Adverse Impact of Earthquake Seismic Loading on Angular Offset Tunnels and Effects of Isolation Grout

Abstract

This paper investigates the effects of seismic loads on tunnels in an attempt to provide better protection from earthquake shaking. Dynamic analysis of angular offset tunnels was performed, and the tunnels’ behavior under earthquake shaking and their response when using seismic isolation were analyzed in detail. The time history analysis was used to compute the stresses and deformation that develop in the tunnels during seismic events. Earthquake records with different frequency spectra were applied as seismic excitation to the twin tunnels. The excitation was applied normally to the tunnel axis, with peak ground accelerations of 0.10 g–0.30 g. The seismic event lasted 15 s, with a time step of 0.02 s utilized in the numerical analysis. Finite element modeling was employed to simulate the soil–tunnel interaction. Numerical models simulated twin tunnels passing through soft clay or stiff clay, with various earthquake records applied as seismic inputs. The effects of a silicon-based isolation material composed of silicon oil and fly-ash were compared with the use of traditional grout. The numerical model results show how seismic isolation affects the stresses and deformations that happen in tunnel bodies during earthquakes.

1. Introduction

Tunnels are essential for carriage and utility purposes at national and urban levels. The construction of tunnels increases rapidly to facilitate the additional space required in mega-cities. According to the Tunnel Market Survey [1], 5200 km of tunnels were being built in 2016, and the global tunnel market was estimated to be worth €86 billion. Projects in China account for about half of the total, with annual growth of 7% predicted over the next 5–10 years. In modern societies, even minor seismic effects on tunnels can result in significant direct and indirect losses. So, it is crucial to think carefully about how earthquakes will affect the planning, building, and maintenance of tunnels.

Since the 1970s, several reports have discussed the damage to tunnels from earthquake loading [2,3,4]. Wang [5] concluded that the deformation of tunnels interacting with the adjacent ground due to seismic loadings is highly related to their relative flexibility. A major failure at the Daikai Station in Kobe, Japan during the Hyogoken-Nambu earthquake in 1995 showed that improperly designed underground structures are vulnerable to wave propagation effects [6,7,8,9].

Two cases based on real-world cases of damage or collapse, the Bolu tunnel failure [10] and the Longxi tunnel collapse [11] have been used to understand the structure–ground interaction during an earthquake event. Several studies have shown that the existing analysis methods work and that the relevant constitutive models [12,13,14] or interface conditions [12,15,16] are necessary to explain the observed response. These cases have taught us a lot about how tunnels really work, especially when scaling effects that cannot be estimated in the lab, at least not to the extent that is needed.

The most common methods used for analyzing the dynamic behavior of tunnels are physical and numerical modeling. Centrifuge testing has been commonly used to advance and calibrate finite element (FE) models for the seismic investigation of tunnels [17,18,19,20,21,22,23,24,25,26,27,28,29,30]. Other analysis methods are beneficial for preliminary planning and design purposes.

Numerical models have made valuable contributions to the full dynamic analysis of tunnels and underground structures [31]. Different numerical approaches have been used to investigate the tunnel response, enabling improvements in the design and dynamic behavior of tunnels [12,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52]. Fully dynamic analysis based on the coupled soil–tunnel configuration’s seismic event time history is probably the most accurate method for tunnel seismic analysis [33].

Numerical analyses can fundamentally define the kinematic and inertial aspects of the soil–structure interaction, and they can also simulate the geometries and heterogeneities of soil deposits as complex materials. It is possible to model the nonlinear behavior of the tunnel structure, the surrounding soil, and the soil–structure interface. The discrete element method (DEM) is often used for tunnels into broken rock, while the finite element method (FE) is often used for structures that are buried in the ground [53].

The fundamental impetus for this study was that the current literature on mitigation and remediation approaches for enhancing seismic tunnel response is limited and mostly based on outdated principles [54]. Experimental isolation techniques for tunnels subjected to ground shaking have been investigated in some research [55,56]. However, the results of these investigations are limited to the tunnels that were examined.

This study compares the effects of a silicon-based isolation material consisting of silicon oil and fly-ash to ordinary grout. The numerical models were created to explore how the isolation grout affected the behavior of angular offset tunnels during earthquakes. The stresses and deformation that arise in the tunnels were computed using a fully dynamic approach based on the seismic event time history of the coupled soil–tunnel configuration. Earthquake records with various frequency spectra are used as seismic stimulation for the twin tunnels. The results of the numerical model show how seismic isolation affects the stresses and deformations that happen in tunnel bodies during earthquakes.

2. Seismic Design of Tunnels

2.1. Tunnel Seismic Performance

Rock tunnels have been found to be less vulnerable to earthquake damage than traditional buildings and aboveground civil infrastructure. Dowding and Rozen [2] used 70 case histories to correlate the damage to tunnels with surface peak ground acceleration. In 127 cases, Owen and Scholl [57] found that peak ground accelerations of less than 0.4 g caused minor damage in rock tunnels.

An increase in earthquake magnitude and a decrease in the epicentral distance enhances the level of damage to tunnels. Deeper tunnels or rock tunnels were generally safer. Sharma and Judd [58] have described the relationship between tunnel damage and factors such as the shape of the tunnel lining that affect how it reacts to earthquakes.

Minor tunnel damage is likely to occur for PGAs of less than 0.2 g, with slight to heavy damage expected under higher PGAs. More than 12% of the tunnels damaged in the 1995 Hyogoken-Nambu earthquake were severely damage [54]. Many studies have focused on the damage mechanisms of tunnels [6,7,48,59,60,61,62,63,64].

Generally, most damaged tunnels did not have appropriate seismic assessments during the design and construction stages [65,66,67,68,69,70]. The collapsed tunnel at Daikai Station has been used as a case study to investigate how to keep tunnels safe from earthquakes [68].

2.2. Mechanisms of Seismic Response

When struck by earthquakes, tunnels behave differently than aboveground buildings. The kinematic loading induced by the ground around the tunnel outweighs the inertial loads caused by the tunnel’s oscillation [5,70]. When designing tunnels in seismic-prone locations, the expected ground behavior owing to wave propagation and persistent ground deformations should be considered [57]. Figure 1 illustrates underground structure deformation modes caused by earthquakes.

Seismically induced ground failures may cause permanent ground deformations, such as fault movements, slope failures, or liquefaction. The surrounding ground type and its response, the buried depth, the relative stiffness between the soil and the tunnel, and ground motion impact tunnel behavior during seismic events [5,70,71,72,73].

Tunnel structures are challenging to analyze against the aforementioned seismic effects. The complexity arises from tunnel distortion patterns and the resulting degree of possible damage caused by longitudinal and transverse ground shaking and seismically induced ground failures [74,75,76,77]. Tunnels have been analyzed for ground shaking in both transverse and longitudinal directions and ground collapses owing to seismic stress, using a variety of approaches. These methods are explained in the cited references [32,78].

Several experimental and numerical investigations have concentrated on one of the above seismic impacts in seismic isolation for tunnels. Very little research has been done on how ground shaking and faulting affect the seismic response of underwater tunnels [79].

2.3. Tunnel Seismic Design Concepts

The goal of seismic design is to provide a tunnel structure that can carry loads or handle the displacement and deformation that may be applied to it. However, seismic tunnel design differs from traditional design [5]. First, the seismic loads are difficult to calculate or accurately confirm. Second, seismic motions are cyclic and generally have a high frequency. Finally, seismic loads have a more significant impact than other permanent or regular loads. Structures in underground tunnels can be damaged by fault slides, earthquakes, and ground failures such as liquefaction, fault displacement, and unstable slopes (Figure 2).

Therefore, careful attention to suitable seismic design is essential. This design criteria must balance the structure’s importance, monetary value, and risk assessment. As shown in Figure 3, earthquake effects should be considered in the following cases:

When seismic waves travel through the Earth’s crust, the resulting ground motion is commonly referred to as ground shaking. The severity of the shaking reduces with increasing distance from the fault rupture. There are two different types of seismic waves, and each type has two subtypes. As shown in Figure 4, the different types of seismic waves are what cause the ground to move.

The methods used for seismic analysis and tunnel design may be categorized into the following approaches: free-field deformation, soil–structure interactions, and dynamic earth pressure. Numerous sub-methods are characterized by different degrees of evaluation depending on the initial planning and design, the geological conditions, and the index properties of the ground materials. The analyses are generally grouped into static, dynamic, and fully dynamic categories.

2.4. Concept of Seismic Isolation Systems

A flexible seismic isolation grout covering the outer tunnel perimeter insulates it from induced deformations of the nearby ground and reduces the stresses induced in the tunnel. The same construction methods used to backfill grout into the tail void apply to shield-driving tunnels or injecting material inside the tunnel, as shown in Figure 5. Additionally, shield segments can be sprayed with silicone paints with a kinetic friction coefficient as low as 0.15 (see Figure 6).

Seismic isolation materials applicable to underground structures must perform seismic isolation functions as backfill materials. The performance requirements for seismic isolation materials for shield-driving tunnels are listed in

Table 1. Requirements for seismic isolation materials.

Item No.	Description
1	Low shear modulus and high shear deformability
2	High durability, long-term stability, and small volumetric changes
3	High construction ability (i.e., for shield-driving tunnels, transportability by pumping in a liquid state and high filling-up performance)
4	Water tightness
5	No dilution by groundwater
6	No contaminants

. Some frequently used seismic isolation materials are described in

Table 2. Types of seismic isolation materials [79].

Construction Method	Isolation Material	Material Contacts
Shield-driving tunnel	Asphalt-based material	Asphalt and Portland cement with high-water-absorbing polymer
	Urethane-based material	Urethane with fly ash and polymer
	Silicon-based material	Silicon oil and fly ash with polyether

.

The seismic isolation mechanism depends on the stiffness of the isolation layer, which is related to the shear modulus ($G_{iso}$) and Poisson’s ratio (ν) along with the longitudinal and transverse directions of the tunnel, as indicated in the following expressions [79]:

$$K_x=\frac{2\pi G_{iso}}{ln\left(\frac{R}{r}\right)}$$

(1)

$$K_y=\frac{8\pi G\left(3-4\nu \right)\left(1-\nu \right)}{{\left(3-4\nu \right)}^{2}ln\left(\frac{R}{r}\right)-\left[{\left(\frac{R}{r}\right)}^2-\frac{1}{{\left(\frac{R}{r}\right)}^2}+1\right]}$$

(2)

where $K_x$ is the stiffness coefficient of the isolation layer along the longitudinal direction of the tunnel, $K_y$ is the stiffness coefficient of the isolation layer along the transverse direction of the tunnel, R is the isolation layer outer diameter, r is the isolation layer inner is diameter, $G_{iso}$ is the shear modulus of the isolation layer, and $\nu$ is Poisson’s ratio of the isolation layer.

3. Numerical Modeling

The main goal of this research is to show that 3D numerical modeling may be used to forecast and mitigate the effects of seismic loading on tunnels in urban and rural settings. Using a commercial tool called the 3D Finite Element Method, numerical models were made to simulate how soil and tunnels interact with each other.

3.1. Model Establishment

This study considers angular offset tunnels buried in soil with an outer diameter of 6.4 m and a lining cover of 300 mm. As shown in Figure 7, the horizontal and vertical distances between the two centers of twin tunnels are both 16.0 m, which is equivalent to 2.5 times the diameter of the tunnels. The upper tunnel has a burial depth (H) of 12.8 m, while the lower tunnel is 28.0 m from the ground surface and has a segment width of 1.5 m. The dimensions of the overall model in the x-, y-, and z-directions are 76 m $\times$ 90 m $\times$ 60 m, respectively. Solid elements were chosen for the ground, tunnel, grout, and isolation coating. The element length was equal to one-eighth of the wavelength of the slowest body wave propagating in the elastic material [80]. The tail hole of the shield machine was thought to need 150 mm of grout or isolation coating to fill it.

The ground had two soil layers, as shown in Figure 8a: an upper layer of soft clay or stiff clay and a lower layer of sand. Another model used in this study assumed that the ground consisted of three soil layers, as shown in Figure 8b. The non-associated Mohr–Coulomb (MC) criteria define the soil behavior.

Table 3. Properties of soil materials.

Material	Modulus of Elasticity (E) (kN/m2)	Poisson’s Ratio (ν)	Unit Weight (γ) (kN/m3)	Cohesion (cu) (kN/m2)	Friction Angle (φ) (0)
Soft clay	25,000	0.48	19.00	30.00	0.00
Stiff clay	75,000	0.45	20.00	60.00	0.00
Lower sand	90,000	0.35	20.00	0.00	38.00

shows the material parameters of the soil.

The elastic properties of the materials used in the model are presented in

Table 4. Properties of concrete lining and grout materials.

Material	Modulus of Elasticity (E) (kN/m2)	Poisson’s Ratio (ν)	Unit Weight (γ) (kN/m3)
Concrete for segment	30 × 106	0.20	25.00
Grout for tunnel in soft clay	40,000	0.30	20.00
Grout for tunnel in stiff clay	100,000	0.30	20.00

. The grout properties should be the same or better than the surrounding ground properties in the final state [81].

The MIDAS/GTS-NX FEM software is capable of automatically constraining the model. The nodal degrees of freedom (DOF) along the model’s vertical sides are constrained in the x-direction, and the model is constrained in the y-direction at the front and back. For the bottom nodes, the DOF in the z-direction is constrained in the y-and x-directions. The DOFs along the ground surface are not constrained.

The isolation material used in the model is silicon-based [82,83]. Silicon is the most common material used for seismic isolation. This material is composed of silicon oil and fly-ash and has a shear modulus ($G_{iso}$) that is ($\frac{1}{500}$ and $\frac{1}{1000}$) of the shear modulus of the soil ($G_{soil}$) around the tunnel. A lower shear modulus in the isolation material produces a better effect in the isolation layer [83]. The remaining properties of this material are listed in

Table 5. Material properties of silicon-based isolation material.

Material	Shear Modulus (G) (kN/m2)	Poisson’s Ratio (ν)	Unit Weight (γ) (kN/m3)
Isolation for tunnel in soft clay	20/10	0.48	10.00
isolation for tunnel in stiff clay	50/25	0.48	10.00

.

A linear dynamic time history analysis using the direct integrating method was applied. The dynamic excitation sources applied perpendicular to the tunnel axis were the El Centro 1940, San Fernando 1971, and Northridge 1994 data from the MIDAS/GTS-NX library, as shown in Figure 9. The peak ground acceleration was 0.30 g. The duration of excitation in this study was 15 s with a time step of 0.02 s, i.e., 750 steps.

3.2. Model Development

The 3D model calculations were processed by MIDAS/GTS-NX, which calculates stresses and deformations in the soil and the structure, taking into account the elastoplastic behavior of the soil modeled using the MC criteria. As shown in Figure 10, thirty-six FEM models were looked at to see how stable the tunnel was under seismic loading.

4. Results and Discussion

The effects of using isolation on the tunnel’s vertical displacement (settlement or heave) are currently being examined. This study focuses on the final displacement of the tunnels and their induced stresses in the transverse direction, where the tunnels are structures that resist movement in the transverse direction. According to the European design code, the principal compression and tension stresses and the allowable stress are equal to 400 kN/m², leading to allowable tensile stress of 3200 kN/m² and compression stress of 23,000 kN/m². The three earthquake time histories used in this study are thought to be accurate for actual design work because they get the best response.

The seismic response of the lower (deeper) tunnel is greater than that of the upper tunnel. In all cases, the compression stresses on the twin tunnels are safe and do not exceed the permissible limits. If twin tunnels are in stiff soil, the tensile stresses induced on the tunnel are unsafe when using traditional grout under the El Centro and Northridge loading. On the other hand, if the twin tunnels are in soft soil, the tensile stress is unsafe in the upper one under Northridge loading, and the lower one is unsafe under both El Centro and Northridge loading. Suppose twin tunnels are in stiff soil when the lower tunnel is in soft soil or stiff soil under a soft soil layer. In that case, the permissible tensile stresses exceed permissible limits when using traditional grout under the El Centro and Northridge loadings. The tensile stresses (maximum stresses) are presented in Figure 11, Figure 12, Figure 13 and Figure 14. In

Table 6. Effect of using isolation instead of traditional grout.

Tunnel Description	Isolation Shear Modulus	Lower Tunnel		Upper Tunnel
		Compression (Minimum Stresses)	Tension (Maximum Stresses)	Compression (Minimum Stresses)	Tension (Maximum Stresses)
Twin tunnels in stiff soil	$(\frac{1}{1000}$$) G_{soil}$	––(73.0–74.9)%	––(74.0–76.9)%	––(70.4–71.4)%	––(69.0–61.3)%
	$(\frac{1}{500}$$) G_{soil}$	––(57.0–59.0)%	––(56.5–62.7)%	––(52.5–54.8)%	––(51.3–54.7)%
Twin tunnels in soft soil	$(\frac{1}{1000}$$) G_{soil}$	––(72.9–77.3)%	––(75.7–77.4)%	––(68.9–71.0)%	––(68.0–71.0)%
	$(\frac{1}{500}$$) G_{soil}$	––(56.5–63.0)%	––(60.5–62.6)%	––(51.6–54.7)%	––(50.5–54.0)%
Upper tunnel in soft soil and lower tunnel in stiff soil	$(\frac{1}{1000}$$)G_{soil}$	––(72.3–73.8)%	––(71.0–73.7)%	––(72.9–74.7)%	––(73.3–75.6)%
	$(\frac{1}{500}$$) G_{soil}$	––(55.5–57.5)%	––(53.6–58.0)%	––(57.0–59.4)%	––(57.2–60.8)%
Upper tunnel in stiff soil and lower tunnel in soft soil	$(\frac{1}{1000}$$) G_{soil}$	––(77.2–79.4)%	––(76.3–77.6)%	––(63.8–64.6)%	––(63.8–66.6)%
	$(\frac{1}{500}$$) G_{soil}$	––(63.8–64.6)%	––(61.8–63.3)%	–(44.8–44.0)%	–(44.2–47.5)%

(–) sign means reduce.

, the maximum and minimum stresses put on the tunnel by traditional grout and silicon isolation are compared.

A comparison of the stresses under the three earthquake time histories when using traditional grout and using isolation with a shear modulus ratio of $\frac{1}{500}$ and $\frac{1}{1000}$ indicates the following:

• In the case where both tunnels are in stiff soil, the average stress decreases by 51.3–76.9% when using isolation instead of traditional grout.
• In the case where both tunnels are in soft soil, the average stress decreases by 50.5–77.4% when using isolation instead of traditional grout.
• In the case where the upper tunnel is in soft soil, and the lower tunnel is in stiff soil, the average stress decreases by 53.6–73.3% when using isolation instead of traditional grout.
• In the case where the upper tunnel is in stiff soil, and the lower tunnel is in soft soil, the average stress decreases by 44.2–79.4% when using isolation instead of traditional grout.

Figure 15, Figure 16 and Figure 17 show that isolation mostly causes the twin tunnels to settle or to move up and down more if there is a quake.

A comparison of the vertical displacement of twin tunnels under the El Centro and Northridge time histories, which recorded the highest values for deformation in comparison with the San Fernando lodging when using traditional grout and using isolation with a shear modulus ratio of $\frac{1}{500}$ and $\frac{1}{1000}$ indicates the following:

1.

When both tunnels are in stiff soil, the maximum vertical displacement increases by an average of 23.0% when using $G_{iso}=\frac{1}{500} G_{soil}$ and 36.0% when using $G_{iso}=\frac{1}{1000} G_{soil}$ for the upper tunnel and by 14.0–23.0%, respectively, for the lower tunnel.

2.

When both tunnels are in soft soil, the maximum vertical displacement increases by an average of 17.0% when using $G_{iso}=\frac{1}{500} G_{soil}$ and 17.0% when using $G_{iso}=\frac{1}{1000} G_{soil}$ for the upper tunnel and by 36.0–93.0%, respectively, for the lower tunnel.

3.

The maximum is when the upper tunnel is buried in soft soil and the lower tunnel in stiff soil. Vertical displacement increases by an average of 9.0% when using $G_{iso}=\frac{1}{500} G_{soil}$ and 11.0% when using $G_{iso}=\frac{1}{1000} G_{soil}$ for the upper tunnel and by 46.0–109.0%, respectively, for the lower tunnel.

4.

The maximum is when the upper tunnel is in stiff soil, and the lower tunnel is in soft soil. Vertical displacement increases by an average of 10.0% when using $G_{iso}=\frac{1}{500} G_{soil}$ and 35.0% when using $G_{iso}=\frac{1}{1000} G_{soil}$ for the upper tunnel and by 7.0–34.0%, respectively, for the lower tunnel.

5. Conclusions

Numerical models were used to simulate twin tunnels passing through soft or stiff soil. Various earthquake records were applied as seismic inputs. The effects of a silicon–based isolation material composed of silicon oil and fly–ash were compared with the use of traditional grout for the same results. The models’ results showed that isolation grout produces positive effects on both the compression and tension stresses in the transverse directions of the tunnels.

It cannot insulate the tunnels from the surrounding ground–induced deformation through an isolation layer. Using isolation grout instead of traditional grout has tangible results, especially on average stress. The average stress decreases by 64.10% and 63.95% in the cases where both tunnels are in stiff and soft clay, respectively. In the case where the lower tunnel is in soft soil, the average stress decreases by 61.80%. When the upper tunnel is in soft soil, the average stress has a lower stress of 63.45%.

It is essential to study the reduction in displacement produced by decreasing the shear modulus of the isolation material. In actual design, construction testing should be combined with dynamic results. The compression stresses induced by construction may reduce the tensile stresses resulting from dynamic motions.

This research presents new horizons for using an insulating cover instead of the traditional cover used in tunnels. One of the advantages of using this type of cover is that it significantly reduces the stresses to which the tunnel body is exposed under the influence of seismic activity, exceeding 50% in the case of normal loads. There are different materials that can be used as an insulating cover for tunnels and their suitability and effectiveness need to be proven.