Physical Model Test on the Deformation and Fracturing Process of Underground Research Laboratory during Excavation and Overloading Test

Abstract

Understanding the excavation-induced deformation and failure behaviors of the URL (underground research laboratory) for the geological disposal of HLW (high-level radioactive waste) before its construction is essential due to its high safety requirements. To reveal the interaction between structures, the effect of supporting and the characteristics of the overloading-induced damage and safety factor, we carried out a physical model test on the deep underground chamber groups consisting of one main roadway and two parking lots (one is supported, the other is not supported), and the engineering background is the URL of HLW for the geological disposal in Beishan. This type of geomechanical model test is still the first to be carried out so far. The test results confirm that the chamber group is generally stable during the excavation process. After the excavation, the displacement of the intersection is 7–33% larger than that of the non-intersection. The displacement of the supported chamber is reduced by 14–22% compared with that without support. The tension of the bolt at the vault top is greater than that at the waist of the cave. Without support, the safety coefficient of crack initiation is 1.7; the safety coefficient of local destruction is 2.1; and the safety coefficient of general demolition is 2.3. In contrast, the safety coefficient of crack initiation is 1.9; the safety coefficient of local destruction is 2.2; and the safety coefficient of general demolition is 2.4 when the rock mass is supported. The research results provide an important basis for optimizing design schemes and evaluating the safety of the construction process for URL.

1. Introduction

A power shortage has become a principal question in many coastal areas accompanied by the rapid development of China’s economy. Faced with this situation, the Chinese government has changed its policy on the development of nuclear power and many new nuclear power plants have been constructed or are under construction [1]. However, fast development of nuclear power causes an emergency challenge, i.e., the total amount of high-level radioactive waste that needs to be disposed of will reach 83,000 tons by 2050 [2]. The safe disposal of the HLW is an important task for sustainable development and environmental protection. The safest and most feasible method is deep geological disposal [2,3].

The underground engineering of burying HLW is called deep geological repositories (DGRs) whose service life should be at least 1 × 10⁴ a because waste in a repository is toxic and has a long half-life. This requirement is not considered in the projects encountered previously. The development of DGRs is a long-term and systematic process, which generally involves basic research, site evaluation of repositories, URL study, repository design, construction and closure [4].

The URL is an essential key facility linking the various procedures during the development of DGRs [3]. The purposes of URL construction are to ultimately evaluate the long-term performance and safety of DGR through various studies [2]. So far, a number of URLs have been constructed around the world [5,6,7,8]. To satisfy the many functions, most URLs are deeply buried and have relatively complex layouts. For instance, the Meuse/Haute-Marne URL in France consists of two levels of experimental drifts at depths of 445 m and 490 m, which consist of two shafts and drift networks [9]; the Äspö Hard Rock Laboratory in Sweden consists of a shaft, a spiral ramp and horizontal roadways with a maximum burial depth of 420 m [10].

Therefore, it is necessary to master the construction technology of DGRs, to understand the effects of various factors on the disposal system and to evaluate the performance of the repository barrier. A large number of laboratory experiments and in situ tests have been carried out, for instance, research on the site characteristic evaluation method including the new technology, method and equipment for obtaining rock and groundwater characteristics of sites [11,12,13]; study on the manufacturing and performance of the engineering barrier such as to obtain the chemical and physical properties of the artificial barrier and cushioning materials [14,15,16,17]; the service life prediction and corrosion behavior disposal cans [18,19,20]; study on the excavation technology of DGRs such as the excavation technology [21,22] and equipment performance [23] of DGRs with minimum damage to surrounding rock; study on the effect of radioactive waste disposal such as the disposal cans and the cushioning materials’ responses under coupled thermo-hydro-mechanical conditions [24,25]; and the radionuclide migration test including diffusion and adsorption of radionuclides in rocks and their migration with the rock fissure flow [26,27,28], etc.

Numerical simulation has become quite mature and achieved very good results [29]. However, the structure of URL is generally complex and deep-buried; it is difficult to simulate the rupture process of surrounding rock by numerical modeling, and the simulation of overall structural safety is not perfect. Conducting in situ tests is limited by their high costs. In contrast, the physical model test plays an important part in the study of geotechnical engineering [30].

So far, physical model experiments have been extensively applied on excavation processes and the support of underground chambers with remarkable achievements obtained [31,32,33]. For instance, in the aspect of experimental means, Shin et al. [34] carried out model tests on the Umbrella Arch Method while Hu et al. [35] carried out tests on the Pipe-Roofing Method, which verified the rationality of these construction methods; in the aspect of experimental equipment, Bao et al. [36] proposed a multi-scale method to simulate the test model of shield tunnels, Zhu et al. [37] researched and developed a 3D physical model test system and Li et al. [38] realized 3D loading of physical model experiments; in the aspect of measurement methods, Lin et al. [39] and Wang et al. [40] applied the acoustic emission (AE) monitoring system to model experiments, while Chen et al. [41] applied photogrammetry and laser scanning to measure tunnel deformation. Zhang et al. [42] and Zhu et al. [43] used displacement sensing rods based on fiber Bragg gratings and multi-point extensometers to measure the displacement of surrounding rock in model experiments; in the aspect of the support system, Zhu et al. [43] achieved construction simulation of the pre-stressed cable and rock bolt in physical model experiments and Nunes and Meguid [44] studied the effect of the hard layer covering the tunnel on the stress generated in the tunnel lining through model experiments. All of these studies have greatly promoted the development of physical model experiments.

Many previous model tests were subject to the following limitations: most of them were planar or quasi-three-dimensional, which cannot simulate the real state of in situ stress; the size of most of the experimental systems was small, which can only simulate a single chamber rather than complex chamber groups; and most mining was performed manually, resulting in low accuracy and having a negative impact on test results. To overcome these limitations, we have carried out 3D geomechanical model tests [31] and overloading tests [45]. Different from our previous tests, the objective of this study was to assess the interaction between chambers, integral stability and the supporting anchorage effect of the π-shaped intersection chamber composed of one circular main roadway and two three-core arch parking lots. In addition, the characteristics of the overloading-induced damage and safety factor of the whole system were estimated through the overloading test.

2. Project Overview

The pre-selected location for China’s first URL for deep geological disposal of HLW is located in the Beishan area of Gansu Province, Northwestern China.

The terrain of this area is mainly composed of flat Gobi and small hills with the elevation ranging from 1400 m to 2000 m. In situ tests confirmed that the in situ stress can be calculated from the depth (H) as follows:

$$\left.\begin{array}{c}{\sigma }_{\mathrm{H}}=0.0305\mathrm{H} \left(\mathrm{M}\mathrm{P}\mathrm{a}\right)\\ {\sigma }_{\mathrm{h}}=0.0208\mathrm{H} \left(\mathrm{M}\mathrm{P}\mathrm{a}\right)\\ {\sigma }_{\mathrm{v}}=0.0268\mathrm{H} \left(\mathrm{M}\mathrm{P}\mathrm{a}\right)\end{array}\right\}$$

(1)

where σ_H is the maximum horizontal principal stress; σ_h is the minimum horizontal principal stress; and σ_v is the vertical stress [31,45,46].

Figure 1a shows the preliminary design scheme of the Beishan URL, which consists of one ramp, three shafts and two-level experiment chambers [2]. The experiment chambers will be located on two levels, namely the main level of −560 m and the auxiliary level of −240 m. In order to study the stability, supporting effect and overloading safety of the typical large section of chambers, we select two parking lots at the depth of 560 m and the main roadway intersecting with them as the research target (Figure 1b). The scale of the prototype is 125 m × 125 m × 100 m. In this range, there are one main roadway (diameter of 7 m) and two parking lots (cross-section size of 12 m × 9 m) (see Figure 1c).

3. Physical Model Test

3.1. Similarity Principles

According to the similitude theory, the following relationships should also be satisfied [31,45,47]:

$$C_{\sigma }=C_{\gamma }{C}_L$$

(2)

$$C_{\delta }=C_{\epsilon }{C}_L$$

(3)

$$C_{\sigma }=C_{\epsilon }{C}_E$$

(4)

$$C_{\epsilon }=C_f=C_{\phi }=C_{\mu }=1$$

(5)

where C_E, Cε, C_δ, C_L, C_γ, C_σ, C_f, C_φ and C_μ are the similarity coefficients of the elastic modulus, strain, displacement, geometry, volume–weight, stress, coefficient of friction, frictional angle and Poisson’s ratio, respectively.

Based on the scale of the test system and the range of the project, the similarity coefficient of geometry C_L was selected to be 50. The overall dimension of the analogue model is 2500 mm × 2500 mm × 2000 mm, accordingly. The analogue model consists of the main roadway (with a diameter of 140 mm) and two parking lots (with the cross-section size of 240 mm × 180 mm) (see Figure 2). The physical model test was conducted using the 3D physical model test system. Photos of the system can be found in Figure 3 and more details about it can be found in our previous publications [31,45].

3.2. Development of the Similar Materials

3.2.1. Similar Materials of Surrounding Rock

One of the most important prerequisites to conduct a geomechanical model test is that the similar materials should behave similarly with the real rock. We used the IBSCM (iron–barites–silica cementation material) [31,45] as the similar material of surrounding rock in this study.

The similarity coefficient of volume–weight C_γ was selected to be 1. Then, the similarity coefficients of other parameters could be determined according to Equation (3).

Table 1. Mechanical and physical parameters.

Parameters	Uniaxial Compressive Strength (ucs) (MPa)	Tensile Strength (τ) (MPa)	Deformation Modulus (Eo) (GPa)	Cohesion (c) (MPa)	Friction Angle (φ) (°)	Poisson’s Ratio (μ)	Unit Weight (γ) (kN/m3)
Original rock	132.37	6.86	49.17	28.13	50.6	0.264	26.80
Similar materials (calculated from similarity principles)	2.647	0.134	0.983	0.563	50.6	0.264	26.80
Similar materials (measured by experiments)	2.611~2.683	0.123~0.142	0.955~0.992	0.541~0.571	49.9~50.6	0.25~0.27	26.2~27.1

shows the mechanical and physical parameters of the original rock and the similar materials, respectively.

Table 2. The mix proportion of the similar materials (from refs. [31,45]).

Similar Scale	I:B:S	Concentration (%)	Proportion of Mass of Binder (%)
CL = 50	1:0.45:0.25	18	6

I, B and S refer to the proportion of the refined iron powder, the barite powder and the quartz sand, respectively.

shows the mix proportion of the similar materials.

3.2.2. Simulation of the Support

Three types of materials were normally used in previous studies to simulate bolts in model tests: metal materials (aluminum wire, iron wire, copper wire, tin wire, etc.), plant reinforcements (bamboo, wood, etc.) and composite materials (glass fiber, nylon rod, high-pressure polyethylene, etc.) [30]. The grouting materials were simulated by a cement slurry, gypsum slurry and high-concentration alcohol rosin silicone oil solvent [31,45]. In this study, semi-hardened aluminum wire (2 mm in diameter) was used to simulate the bolt with the consideration of the similarity of the bolt length, elasticity modulus, yield strength and tensile strength. The high-concentration rosin alcohol solution was selected as the grouting material. The properties of the prototype and analogue bolt are listed in

Table 3. Parameters of the original bolt and the analogue bolt.

Parameters	Length (L) (m)	Elastic Modulus (E) (GPa)	Yield Strength (σs) (MPa)	Tensile Strength (σt) (MPa)
Original bolt	2.5	206	315	490
Analogue bolt	0.05	3.7	6.3	8.21

.

3.3. Construction of the Physics Model

3.3.1. Construction Procedures

The physical model was paved, compacted and air-dried layer-by-layer to ensure the integrity and homogeneity of the surrounding rock [48,49,50,51,52,53].

Due to the limitation of the bolt installation technology and model chamber size, the bolt support is frequently simulated by pre-embedding the bolt [31,50,52]. The detailed procedures of pre-embedding the bolt are as follows: determining the position of pre-embedding the bolt (see Figure 4a); drilling holes in the position of the pre-embedded bolt (see Figure 4b); inserting similar materials of the bolt (see Figure 4c); injecting grouting similar materials (see Figure 4d); and air-drying grouting similar materials. Three sections of bolts are selected as monitoring objects and strain gauges are pasted in the middle of the bolts.

3.3.2. Installation of the Monitoring Sensors

Figure 5 shows the positions of the monitoring sensors in the test. All monitoring sensors are installed at the key parts in five monitoring sections. The main steps to install the sensors can be found in Figure 6.

3.4. Model Excavation

Once the physical model was constructed, 3D gradient loading was applied on its boundaries to simulate the in situ stress at a depth of 560 m. A realistic initial stress state calculated from Equation (1) was applied, as shown in Figure 1c. Constant initial stresses were applied on the model for 24 h, so as to form a stable initial stress field within the model.

The in situ stress of the whole model remained constant during the entire excavation process. The sequence of excavation is as follows: the main roadway, upper step of parking lot II, lower step of parking lot II, upper step of parking lot I and lower step of parking lot I.

Table 4. The excavation controlling parameters in the model test.

Order of Excavation	Length (mm)	Excavation Method	The Advance Rate (mm/step)	Number of Steps
1. Main roadway	2500	Full section	40	60
2. Parking lot II	1090	Upper and lower steps	40	56
3. Parking lot I	1090	Upper and lower steps	40	56

shows the excavation controlling parameters in the model test. The mini automatic excavation device is used for chamber group excavation.

3.5. Test Results

In this section, in order for the convenience of the analysis and research, we converted all the test data obtained from the physical model experiments into prototypes.

3.5.1. Test Results of Surrounding Rock

Figure 7 and Figure 8 show the variations of the radial displacements in the different sections of the chamber group, respectively.

From these results, we can conclude the following:

Variation of radial displacement is basically consistent with the phenomena from previous tests [40,41]; namely, the radial displacement gradually reduces with the increase in distance from the periphery. The difference is that the maximum displacement in this test (4 mm) is larger than that of the previous one (2.75 mm) [4] because the interface size of the parking lot in this study is larger than that of all the chambers in the previous test.

After excavation, the displacement of the unsupported parking lot I is greater than that of the supported parking lot II at the same location. The displacement of the supported chamber is reduced by 14–22% compared with that of the unsupported chamber.

Figure 9 and Figure 10 present the typical curves of radial stresses calculated from the strains measured by strain bricks after excavation. Figure 11 presents the typical stress curves measured by pressure cells after excavation. From these results, we concluded the following:

The variation of stress after excavation is basically the same as that of previous tests [31,45,53]; namely, the stress measured by the pressure cell and strain brick is basically the same. There is obvious interaction between the chambers during excavation, e.g., the stress curve of the middle part between two parking lots is parabolic rather than a monotonic decreasing trend. The difference is that the maximum tangential stress at the intersection in this experiment (46.67 MPa) is larger than that of the previous test (39.2 MPa) [31] because the interface size of the parking lot in this experiment is larger than that of all the chambers in the previous test.

3.5.2. Test Results of the Bolt

The axial force (N_i) of the bolt can be calculated by the following formula:

$$N_i=E_b{\epsilon }_i\pi {\varnothing }^2/4$$

(6)

where E_b, ε_i and ∅ are the elastic modulus, monitored axial strain and bolt diameter, respectively.

Figure 12 shows the curve of the axial force along the bolt at Section M-1 after the chamber excavation. The experimental chamber is axisymmetrical, so the displacement of the symmetrical part of the supporting chamber can be compared with that of the unsupported chamber, to reveal the supporting effect of the bolt. As shown in Figure 5a, the selected parts of the red and blue border are two symmetrical parts, respectively. Comparison of the displacements between supported and unsupported chambers at the same position is shown in Figure 13.

The following can be observed:

The axial force of the bolt is very small, which indicates the interaction between the bolt and rock is very weak before the chamber excavation. During the excavation of the upper and lower steps of the chamber where the embedded bolts are located, the axial force tends to increase rapidly. After the excavation, the axial force of the anchor tends to be stable.

After the excavation, the axial force of bolts is all tensile force. The tension of the bolt at the vault top is greater than that at the waist of the cave. This indicates that the supporting effect of the bolt at the vault top of the chamber is greater than that of the waist bolt.

The displacement of bolted measuring points in the same part of the chamber is less than that of non-bolted measuring points, and the deformation around the chamber decreases by about 14–22% after supporting, suggesting that bolt support controls the development of surrounding rock deformation.

The tensile force in the bolt around the chamber is not large, and the maximum is only 46.23 MPa, which is far lower than the ultimate strength of the bolt. All the bolts remain intact during the evolution process. These results demonstrate that the support scheme is reasonable and reliable.

4. Overloading Test

To further assess the overall safety factors of the URL, we carried out overloading tests on the model after the excavation.

The detailed steps of the overloading model test are as follows: (1) gradually increase crustal stress according to the growth rate of 0.1 times; (2) the stress at each stage is kept constant for half an hour and deformation and failure of the chamber group in real time are recorded; and (3) Steps (1) and (2) are repeated until the chamber group is completely destroyed. In order to observe and record the deformation and destruction of the chamber group in the process of overloading, four micro-HD cameras were placed at the specific locations shown in Figure 14a. Figure 14 shows the pictures of the model after excavation.

4.1. Process of the Overloading Test

The safety coefficient of overloading (K_S) is defined as the following formula:

$$K_s=\frac{P_f}{P_0}$$

(7)

where P₀ and P_f are the loads at the initial and failure stages, respectively.

K_S can especially be divided into three stages based on the displacement changes and the degree of failure of surrounding rock [45]:

$$K_{s1}=\frac{P_1}{P_0};K_{s2}=\frac{P_2}{P_0};K_{s3}=\frac{P_3}{P_0}$$

(8)

where K_S1, K_S2 and K_S3 are the safety coefficient of crack initiation, the safety coefficient of local destruction and the safety coefficient of general demolition, respectively. P₁, P₂ and P₃ are the loads when the crack initiation, local destruction and general demolition start to appear, respectively.

4.2. Destruction Phenomena and Fracturing Patterns

The evolution of fractures at different intersection areas during the overloading test is shown in Figure 15, Figure 16, Figure 17 and Figure 18. We can observe the following from these pictures:

In the overloading stage of 1.1–1.6 P₀, the interior of each chamber and the intersection parts are intact without any obvious cracks in the surrounding rock (see Figure 15a, Figure 16a, Figure 17a and Figure 18a). Therefore, the URL is in a stable state under overloading of 1.1–1.6 P₀.

When the loading exceeds 1.6 P₀, some visible micro cracks appear at the intersection area of the chambers. When overloading increases to 2.0 P₀, slag dropping phenomena appear locally, mainly concentrating at the following locations:

(1) Micro cracks and slag dropping appear at the intersecting roof of the main roadway and parking lot I (hereinafter, RP1) (Figure 15b). (2) Horizontal micro cracks appear at the intersecting roof of the main roadway and parking lot II (hereinafter, RP2) (Figure 16b). (3) Vertical micro cracks appear at the intersecting waist of parking lot I and the main roadway (hereinafter, WP1) (Figure 17b). (4) Micro cracks appear at the intersecting corner of parking lot II and the main roadway (hereinafter, CP2) (Figure 18b).

In the overloading stage of 2.1~2.2 P₀, the micro cracks in the chamber began to expand gradually. With the continuous increase in overloading, the cracks in the chamber gradually changed from narrow to wide, and from short to long, which led local compression–shear and tensile–shear failures to appear in the surrounding rock, specifically manifesting as: (1) Local spalling failures constantly appear at RP1 (see Figure 15c); the initial micro cracks at these interaction areas gradually expand, accompanied by a new vertical fracture emerging at WP1 (Figure 15c). (2) The initial horizontal micro crack at RP2 gradually expands and leads to a horizontal fracture, which is about 1 mm wide (Figure 16c). (3) The initial vertical micro cracks at WP1 gradually expand and lead to local spalling. Several cracks emerge at RP1 (site XX in Figure 17c). (4) Slag dropping appears at the CP2 (Figure 18c).

In the overloading stage of 2.4 P₀, obvious deformation and failure phenomena appear in each part of the chamber groups. This specifically manifests in the following: (1) A large area of collapse appears at RP1. Obvious shrinkage deformation occurs on both sides of the main roadway (Figure 15d). (2) A large area of collapse appears at RP1 (Figure 16d). (3) The cracks at the intersection of parking lot I and the main roadway expand along the wall rapidly. After the formation of the penetrating cracks, the large area of collapse and spalling failures occur (Figure 17d). (4) Parking lot II produces long transverse cracks along the axis of the chamber, causing side walls to be damaged with a large area of spalling (Figure 18d).

4.3. Overloading Induced Deformation

Figure 19 shows the spatial variation of the radial displacements in the horizontal cross-section during overloading while Figure 20 shows the displacements in the vertical cross-section. Figure 21 shows the displacement change curves of Section I in the overloading stage.

From these figures, we concluded the following:

With ongoing overloading, the deformation around the chamber increases gradually. The deformation of the unsupported parking lot (parking lot I) is obviously larger than that of the supported one (parking lot II). The deformation of the unsupported parking lot is about 0–25% less than that of the supported one.

When overloading is stable, the displacement of each chamber increases in varying degrees, and then tends to be stable. With the increase in multiple overloading, the slope of the displacement curve of each chamber increases gradually. During the whole overloading process, the maximum displacement is −160.00 mm, which appears in RP1.

We can maintain that without the support, the safety coefficient of crack initiation is 1.7, the safety coefficient of local destruction is 2.1 and the safety coefficient of general demolition is 2.3. Corresponding with the support, the safety coefficient of crack initiation is 1.9, the safety coefficient of local destruction is 2.2 and the safety coefficient of general demolition is 2.4.

4.4. Discussions

The safety factor after support has been improved, and all the safety factors in this study are smaller than those obtained in previous studies [31,45]. It shows that the interface size of the chamber has obvious influence on the safety factor.

The study of overload tests found that the failure of surrounding rock firstly occurs in the intersection area of the chamber group, and the damage degree in the intersection area is significantly more severe than in other parts. This is also consistent with previous studies [31,45].

5. Conclusions

Three-dimensional physical model tests were carried out on a deep underground chamber group consisting of a main roadway and two parking lots (one was supported, the other was not supported), and the engineering background was the URL of HLW for the geological disposal in Beishan. We have reached the following conclusions:

(1)

After the excavation, convergent deformation occurs in the surrounding rock with the maximum value of more than 4 mm. The displacement of the intersection is 7–33% larger than that of the non-intersection. The displacement of the supporting chamber is reduced by 14–22% compared with that of the unsupported chamber.

(2)

After the excavation, the axial force of bolts is all tensile force. The tension of the bolt at the vault top is greater than that at the waist of the cave, indicating that the supporting effect of the bolt at the vault top of the chamber is greater than that of the waist bolt.

(3)

Support significantly increased the safety factor. Specifically, the safety coefficient of crack initiation is increased from 1.7 to 1.9, the safety coefficient of local destruction is increased from 2.1 to 2.2 and the safety coefficient of general demolition is increased from 2.3 to 2.4.

(4)

The failure of surrounding rock firstly occurs in the intersection area of the chamber group, and the damage degree in the intersection area is significantly more severe than in other parts. Therefore, intensive monitoring should be performed on the large intersection, and appropriate support should be carried out according to the monitoring results. In the next step, we will improve the traditional strength reduction method based on the safety factor obtained from the research to obtain a more accurate and reliable numerical calculation method for evaluating the safety factor of the chamber group.