be expressed as(6)Wfd=Wfd1+Wfd2=We1+Wp1+We2+Wp2,where Wf1 and Wf2 are the energy absorbed by the support structure of the first primary and the second primary supports, respectively, and We1 and We2 are the elastic energy absorbed by the supporting structure of the first primary and the second primary supports, respectively. Wp1 and Wp2 are the plastic energy absorbed by the first primary and the second primary support structures.Because the double primary support allows the surrounding rock to do work on the support structure by allowing greater deformation, compared with the single primary support, the surrounding rock deformation energy absorbed by the support structure is increased.For example, whenKD=Ks, point F coincides with point D and Uf=Ud>Ub; then, We1+We2>Wes and Wp1+Wp2>Wps, so Wfd>Wfs.The support parameters of the second primary can be dynamically adjusted with the support effect of the first primary. Generally speaking, under the condition that single primary support can stabilize surrounding rocks, the equivalent stiffnessKD of double primary support can be less than that of single primary support and greater than that of the first primary support, K1<KD<Ks. Therefore, point F is in the DE interval of the surrounding rock characteristic curve.


## 2.3. Dynamic Design Method of Double Primary Support

To cope with the impact of large deformation in soft rock on tunnel structure, railway tunnels built in western China, such as Yu-Lan line tunnel, adopt secondary lining with a thickness of 1.5∼2.1 m to solve large extrusion deformation of the surrounding rock in high in situ stress-broken phyllite rocks. The secondary lining is a formwork concrete structure with high stiffness and easy to be crushed and broken, which affects the operation safety and service life of railway tunnels. At the same time, the construction cost has been greatly increased. Therefore, the dynamic design method of double primary support is put forward. Considering that the secondary lining can be set after monitoring the deformation amount and deformation rate of the first primary support, its support parameters can be dynamically adjusted according to the actual situation. The dynamic design method of double primary support is shown in Figure3. Its design idea is as follows:(1)
The double primary support structure is designed based on geological prospecting data, and the initial values of the support parameters of the first primary and the second primary are determined. The equivalent flexural stiffness of the double primary support isKd=λ1K1+λ2K2.(2)
Construct the first primary support according to the design parameters, and monitor the deformation of the first primary in real time.(3)
Draw the relation curve between support deformationUc and time t, get the function of Uc=ft, and calculate deformation acceleration dUc2/dt2.(4)
After the timeT (the deformation time of the first support design under the compression of surrounding rocks), the dynamic support design scheme of the second primary is determined by comparing the deformation limit value UsU1<Us<U2 of the first support with the initial design and the deformation acceleration dUc2/dt2. The deformation limit value of the first-layer primary support Us is an empirical parameter in the range of 20∼50 cm, which is equal to the reserved deformation between two primary supports.(5)
WhenUc>Us, the deformation of the first primary support exceeds the deformation limit value Us, and it is necessary to remove and replace the first primary support or take other treatment measures, such as temporary or permanent enhancement of the first-layer primary support, to improve the stiffness of the first primary support. In particular cases, the deformation of the first-layer primary support can be adjusted to exceed the deformation limit value Us with the evaluation and approval of experts, and the parameters of the second-layer primary support can be further evaluated and modified.(6)
WhenUc=Us and dUc2/dt2≥0, the deformation of the first primary support Uc reaches the deformation limit value Us, and the deformation rate is still increasing. However, as the deformation of the first primary support does not exceed the deformation limit Us within the design time T, considering the setting of double primary support, the stiffness of the second primary of support (K2′) should be higher than the design value K2. After the construction of the second primary support, continue to monitor the deformation Ud and calculate dUd/dt. According to the in situ test, combined with relevant experience and the regulation of the Code for Tunneling in Squeezing Rocks, if Vda<1mm for the small- and medium-span tunnels or Vda<2mm for the large-span tunnel [17], where Vda is the deformation rate of average for 7 d, Vda=∑m=17dUdm/7dt, and dUdm is for the m days, when the second primary support is finished. Otherwise, it is necessary to change a support structure or take other measures.(7)
WhenUc<Us and dUc2/dt2≥0, the supporting deformation Uc of the first primary does not reach the deformation limit value Us, but the deformation rate is still increasing. Measures can be taken to delay further release of surrounding rock deformation to make the supporting deformation Uc reach the deformation limit value Us, and then, the deformation rate can be calculated. If dUc2/dt2≥0, it indicates that the deformation of the surrounding rock has slowed down, and the second primary of support can be set without further increasing the support stiffness, that is, K2′=K2. If dUc2/dt2≥0, it indicates that the deformation of the surrounding rock is still not obviously controlled. The second primary support should be set as soon as possible, and the supporting stiffness should be improved, that is, K2′>K2. After the construction of the second primary support is completed, continue to monitor the deformation Ud, and calculate dUd/dt. The next step is the same with Step (6).(8)
WhenUc<Us and dUc2/dt2<0, the deformation of the first support primary Uc does not reach the deformation limit value Us, and the deformation rate also slows down, indicating that the deformation of the surrounding rock is well controlled after the first support primary. By calculating Vda, if it meets the requirements lining timing of [17], the second primary support cannot be applied. Otherwise, it is still necessary to apply the second primary support to ensure the safety of the structure.Figure 3
Dynamic design method of double primary support.


## 2.4. Application of the Proposed Method

The Chenglan Railway is a plateau railway over 3,000 meters above the sea level, rising from the Chengdu Plain at 500 meters above the sea level to the eastern edge of the Qinghai–Tibet Plateau at 3,400 meters above the sea level. There are a large proportion of bridges and tunnels in this project. The Maoxian tunnel is located in Guangming Town, Maoxian County, Sichuan Province. The tunnel runs through the core of the active fault zone in the back mountain of Longmen Mountain, with a total length of 9,913 meters. It is a key and difficult project in the whole line. The Maoxian tunnel will pass through three faults, two anticlines, and one synclinal fault zone with a maximum depth of about 1650 m. The strata are mainly carbonaceous phyllite, argillaceous limestone, sericite, and sandstone. The strength of the soft surrounding rock is extremely low, and its own stability is extremely poor. Figure4 shows the support failure caused by the large deformation of the tunnel.Figure 4
Support failure caused by the large deformation of the tunnel. (a) Shotcrete squeezed off. (b) Failure and deformation of steel frames.
(a)(b)According to a large number of engineering practices, it is likely to have large deformation of the surrounding rock in the construction of phyllite tunnel in western China. To study the deformation mechanism of phyllite tunnels, Chen et al. [18] statistically analyzed the buried depth, maximum ground stress, rock compressive strength, and other data of 93 phyllite tunnels in western China. To describe the high in situ stress caused by the release of strain energy in soft rock, the strength-stress ratio of rock mass is defined as the indicator to anticipate the extrusion deformation according to Hoek E [19], as shown in Table 1, where σcm is the uniaxial compressive strength and P0 is the initial ground stress.Table 1
Compressibility classification of the soft surrounding rock.
Classificationσcm/P0Strainε (%)Deformation descriptionI>0.4<1LowII0.4∼0.21∼2.5MediumIII0.2∼0.152.5∼5SevereIV0.15∼0.15∼10Very severeV<0.110∼15Extremely severeAccording to the Hoek E classification method, the statistical data of Chen et al. [18] and other scholars are classified as shown in Figure 5. The proportion of tunnels with severe large deformation exceeds 20%, and the proportion of tunnels with medium grade and above large deformation exceeds 60%. Thus, it can be seen that there is a high probability of large deformation in the excavation process of phyllite tunnel in western China, so it is necessary to focus on the analysis of the mechanical properties of surrounding rocks in the investigation and design stage and determine the classification of compressible surrounding rocks according to the intensity stress ratio of surrounding rocks.Figure 5
Schematic diagram of the intensity stress ratio classification of phyllite tunnel in western China.To further understand the mechanical properties of surrounding rocks of Maoxian tunnel and determine the level of surrounding rocks that can be compressed, uniaxial compression tests were conducted on the samples of surrounding rocks of No. 1 inclined well of Maoxian tunnel. The rock specimens at XJ1K0 + 350 and XJ1K0 + 270 points are shown in Figures6 and 7.Figure 6
Rock specimens at XJ1K0 + 350. (a) Surrounding rock. (b) Rock specimens.
(a)(b)Figure 7
Rock specimens at XJ1K0 + 270. (a) Surrounding rock. (b) Rock specimens.
(a)(b)Multiple test results show that the uniaxial compressive strength of the rock is 1.95∼2.38MPa, which belongs to the category of extremely soft rock according to the standard in [20]. In the test section, the ground stress of the surrounding rock is 20–25 MPa, and its intensity stress ratio is lower than 0.1. According to the conclusion in Table 1, it is likely to encounter large compressive deformation in the process of tunnel excavation.According to the above research results, the dynamic design method of double primary support is adopted in the large deformation section of the Maoxian tunnel. Satisfactory engineering results have been obtained through field application. The design of double primary support is shown in Figure8, and the design of double primary support and secondary lining is shown in Figure 9.Figure 8
Large deformation support design of the Maoxian tunnel.Figure 9
Schematic diagram of double primary support and secondary lining.HW175 and C30 high-strength concrete, ∅8 steel net, resin bolt, and automatic bolt are all used for the steel frames of double primary support. The specific support parameters are shown in Table2.Table 2
Parameters of double primary support.
Double primary supportDeformation allowanceGunite concreteReinforcing meshBoltLocationGap (mm)LocationThickness (mm)LocationSpace (cm)LocationTypeLength (m)Space (m)Resin4Primary 1Arch wall25Whole ring245Whole ring20∗20ArchAutomatic101.0∗1.2Side wallAutomatic101.0∗1.2Primary 2Arch wall15Whole ring230Arch wall20∗20————The compressive stress values between surrounding rocks and the first primary support, between the first primary support and the second primary support, and between the second primary support and the secondary lining are measured, respectively. After the tested values are stable, the compressive stress values at the arch roof, arch waist, and side wall are read, as shown in Figure10. The red line represents the compressive stress between the surrounding rock and the first primary support, the yellow line represents the compressive stress between the first primary support and the second primary support, and the green line represents the compressive stress between the second primary support and the secondary lining. The results show that the stress values of the second primary support and the secondary lining at the vault decreased by 30.5% and 42.1%, respectively, compared with that of the first primary support. The stress values of the second primary support and the secondary lining at the arch waist decreased by 22.1% and 44.6%, respectively, compared with the first primary support. The stress values of the second primary support and the secondary lining at the side wall decreased by 23.7% and 54.1%, respectively, compared with the first primary support. The double primary support has a significant effect on the energy release of the surrounding rock and significantly reduces the load on the secondary lining.Figure 10
Schematic diagram of double primary support and secondary lining.


## 3. Conclusions

Based on the theory of energy conversion, this paper analyzed the support characteristic curve of double primary support and put forward the dynamic design method of double primary support. This method was verified by the application of ChengLan railway tunnel. Some conclusions are as follows:(1)
By appropriately increasing the inelastic strain energyWn lost in the surrounding rock and the energy Wf absorbed by the supporting structure, the reaccumulation of energy Uc in the surrounding rock can be reduced and the stability of the surrounding rock can be maintained as far as possible. However, Wn is the inelastic loss of work, and the large deformation of the surrounding rock will cause excessive loose pressure, so the increase of Wn should be limited within a certain range. Therefore, lowering Uc should consider primarily raising Wf.(2)
Because the double primary support allows the surrounding rock to do work on the support structure by allowing greater deformation, compared with the single primary support, the surrounding rock deformation energy absorbed by the support structure is increased.(3)
Compared with the traditional single primary support, the double primary support design method has obvious technical advantages. Firstly, under the same stiffness condition, the double primary support has a higher safety factor than the single primary support under the pressure on the secondary lining. Secondly, the second primary of the double primary support can be dynamically adjusted according to the actual monitoring situation of the first primary. When the deformation amount and deformation rate of the first primary are higher than the original design expectation, the support strength and stiffness of the second primary can be increased to further control the surrounding rock deformation and ensure the construction safety. When the deformation amount and deformation rate of the first primary support are lower than the original design expectation, the strength and stiffness of the second primary support can be reduced, and even the second primary support can be cancelled, thus reducing the project cost. The dynamic design process gives timely feedback to the construction information. When the deformation of the first primary support exceeds the design deformation limit valueUs, it can quickly guide the decision to remove and replace the first primary support or take other treatment measures and adjust the design scheme, so as to reduce the project risk.(4)
By applying the double primary support design method in the Maoxian tunnel of Chenglan Railway, the field monitoring results show that the double primary support has a significant effect on the energy release of surrounding rocks, greatly reducing the load acting on the secondary lining and ensuring the safety and reliability of the tunnel structure.



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*Source: 8832797-2020-09-19.xml*