Dynamic Response of Tunnels with a Rubber-Sand Isolation Layer under Normal Fault Creep-Slip and Subsequent Seismic Shaking: Shaking Table Testing and Numerical Simulation

Abstract

Tunnels may suffer severe damage when passing through an active fault in high-intensity earthquake zones. The present study aims to investigate the performance of an isolation layer composed of a rubber-sand mixture, an emerging trend in low-cost seismic mitigation studies. Based on the Ngong tunnel in the Nairobi-Malaba Railroad in Kenya, Africa, the effect of the rubber-sand isolation layer on the acceleration and strain of the tunnel lining was investigated through a shaking table test under small normal fault creep-slip and subsequent seismic shaking. The influences of the length of the isolation layer and the rubber content in the mixture were analyzed by numerical simulation. The results indicate that the isolation layer slightly reduces the acceleration response of the tunnel lining within the fault and obviously reduces the permanent strain of the invert and crown within the fault under small normal fault creep-slip and subsequent seismic excitation. The mitigation effect of the isolation layer is related to the length of the isolation layer and the rubber content in the mixture. In the case of this study, the length of the isolation layer is triple the fault width (influence range of the fault) and the appropriate enhancement of the rubber content of the isolation layer offers favorable conditions for mitigation effect, respectively.

1. Introduction

Tunnels are considered one of the greatest achievements of civil engineering in the 20th century, enabling railways and highways to traverse mountains and rivers. Although underground structures are generally considered safer than aboveground structures, tunnels all over the world have suffered severe damage from devastating earthquakes, such as the Chi-Chi Earthquake (Taiwan, China, 1999), the Wenchuan Earthquake (Sichuan, China, 2008), and the Kumamoto Earthquake (Kumamoto, Japan, 2016) [1,2,3].

The above devastating earthquakes always occurred in active fault zones. The threat of active faults to the tunnel is manifested in the form of stick-slip dislocation and creep-slip dislocation. The stick-slip dislocation can release tremendous energy and thus induce earthquakes. Compared with fault stick-slip, the fault creep-slip occurs at a certain low and lasting velocity. The literature [4,5] indicated that the occurrences of devastating earthquakes are primarily responsible for relative movements and interactions between adjacent active tectonic blocks, which often result in fault stick-slip and creep-slip. Therefore, a tunnel located in an active fault zone is subject to fault creep-slip and seismic shaking. For example, the tunnels of the Sichuan-Tibet railway through the Qinghai-Tibetan Plateau are challenged by frequent earthquakes and the dense distribution of deep and large active fault zones [6]. The tunnels of the Nairobi-Malaba Railroad in Kenya are vulnerable to damages from active fault creep-slip with a rate of 0.2–2mm/year and potential strong earthquakes in the East African Rift Valley [7,8].

The influence of combined fault creep-slip and subsequent earthquakes on tunnels has attracted much attention. Anastasopoulos et al. [9] first showed that tunnels should have a relatively small segment length under combined normal fault dislocation with a magnitude of 2 m and subsequent seismic shaking. Fan et al. [10] found that initial normal fault creep-slip reduces the overall stiffness of the tunnel in subsequent seismic excitation. Cui et al. [11] elucidated the damage mechanism of normal fault-crossing tunnels under fault rupture and subsequent seismic excitation. Flexible joints and segmented tunnels were investigated for the adaptation of mountain tunnels to fault dislocation with amplitude ranges from 1.5 to 5 m and subsequent seismic shaking, as well as fault dislocation alone, by Yan et al. [12] and Shen et al. [13,14,15,16,17,18]. The fault dislocations in the above studies were meter-level dislocations. The literature [19,20,21] showed centimeter-level dislocations in faults moving with creep-slip rates of 0.1–1mm/year, which resulted in a 1–10 cm displacement within a century. Fault-crossing tunnels may be subjected to centimeter-level dislocation and strong earthquakes. Therefore, besides flexible joints and segmented tunnels, isolation layers may be a theoretical method for the adaption of tunnels to small normal fault creep-slip and subsequent seismic shaking.

Isolation layers have been extensively studied as an aseismic or shock absorption method for the tunnel [22,23,24]. Flexible materials with a low modulus and high damping ratio of seismic isolation layers, such as foamed concrete, geofoam, rubber-sand, and rubber, can be adapted to the larger deformation aroused by low-frequency seismic excitation [25,26,27,28]. Rubber-sand mixtures are considered as an environmentally friendly and low-cost geotechnical seismic isolation (GSI) technology [29,30]. GSI can be achieved by introducing a low-modulus layer for decoupling the structure from the ground shaking [27]. Kaneko et al. and Nikitas et al. [31,32,33] revealed through shaking table tests that the addition of a rubber-sand mixture beneath a structure can activate some effective detuning mechanisms, thus protecting the structure from earthquakes. The same results were supported by numerical and analytical studies [34,35]. Besides the research on the protection of the superstructure by the rubber-sand isolation layer, some scholars have explored its effect on the dynamic response of underground structures. Mehrjardi et al. [36,37] investigated the effect of a geogrid combination rubber-sand mixture on the performance of pipes. The results showed that a mixture with 5% rubber content could reduce the accumulated strain of pipes under cyclic loading. Zhuo et al. [38] studied the application of rubber-sand granular mixtures in high-filled cut-and-cover tunnels through numerical and experimental methods. Mei et al. [39,40] proposed a new rubber-sand-concrete (RSC) consisting of rubber particles, sand, and cement, and experimentally investigated its performance as a seismic isolation layer. Dadkhah et al. [41] researched the effect of rubber-sand mixtures in controlling the ground explosion hazard of underground structures. In addition, several studies have been devoted to the dynamic properties of rubber-sand mixtures. As the rubber content increases, the shear modulus of the mixture decreases, and the damping ratio increases accordingly [42,43,44]. However, there is no analysis of isolation layers for tunnels under small normal fault creep-slip and subsequent seismic shaking or the effect of isolation layer properties on the mitigation of dynamic response.

To solve this problem, rubber-sand is used as an isolation layer material. Rubber-sand samples with different rubber content and rubber-sand isolation layers are fabricated in the lab for the test scale. Then, based on the Ngong tunnel of the Nairobi-Malaba Railroad in Kenya, Africa, the effect of the isolation layer on the dynamic responses of the tunnel is observed through the shaking table test under small normal fault creep-slip and subsequent seismic shaking. In addition, the influences of isolation layer parameters, such as length, elastic modulus, and damping ratio affected by rubber content, are also analyzed by numerical simulations.

2. Experimental Model Tests

Scale model shaking table tests were conducted to study the effect of a rubber-sand isolation layer on the seismic response of soil–horseshoe shape tunnel systems at the National Engineering Laboratory of Construction Technology at Central South University.

2.1. Prototype Description

The Ngong railroad tunnel (Nairobi-Malaba Railroad in Kenya, Africa) is located in the transition zone from the Kapiti Plateau to the East African Rift Valley. This tunnel, with a length of 1.752 km, passes through a creep-slip normal fault (fb9-2) with a rate of 0.2–2mm/year [10], as shown in Figure 1. The fb9-2 fault has an inclined angle and width of 85° and 5–9 m, respectively. Therefore, the fault in the model test is a 90° inclined angle with 7 m width and runs perpendicular to the tunnel axis. This fault is mainly filled with broken rock mass. The surrounding rock of this tunnel consists of fully, strongly, and weakly weathered trachyte. The tunnel has a horseshoe shape with excavated dimensions of 7.34 m in width and 9.60 m in height, as shown in Figure 2. The primary lining is 15 cm of shotcrete for stabilizing the surrounding rock during construction. The secondary lining is a permanent structure made of C30-grade 35 cm concrete and steel arches to bear the loading during the tunnel service stage. Therefore, only the secondary lining was considered in the following model and numerical analysis [14].

2.2. Test Facilities

The shaking table has a plain dimension of 3.6 m × 3.6 m, a maximum load capacity of 10 t with 1.0 g acceleration, and a maximum controlled frequency of 50 Hz. The rigid model box with external dimensions of 3.3 m × 2.3 m × 2.4 m (length × width × height) was applied, as shown in Figure 3a. A synchronous jack was installed at the bottom of the model to simulate the movement of the creep-slip fault, as shown in Figure 3b. In addition, grooves below the jack in which steel roller balls were placed, used to simulate the effect of fault slippage under seismic excitation, are shown in Figure 3c. A 20 cm thick polyethylene foam sheet was laid around the inner walls of the model box to reduce the boundary effect; an approximately 5 cm thick mortar gravel layer was laid at the bottom of the model box to limit the relative displacement between the model box and the surrounding rock.

2.3. Similarity Ratio and Similar Material

To simulate the reliable dynamic response of the fault-rock-tunnel system, similitude relations need to be carefully considered in the test design. The similarity correlation between the prototype and the model was derived from the law of similarity for the model experiment [45,46]. The geometry similarity ratio ($C_L$), density similarity ratio ($C_{\rho }$), and elasticity similarity ratio ($C_E$) are selected as fundamental independent ratios with values of 1:20, 1:30, and 1:1.25, respectively. The strain similarity ratio should be kept to an approximate level of 1 to guarantee that the seismic response and damage of model tests more realistically reflect the prototype. The remaining similarity ratios and parameters can be obtained based on the above three fundamental scale factors. Furthermore, the lining thickness ($C_H$) is 1:6.44 based on the equation $C_H=C_L/{C_E}^{-1/3}$, used in the literature [10]. All of the model to prototype similarity ratios are listed in

Table 1. Similitude relations for the shaking table test.

Item	Dimensions	Similarity Relation	Similarity Ratio
Geometry	L	$C_L$	1/20
Density	ML−3	$C_{\rho }$	1/30
Young’s modulus	ML−1T−2	$C_E$	1/1.25
Strain	-	$C_{\epsilon }$	1
Acceleration	LT−2	$C_{\epsilon }{C}_E/\left(C_L{C}_{\rho }\right)$	1/1.2
Time	T	$C_L/{C_A}^{-1/2}$	1/4.08

.

Based on Table 1, a series of similar material proportioning tests were carried out. The simulated materials of the surrounding rock and tunnel lining consist of a mixture of quartz sand, barite powder, cement, gypsum, and water with a weight ratio of 590:10:90:60:150 and 590:10:35:60:150, respectively [47]. The fault zone was simulated by gravel with 10–20 mm particle size. The mechanical properties of the prototype and model are listed in

Table 2. Mechanical properties of the prototype and model.

Component	Elastic Module/MPa			Density/g/cm³
	${\mathit{C}}_{\mathit{E}}$	Prototype	Model	${\mathit{C}}_{\mathit{\rho }}$	Prototype	Model
Strongly weathered trachyte	1/30	6500	208	1/1.25	2.40	1.92
Weakly weathered trachyte		6500	208		2.40	1.92
Fault zone		2000	64		2.20	1.76
Tunnel lining		30,000	1000		2.5	2

.

2.4. Isolation Layer

The isolation layer material is a rubber-sand mixture. Standard quartz sand with a particle size ranging from 0.5 mm to 1.0 mm was adopted. The rubber has a particle size of 420 μm. According to American Society Testing and Materials (ASTM) specification [48], this material is classified as granulated or particulate rubber. Rubber content ($RC$) is defined as the mass ratio of rubber to sand to assess rubber’s effect on the rubber-sand isolation layer. According to the method presented by the literature [49,50], rubber-sand samples with different rubber content were prepared. The material’s elastic modulus ($E$) and damping ratio ($D_r$) were calculated by the method of the literature [51]. Figure 4 shows that the rubber-sand mixture samples have a decreasing elastic modulus and a monotony-increasing damping ratio with increasing rubber content. When the rubber content is too low, the damping of the material is reduced, and the effect of energy absorption and shock absorption cannot be achieved; while the rubber content is too high, the stiffness of the material is too low to bear the essential load-bearing capacity. Based on the available experimental studies, a 5% rubber content was proven effective in reducing the strain response of the pipe [36]. Therefore, a rubber-sand mixture with a 5% content of rubber was selected to fabricate the isolation layer in this paper.

A biaxial geogrid mold with a mesh size of 40 mm was used as a skeleton to prefabricate the isolation layer easily. Then, the standard quartz sand and rubber granules with a mass ratio of 190:10, i.e., 5% rubber content, were added into the biaxial geogrid molds. Thus, the rubber-sand isolation layer was prefabricated in the lab. The mechanical properties of the prefabricated isolation layer are listed in

Table 3. Mechanical characteristics of the isolation layer.

Component	Density (kg/m3)	Elastic Modulus (MPa)	Damping Ratio (%)	Component	Tensile Strength (KN/m)
					Longitudinal	Transverse
Rubber-sand mixtures	1370	10.05	10	Biaxial geogrid	60	60

. The prefabricated isolation layer was assembled between the fault and the tunnel and made to fit tightly (Figure 5) for the shaking table test.

2.5. Sensor Layout

To study the dynamic response characteristics of the tunnel lining in the model test, four sections (1-1, 2-2, 3-3, and 4-4) were selected to observe the acceleration and strain of the tunnel lining, as shown in Figure 6a. There are two main sections (2-2, 3-3) in the fault-dislocated zone for analysis of the dynamic response of the tunnel lining. Another two auxiliary sections (1-1,4-4) are located in the fault-affected zone. The system was equipped with an advanced integrated measurement architecture (IMC) data acquisition system that can acquire up to 144 acceleration and strain channels of data. Two accelerometers were installed at the tunnel lining crown and invert in each section. All accelerometers are piezoelectric accelerometers with a measurement range of ±10 g and a sensitivity of 0.516 V/g. Meanwhile, 14 strain gauges were evenly installed in each tunnel section and had resistance values of 120.2 Ω ± 0.1% and sensitivity coefficients of 2.05% ± 0.28%, as shown in Figure 6b.

2.6. Test Cases

Tunnels with and without the isolation layer were the experimental and control groups, respectively. The whole loading process was divided into two steps: the first fault movement was achieved by the jack and then seismic excitation was input by the shaking table system.

Specifically, turning on the four jack oil pressure switches, the tunnel and the surrounding rock at the hanging wall were lifted with a vertical displacement of 1 mm and fixed by the jacks. The ones at the footwall were fixed with zero displacements. Next, two kinds of seismic records, El-Centro and Kobe waves, were successively applied to the tunnel model. Figure 7 presents the acceleration-time histories and Fourier spectra of the input motion. Based on the time similarity ratio of 1:4.08, the El-Centro and Kobe waves were scaled in time to the durations of 8.32 s and 8.32 s, respectively. The peak acceleration of the El-Centro and Kobe waves was adjusted to 0.4g to investigate the effect of strong excitation. The dominant frequencies of El-Centro and Kobe waves were 8.81 and 6.65 Hz, respectively. The input seismic excitation in different directions produces different response characteristics [52]. Specifically, the input motion was applied in three directions: orthometric, longitudinal, and perpendicular to the tunnel axis. They were denoted as x-, y-, and z-directions, respectively. It should be emphasized that the z-directional motion occurs in a perfectly vertical direction, orthogonal to the tunnel axis. Thus, a total of 6 loading cases for each group are shown in

Table 4. Mechanical characteristics of the isolation layer.

Condition	Number	Creep-Slip Displacement/mm	Input Motion
			Type	Direction	PGA/g
#1 (without isolation layer)	#1-1	1	El-Centro	x	0.4
	#1-2	1	El-Centro	y	0.4
	#1-3	1	El-Centro	z	0.4
	#1-4	1	Kobe	x	0.4
	#1-5	1	Kobe	y	0.4
	#1-6	1	Kobe	z	0.4
#2 (with isolation layer)	#2-1	1	El-Centro	x	0.4
	#2-2	1	El-Centro	y	0.4
	#2-3	1	El-Centro	z	0.4
	#2-4	1	Kobe	x	0.4
	#2-5	1	Kobe	y	0.4
	#2-6	1	Kobe	z	0.4

. At the end of each working case, white noise with a peak acceleration of 0.05 g was used to check the sensitivity of the sensor and the degree of damage to the model.

3. Model Test Results

3.1. Acceleration and Spectral Responses

The junction of the hanging wall and fault usually has a great acceleration response [23]. Therefore, the acceleration response-time histories and corresponding Fourier amplitude spectra of the crown of the tunnel lining at the fault creep-slip cross-section (monitoring section 2-2) under El-Centro and Kobe excitation are shown in Figure 8 and Figure 9, respectively. It can be observed that the z-direction recorded the maximum value both in El-Centro and Kobe excitation compared with the y-direction and x-direction. This reveals that z-direction motion causes a more intense dynamic response in the tunnel structure. Similar responses were also pointed out by the literature [22].

The model with an isolation layer has a lower level of peak acceleration response compared to the model without an isolation layer, although the two models have similar acceleration-time histories. The peak accelerations of the tunnel without an isolation layer for tests #1-1 to #1-6 are 0.64 g, 0.75 g, 0.88 g, 0.69 g, 0.81 g, and 0.95 g, respectively. The peak accelerations of the tunnel with an isolation layer for tests #2-1 to #2-6 are 0.6 g, 0.69 g, 0.80 g, 0.64 g, 0.74 g, and 0.87 g, respectively. This means that the isolation layer can reduce the peak acceleration of the tunnel crown in the fault by 5–10% for same-direction excitation. The isolation layer did not change the acceleration response characteristics of the tunnel. Meanwhile, from the energy point of view, harmonic energy ($E$) is positively related to the square of amplitude ($A$), frequency ($f$) of acceleration, and volume of medium ($W$), expressed as $E\propto \rho A^2{f}^{2}W$. The indicator $\xi =\sum Af$ was suggested by the literature [23]. Indicator $\xi$ of this experiment was calculated and tabulated in

Table 5. Indicator of $\xi$.

Group	El-Centro Wave			Kobe Wave
	x-Direction	y-Direction	z-Direction	x-Direction	y-Direction	z-Direction
1# (without isolation layer)	0.26	0.40	0.65	0.20	0.30	0.45
2# (with isolation layer)	0.23	0.35	0.56	0.17	0.26	0.33

. Table 5 shows that the tunnel with an isolation layer has smaller value of $\xi$ than the tunnel without an isolation layer. This demonstrates that the energy of seismic waves is effectively absorbed by the rubber-sand isolation layer.

3.2. Dynamic Strain Responses

Based on the larger dynamic response produced by z-direction excitation and creep-slip of a normal fault, the longitudinal strain responses of the tunnel lining at section 2-2 under the z-direction El-Centro and Kobe excitation (cases #1-3, #1-6, #2-3, and #2-6) are plotted in Figure 10. The positive and negative values are denoted as tensile and compressive strains, respectively. Figure 10 shows the peak strain responses at the invert (SO-5 monitoring point in Figure 6) were greater than the ones at the crown (SO-1 monitoring point in Figure 6), regardless of the existence of the isolation layer. This indicates that the deformation of the tunnel lining at the invert is more severe than at the crown. Similar responses were also pointed out by the literature [53]. Due to the low strength of the fault, there is extensive interaction between the bottom of the tunnel and the strata, as well as the need to withstand the gravity of the top of the tunnel. This resulted in a considerable strain on the lining invert. In addition, the strain response of the tunnel lining with an isolation layer is distinctly lower than that of the tunnel lining without an isolation layer. In the case of El-Centro excitation, the peak strains of the crown and invert were reduced from 97.7 to 61.1 με, with a reduction of 37.5%, and from 212.4 to 124.9 με, with a reduction of 42.2%, respectively. Similarly, in the case of Kobe excitation, the peak strains at the crown and invert were also reduced by 47.7% from 140.6 to 73.6 με and by 46.0% from 359.5 to 194.3 με, respectively. This indicates that the rubber-sand isolation layer can effectively reduce the strain response of the tunnel under normal fault creep-slip and subsequent seismic excitation. The reason is that the rubber-sand mixture with low modulus properties can accommodate limited deformation and absorb seismic energy [30].

The irreversible permanent deformation of the tunnel was led by the creep-slip displacement of the fault and subsequent seismic shaking. Referring to the schematic diagram on the sequence of events used by Antoniou et al. [54], Figure 11 illustrates the variation in permanent strain (accumulated residual strain) in the lining crown and invert (cross-section 2-2), as well as peak strain and seismic strain (peak strain minus residual strain) in each case, respectively. Figure 11 shows the peak strain of the tunnel with the isolation layer was significantly lower than the one without the isolation layer. In terms of the variation pattern of the lining crown, the permanent strain of the tunnel with an isolation layer was significantly lower compared to the tunnel without an isolation layer, while the seismic strain was not much different. From the position of the lining invert, both the permanent strain and the seismic strain were significantly lower in the tunnel with an isolation layer compared to the tunnel without an isolation layer. This also shows that the rubber-sand isolation layer has a favorable aseismic performance. In general, the final tunnel damage was contributed by the seismic strain and the accumulated permanent strain. The permanent strain gradually increases with the working case and increasingly dominates among peak strains. This potentially means that the strain on the tunnel lining cannot be wholly dissipated and gradually accumulates with the continuous effect of fault creep-slip and seismic motion.

4. Numerical Simulations

The model test demonstrated the feasibility of reductions in the dynamic responses of tunnels with a rubber-sand isolation layer. Furthermore, numerical simulations were performed to analyze the effects of various parameters of the isolation layer, including length, damping ratio, and elastic modulus, on the dynamic response under fault creep-slip and subsequent seismic shaking.

4.1. Numerical Modeling

An FLAC3D numerical model for the test-scale tunnel was developed. The dimensions of the numerical model were the same as the test-scale model, as shown in Figure 12. Some critical aspects of the establishment of a numerical model were as follows:

(a) Meshing determines the computational efficiency and reliability of the simulation. Based on the literature [55], the size of the element ($\mathsf{\Delta }l$) is:

$$∆l\le \frac{\lambda }{10},\lambda =\frac{V_S}{f_{max}}$$

(1)

where $\lambda$ is the wavelength of seismic wave propagation in the model and $f_{max}$ is the maximum frequency of the input motions with a value of 40 Hz according to Figure 7. $V_S$ is the shear wave velocity of the model mass surrounding the model test. $V_S$ has a value of 30 m/s with a 2.4 m box height and 0.08 s time difference in peak acceleration response between the model bottom and top in the working case considering an El-Centro wave with z-direction input. Thus, the maximum size of an element in the numerical model in this paper was less than 0.075 cm. A total of 139,840 elements were applied to the tunnel numerical model. Figure 12a shows the established numerical model.

(b) The Mohr-Coulomb Tension Crack model with an inner frication angle ($\phi$) and cohesion ($c$) was selected to simulate the tunnel lining. The Mohr-Coulomb model was adopted for the surrounding rock mass and fault zone. The elastic model was adopted for the isolation layer and the mechanical parameters of the isolation layer of the composite material were determined by the trial-and-error method. An interface element was set to simulate the interface between the surrounding mass and the fault (Figure 12b). The normal stiffness ($K_n$) and shear stiffness ($K_s$) of the interface element were calculated by:

$$K_s=K_n=10max\left[\frac{\left(K+\frac{4}{3}G\right)}{∆Z_{min}}\right]$$

(2)

where $K$ is the bulk modulus, $G$ is the shear modulus, and $∆Z_{min}$ is the smallest width of an adjoining zone in the normal direction. The parameters of these above element types are tabulated in

Table 6. Mechanical parameters of the tunnel numerical model.

Component	Elastic Modulus (MPa)	Poisson’s Ratio	Friction Angle (°)	Cohesion (MPa)
Strongly weathered trachyte	208	0.33	30	0.017
Weakly weathered trachyte	208	0.28	45	0.033
Fault	64	0.30	24	0.013
Lining	1000	0.2	55	0.1
Isolation layer	5–20	0.34	-	-

. The isolation layer has an elastic modulus with a range of 5 MPa to 20 MPa.

(c) The bottom boundary of the numerical model was assumed as the rigid boundary [56] (Figure 12c). The lateral boundaries of the model are applied by the built-in absorbing boundary in FLAC3D, i.e., the free field (Figure 12c), expressed as

$$F_i=-\rho C_P\left(v_i^m-v_i^{ff}\right)A+F_i^{ff}i=x,y,z$$

(3)

where $\rho$ is the density of the rock mass, $C_P$ is the P-wave velocity at the model boundary, $C_S$ is the S-wave velocity at the model boundary, A is the area of influence of a free-field grid point, $v_i^m$ is the i-drection velocity of a grid point in the main grid at the model boundary, $v_i^{ff}$ is the i-direction velocity of a grid point in the side free field, and $F_i^{ff}$ is the free-field grid point force in the i-direction.

(d) After the application of gravity, the vertical sliding support at the vertical sides, the fixed support at the bottom of the model and the free boundary at the top of the model, and the initial stress equilibrium of the numerical model were obtained. Then, creep-slip displacement in the z-direction (Figure 11d) was achieved by moving the hanging wall with a small normal velocity, which kept the whole creep-slip process quasi-static to avoid dynamic effects. Finally, the lateral and bottom surfaces were applied to the free-field and rigid boundaries, respectively. The subsequent seismic excitation was simulated by inputting the acceleration-time histories (Figure 7) at the bottom of the model. The monitoring section was set along the longitudinal tunnel axis with an interval of 0.1 m. The monitoring points at each section are plotted in Figure 6b.

4.2. Comparisons between Numerical and Experimental Result

Figure 13 shows the experimental and numerical results of the acceleration response of the model tunnel with the isolation layer under normal fault creep-slip and subsequent z-direction seismic excitation (working cases #2-3 and #2-6) at the lining crown. It can be observed that there is a good agreement between the results of the numerical simulation and the model tests in terms of both acceleration response records and the magnitude of peak acceleration. Figure 14 plots the peak strain in the tunnel axis direction at the crown and invert of the typical section (1-1, 2-2, 3-3, 4-4) for the #2-2 and #2-6 working cases. The consistency of the strain responses in the longitudinal direction of the tunnel between the numerical simulation and the model test can also be seen in Figure 14. This indicates that numerical simulation can be used to reliably predict the dynamic responses of the model tunnel with an isolation layer.

5. Parametric Studies by Numerical Simulation

A numerical study is presented in terms of the effects of the parameters of the isolation layer, such as length, damping ratio, and elastic modulus, on the dynamic response under fault creep-slip and subsequent seismic earthquakes.

5.1. Effect of the Length of the Isolation Layer

The peak tensile and shear strain responses of the tunnel invert were discussed because the tunnel invert has a more intense strain response than other positions at the same monitoring cross-section from Section 3.2. The peak tensile and shear strain responses are the maximum value of the tensile strain-time history curve and shear strain-time history, respectively.

Figure 15 plots the peak tensile and shear strain responses at the tunnel invert affected by the isolation layer length under small normal fault creep-slip and subsequent z-direction seismic excitation (El-Centro and Kobe wave). The isolation layer length ranges from 0D (without the isolation layer, D is the fault width) through to 1D, 2D, 3D, 4D, 5D, 6D, and the full loop. It can be observed that the maximum values of peak tensile and shear strains are observed at the fault creep-slip cross-section. The peak tensile and shear strains change sharply at a distance of about 1.5 times the distance to the left and right of the fault creep-slip cross-section. The range where the sharp changes occur does not vary with the length of the damping layer or the type of seismic wave. In addition, it can be observed that under fault creep-slip, the Kobe wave excitation induces a sharper change in peak tensile and shear strain responses within the fault zones compared with the El-Centro wave.

Furthermore, Figure 16 plots the peak tensile and shear strain responses of the tunnel invert at the creep-slip cross-section of the fault versus the length of the isolation layer. The peak tensile and shear strains of the lining invert decrease significantly at first as the length of the isolation layer increases. However, when the length of the isolation layer exceeded 3D, the peak tensile and shear strains decreased very slowly. This means the isolation layer with three times the fault width should be most reasonably deployed under normal fault creep dislocation and subsequent seismic excitation (El-Centro or Kobe wave).

5.2. Effect of the Damping Ratio of the Isolation Layer

Figure 17 illustrates the effect of the isolation layer damping ratio on the peak strain of the tunnel invert response under small normal fault creep-slip and subsequent z-direction seismic excitation (El-Centro and Kobe wave). It can be observed that, compared with the isolation layer length, the damping ratio of the isolation layer induces the same change in peak strains at the lining invert of the monitoring section along the tunnel longitudinal axis. Figure 18 plots the effect of the damping ratio on the peak tensile and shear strain responses of the lining invert at the fault creep-slip cross-section. Figure 18 shows that the peak strain responses decrease with the increase in the damping ratio of the isolation layer. This seems to mean that the higher the damping ratio, the better the effect of the isolation layer. However, indiscriminate increasing is not a rational economic approach [57]. The literature [58] recommended that a damping ratio in the range of 0.3–0.7 can be selected for isolation to reduce the acceleration and displacement response of the structure under low-frequency ground motion, and typically a damping ratio at the level of about 0.3 is preferred in engineering practice for base-isolated structures considering the control effectiveness. For rubber-sand mixtures, the damping ratio increases with the increase in rubber content and the damping ratio of pure rubber is about 0.35 [42]. Therefore, the appropriate enhancement of the rubber content of the isolation layer may provide favorable conditions for the tunnel during small normal fault creep-slip and subsequent seismic excitation, while ensuring the isolation layer bearing capacity.

5.3. Effect of the Elastic Modulus of the Isolation Layer

Based on the above results, the length of the isolation layer and damping ratio were taken as three times the fault width and 0.35, respectively. Figure 19 depicts the peak tensile and shear strains at the tunnel invert under normal fault creep-slip and subsequent z-direction seismic excitation (El-Centro and Kobe wave). From Figure 19, the peak tensile and shear strains of the tunnel elevation arch vary with the length of the damping layer and the modulus of elasticity in basically a similar pattern. Considering Section 5.1 and Section 5.2, it can be inferred that the influence range of fault creep-slip is three times the fault width, and the influence range does not vary with the parameters of the isolation layer.

Figure 20 illustrates the peak strain response at the tunnel invert of the fault creep-slip cross-section. It can be observed that the peak tensile and shear strains slowly increase with the increase in the elastic modulus of the isolation layer. Thus, the small elastic modulus should be chosen to reduce the tunnel peak strain response. On the one hand, it can be deduced that high rubber content can be applied on the basis of the relationship between the elastic modulus and the rubber content. On the other hand, the isolation layer needs to have a certain strength to bear the static load resulting from the release of in situ stress in the rock [59]. In addition, the rubber size and soil type are important factors for the rubber-sand isolation layer properties involving elastic modulus and damping ratio. Hence, when considering the performance of the isolation layer, it is necessary to consider both the damping and deformation characteristics of the isolation material.

6. Conclusions

In this paper, the dynamic response characteristics (acceleration, corresponding spectrum, and strain) of the tunnel under normal fault creep-slip and subsequent seismic excitation were conducted by shaking table tests. The effect of the rubber-sand isolation layer was studied by the test results and validated by numerical simulation. Furthermore, the influence of the isolation layer parameters (length, damping ratio, and elastic modulus) on the dynamic response of the tunnel is discussed. The following conclusions were drawn:

(1) The results from the shaking table model tests indicated that seismic excitation in different directions causes different dynamic response characteristics in the tunnel. The rubber-sand isolation layer can slightly reduce the peak acceleration of the tunnel in the fault and absorb the seismic wave energy.

(2) Under normal fault creep-slip and subsequent seismic shaking, the strain in the lining invert is greater than in the lining crown. The damage of the tunnel is caused by a combination of permanent strain and seismic strain. The rubber-sand isolation layer can effectively reduce the permanent strain at the tunnel lining invert and crown.

(3) Based on the numerical analysis, the peak strain of the lining invert is maximum at the creep-slip cross-section of the fault, and the influence range of the fault does not vary with the parameters of the isolation layer.

(4) As the length of the isolation layer increases, the peak strain in the lining decreases rapidly at first and then tends to become stable. The length of the isolation layer with three times the width of the fault (the influence range of the fault in this study) may be the optimal parameter.

(5) The damping ratio and the elastic modulus of the isolation layer, which are influenced by the rubber content, have an essential effect on the strain response of the tunnel lining invert. A proper increase in the rubber content in the rubber-sand isolation layer can provide favorable mitigation conditions for the tunnel during normal fault creep-slip and subsequent seismic excitation.

The effect of the rubber-sand isolation layer on the dynamic response of the tunnel was initially studied through shaking table experiments and numerical simulations. In the next phase, we will pay more attention to dynamic mechanical experiments in the rubber-sand isolation layer to further study the mechanism of the rubber-sand isolation layer.