Longitudinal shaking of culvert-frame combined underground structure

Abstract

The underground structure with stiffness mutation at the culvert-frame connection suffers from discrepant dynamic responses when earthquakes strike. This paper studies the seismic responses of an underground structure consisting of two portions of box frames and twin jacked culverts in soft soil. The two portions of box frames (Part A and Part C) have the same 2-storey and 3-span cross sections, rigidly connected to the two parallel jacked culverts (Part B) with F-type sockets between joints. A series of 1g shaking table tests is conducted on the modeled soil−structure system. Accelerometers are installed within the model soil, upon culverts, and on the top of mid slabs of box frames. Joint extensions and closures of culverts are measured. The white noise case is carried out to assess dynamic characteristics of the model system. Four synthetic earthquake cases are conducted to investigate the model system’s seismic responses under earthquakes with varying intensities. Ground acceleration responses of the model soil at different distances from Part A are compared. The extent of discrepancy in acceleration of culverts and box frames is quantified by the correlation coefficient. The characteristics of the joint extension and closure are summarized.

Graphical abstract

Keywords

shaking table test / underground structure / culvert-frame / metro station / soft soil

1 Introduction

The term “culvert-frame combined underground structure” (C-FCUS) refers to an underground structure constructed through the integration of jacked culverts and box frames, utilizing the cut-and-cover method to construct these frames. When the underground structure has to pass beneath ground buildings, C-FCUS is an intensive structural form for its lower construction costs compared with the pipe jacking method and smaller impacts on surface traffic compared with the cut-and-cover method. For C-FCUS, the jacked culvert part exhibits flexibility, while the box frame part remains rigid. As a result, the discrepant seismic responses of the culvert and the frame can be anticipated. Detailed studies of dynamic characteristics of C-FCUS are essential, considering stiffness mutation, as well as analyzing the ground responses influenced by C-FCUS. The C-FCUS studied in the following consists of twin jacked culverts (Part B) and two box frames (Part A and Part C), as depicted in Fig.1. In the longitudinal direction, one box frame is longer than twin jacked culverts while the other is not. The two box frames rigidly connect to the two ends of jacked culverts, respectively.

Physical model test is an effective and extensively implemented method of studying the dynamic characteristics of underground structure in soft soil. However, most of the studies were subjected to either culverts [1–5] or box frames [6–16]. A few studies focused on underground structures with stiffness mutation. Saito et al. [17] conducted a series of shaking table tests on a shaft-tunnel junction. Accelerations of the model soil and strains of the shield tunnel were analyzed and compared with those of analytical results. Ma et al. [18] studied seismic responses of a box frame with joints to tunnels in soft soil. The physical model test results showed that in middle columns and side walls, peak dynamic strains at lower parts were higher than those of upper parts. Zhuang et al. [19] concluded that the headwall at the connection part between the tunnel and the box frame could aggravate longitudinal strains of the tunnel and column strains of the box frame by conducting shaking table tests. Zhang et al. [20–22] conducted a series of shaking table tests on a shaft-tunnel junction. Experimental results revealed discrepant acceleration responses of the junction and, consequently, the raised longitudinal joint extensions of tunnels. Through experimental and numerical investigations, Chen et al. [23] attributed the dislocations of the junction structure between the box frame and the tunnel to the inconsistent deformation modes of the two parts. The studies mentioned above assumed the tunnel to be semi-infinite, namely, one end of the tunnel was connected to the box frame (or shaft) while the other end was infinite. Such an assumption is reasonable when the longitudinal dimension of the tunnel is much greater than that of the box frame (or shaft). The C-FCUS studied in this paper with similar longitudinal dimensions of culverts and frames may result in different dynamic characteristics.

Kawamata et al. [24] investigated the seismic responses of an underground structure consisting of two vertical shafts and a cut-and-cover tunnel. In the longitudinal direction, jacked culverts mainly deform in terms of joint extension, while cut-and-cover tunnels do not. C-FCUS consisting of jacked culverts with limited lengths and box frames at both ends, has not been thoroughly studied in its seismic characteristics, which has significant differences from previous studies.

The present paper briefly describes the experimental setup and presents key findings about site characteristics and structural seismic responses. The tests are designed at a scale of 1:20. The synthetic soil, deformed steel, and granular concrete with galvanized steel wires are selected to design the model soil, modeled twin jacked culverts, and modeled box frames, respectively. Accelerometers are installed on the ground surface, within model soil, on jacked culverts, and within frames, respectively. Joint extension transducers are placed on both sides of every circumferential-joint (the joint between two adjacent culvert rings, denoted as joint) in jacked culverts. White noise and synthetic earthquake motion are selected to obtain the dynamic characteristics and seismic responses of the model system, respectively. About key findings, considering time domain and frequency domain, comparisons of site characteristics are presented by acceleration data in terms of the Fourier spectrum, the accelerogram, Arias intensity, and the peak ground acceleration amplification factor. Moreover, comparisons of structural seismic responses are quantified by the Fourier spectrum, accelerogram, and the correlation coefficient of acceleration. Joint extensions and closures are shown to reveal their distribution patterns.

2 Shaking table test

To better present the design of the shaking table test, an introduction to the prototype problem is necessary. The present study is based on a C-FCUS in a subway line in Shanghai, China. The cross-section of the jacked culvert (Part B) is shown in Fig.2(a). Two box frames (Part A and Part C) have the same cross-section of three-story and two-span as shown in Fig.2(b). As summarized in Tab.1, except for 1.7 m artificial fill, the prototype soil profile contains alternating layers of silty clay, mud clay, clay, and silt. The properties listed in Tab.1 are based on geotechnical and geological exploration in situ and laboratory tests.

2.1 Test facilities and scaling relations

With an operation frequency range of 0.1–50 Hz, the shaking table has dimensions of 10 m × 6 m and a loading capacity of up to 140 t. Meanwhile, the maximum acceleration output is 1.5g. The experiments were conducted utilizing a lately designed and constructed laminar box [9], which has internal dimensions of 9.5 m × 5.5 m × 2.16 m (length × width × height). Taking into accounts of both the size and capacity of the experimental facilities, the geometry scale factor was set to S_{\mathrm{l}} = 1/20. Other model properties (density, stiffness, excitation period, etc.) could be scaled down according to relevant scaling laws as follows.

Since the experiments were conducted in 1g, scaling would inevitably result in incompatibilities between the model and prototype when using the same soil material, commonly referred to as “scale effects.” By utilizing the synthetic model soil, where both shear modulus and density can be scaled, it is possible to minimize scale effects from the perspective of physical similarity. In this context, the other scaling factors were derived by combining the dynamic equilibrium, the Vaschy−Buckingham π theorem, and the dimensional analysis [25]. Given the significant role of soil nonlinearity during seismic loading, the hyperbolic model proposed by Kondner [26] is employed in deriving scaling relations (Eq. (1)).

(1){\sigma }_1-{\sigma }_3=\frac{\epsilon }{a+b\epsilon },

where {\sigma }_1 and {\sigma }_3 are the major and third principal stresses, respectively; \epsilon is the strain; a and b are constants. Hence, the similarity ratio of strain must be 1. Assuming the soil as a continuous medium, the dynamic equilibrium in the x-direction, balancing unbalanced external forces and inertial forces, can be written as

(2)\rho \frac{{\mathrm{\partial }}^{2}u}{\mathrm{\partial }{t}^2}=\frac{\mathrm{\partial }{\sigma }_{xx}}{\mathrm{\partial }x}+\frac{\mathrm{\partial }{\sigma }_{xy}}{\mathrm{\partial }y}+\frac{\mathrm{\partial }{\sigma }_{x\mathit{\text{z}}}}{\mathrm{\partial }\mathit{\text{z}}} ,

where x, y, and z are Cartesian coordinates; \rho, u, and t are density, displacement in x-direction, and time, respectively. Based on Hooke’s law [27], Eq. (2) can be written in terms of displacement:

(3)\rho \frac{{\mathrm{\partial }}^{2}u}{\mathrm{\partial }{t}^2}=\left(\lambda +G\right)\frac{\mathrm{\partial }\epsilon }{\mathrm{\partial }x}+G{\mathrm{\nabla }}^{2}u,

where \lambda and G are the Lame’s constants; and {\mathrm{\nabla }}^2 is the Laplacian operator. Equation (3) indicates the relationships of similitude ratios of density, acceleration, displacement, and shear modulus. It could be derived as follows:

(4)S_{\rho }{S}_{\mathrm{a}}=\frac{S_{\mathrm{G}}}{S_{\mathrm{l}}},

where S_{\rho }, S_{\mathrm{a}}, S_{\mathrm{G}}, and S_{\mathrm{l}} are similitude ratio of density, acceleration, shear modulus and geometry, respectively. To maintain compatibilities between the scaling of gravitational acceleration (always 1g) and seismic horizontal acceleration, the similitude factor of seismic acceleration should be 1, or at least close to 1. Thus, the theoretical scale factors of geometry, density, and shear modulus are S_{\mathrm{l}} = 1/20, S_{\rho } = 1/2.3, and S_{\mathrm{G}} = 1/46, respectively, so that S_{\mathrm{a}} = S_{\mathrm{g}} = 1. Tab.2 shows the resulting theoretical scale factors.

2.2 Model soil

As shown in Tab.1, the prototype soil profile is multi-layered. Simulating the detailed layered soil profile in experiments doesn’t fit the scope of this study. Therefore, a rational simplification of the prototype soil profile is needed. Considering the prototype soil deposit as one single idealized soil layer, the average density, and equivalent shear wave velocity are achieved as follows:

(5)\overline{\rho }=\frac{{\displaystyle \sum _{i=1}^n{\rho }_i\times h_i}}{{\displaystyle \sum _{i=1}^n{h}_i}},n=6,

(6)\overline{v_{\mathrm{s}}}=\frac{h_0}{t},

(7)t=\sum _{i=1}^n\frac{h_{\mathrm{i}}}{v_{\mathrm{s}\mathrm{i}}},n=6,

where \overline{\rho } and \overline{v_{\mathrm{s}}} are average density and equivalent shear wave velocity, respectively; {\rho }_i, v_i, and h_i are the density, shear wave velocity, and thickness of i\mathrm{t}\mathrm{h} layer, respectively; h_0 and t are the total thickness of the soil profile and the time required to traverse the entire soil profile, respectively; and i refers to the serial number of the corresponding soil layer listed in Tab.1. The average weight of 1772.9 kg/m³ and equivalent shear wave velocity of 181.6 m/s are thereby derived for the idealized single-layer soil profile.

Synthetic soil has the flexibility in adjusting its proportions of constituents to meet theoretical scaling relations. Within this context, a synthetic model soil composed of dry sand and sawdust is adopted in this study [9,28]. To optimally fit Eq. (4), a mass ratio of sand and sawdust of 2.5:1 is finally selected for the synthetic model soil according to the laboratory tests. By comparing the achieved scale factors with the theoretical ones, the synthetic model soil was selected to the best extent to satisfy the previously discussed similarities. To maintain the density of the model soil, the model site was filled up layer by layer, and the weight of each layer of synthetic soil was strictly controlled to ensure a density of 694 kg/m³.

2.3 Model structure

2.3.1 Box frames

To accurately simulate box frames in tests, granular concrete was employed for Part A and Part C. This granular concrete comprised cement, water, lime, and medium sand in a mass ratio of 1:0.6:0.6:5.8. Galvanized steel wires were utilized to simulate rebars in box frames.

The construction process of the box frame is shown in Fig.3. First, steel wires were made into cages and installed in a temporary formwork. The second step was pouring the granular concrete. After 28 d of concrete curing, the box frame was then allowed to remove the formwork. Fig.3(c) presents the detailed dimensions of the cross section of box frames. As Fig.3(d) shows, Part A is 1000 mm long, containing 3 columns placed in the longitudinal direction. Part C is 3500 mm long, containing 9 columns in the longitudinal direction. Plastic plates were installed at the ends of frames near the laminar container to prevent the model soil from entering the frames.

2.3.2 Twin jacked culverts

Each prototype jacked culvert ring, made of Q345B steel, consists of the exterior steel plate and T-section steel. The T-section steel is melted at the inward face of exterior steel plates in both longitudinal and transverse directions. For each joint of prototype jacked culverts, 22 bolts with a diameter of 30 mm were installed as longitudinal connectors.

Q235 cold-rolled carbon structural steel sheets with thickness of 2 mm were selected as the material of model jacked culvers for the convenience of processing. Owing to the complexity of the prototype culvert, the model culvert was designed in a simplified manner while ensuring that the total amount of steel in the cross-section remained constant. 20 bolts with a diameter of 5 mm were selected as longitudinal connectors. Detailed dimensions of the model culvert are depicted in Fig.4. The longitudinal section presented in Fig.4(b) describes the dimensions of the F-type socket.

The dynamic characteristics of the jacked culvert are notably affected by the relative stiffness of the culvert ring to the joint. Consequently, a comparison of tensile stiffness between the prototype culvert and the model culvert is provided in Tab.3. The relative tensile stiffness ratios of culvert rings to joints exhibit a good fit between the prototype and model culverts. The model culvert, designed in a simplified manner, generally meets the similarity relations in terms of tensile stiffness.

2.4 Instrumentation

The instrumentation layout is summarized in Fig.5. The instrumentation included 19 accelerometers and 160 joint extension transducers modified from strain gauges. 4 accelerometers (SA0, SA1, SA2, and SA3) were installed at the surface of the model soil and SA4 was installed at the same depth as the culvert. In the vertical view, SA1, SA2, SA3, and SA4 located between the twin jacked culverts, while SA0 located 1500 mm away from SA2. Detail locations of the 5 accelerometers are presented in Fig.5(a). 12 accelerometers (A1–A6, A7–A12) were installed on the top of the two culverts (Fig.5(b)). Accelerometers were installed in each culvert at joint positions 2nd, 10th, 18th, 24th, 32nd, and 40th (sequentially ordered from Part A to Part C), maintaining the principle of equal spacing. FA1 and FA2 were installed against the walls of Part A and Part C, respectively. FA1 and FA2 were also at the same depth as the accelerometers on culverts (Fig.5(c)). 160 joint extension transducers were installed at every joint of culverts, at the middle of the height, to record joint extensions and closures during tests.

2.5 Input motions

As summarized in Tab.4, white noise (WN) and synthetic earthquake motions (SEM) were adopted as the input motions for the shaking table tests. Owing to the nonlinearity of the soft soil, white noise motions with low intensity are necessary for investigating the dynamic characteristics of the model soil. The synthetic earthquake motion is representative of the construction site. Synthetic earthquake motions with varying intensities help with investigating the nonlinearity of the model system. Accelerograms and spectra of the earthquake motion with a peak acceleration of 0.1g are depicted in Fig.6. The seismic input motions were imposed in the X direction (longitudinal) of the station (Fig.5).

3 Comparisons of site characteristics

Consisting of twin jacked culverts and two box frames, the underground structure, due to its structural nonuniformity, affects the surrounding soil to varying degrees depending on the location of the sites. Four accelerometers, SA0, SA1, SA2, and SA3, are selected due to their representative locations to compare site characteristics. Acceleration Fourier spectrum, acceleration time histories, Arias intensities, and peak ground acceleration (PGA) amplification factors are discussed to evaluate site characteristics.

3.1 Acceleration Fourier spectrum

Fig.7 plots the Fourier spectra of SA0, SA1, SA2, and SA3 during the white noise motion with the peak acceleration amplitude of 0.05g. SA0, SA1, SA2, and SA3 were installed at the same surface level but different locations (refer to Fig.5). SA0 was installed with a separation of 1500 mm from SA1, SA2, and SA3 in Y direction. Due to this distance, the underground structure minimally impacts the dynamic characteristics of the site where SA0 is situated. The Fourier spectra of SA0, SA1, SA2, and SA3 peaked at the same frequency (7.34 Hz), with amplitudes of 0.022g, 0.018g, 0.016g, and 0.013g, respectively. The findings indicate that the four sites have the same dominant frequency. The restrain effect of the underground structure to the surrounding soil results in the amplitude declines of SA1, SA2, and SA3 in the Fourier spectra.

3.2 Acceleration amplitude

Synthetic earthquake motion is adopted to investigate the seismic responses of the model system. Fig.8 displays a representative comparison of accelerograms among SA0, SA1, SA2, and SA3 during the synthetic earthquake motion with the peak acceleration amplitude of 0.1g. The accelerograms reveal a consistent trend in the accelerations of the four accelerometers, with variations in the amplitude. Notably, SA0, located furthest from the underground structure, exhibits the highest amplitude (0.26g), while SA3, positioned closest to the station, registers the lowest amplitude (0.14g). SA1 and SA2 have similar accelerations of 0.20g and 0.19g.

The results demonstrate that the underground structure has a restrained effect on the acceleration of the site soil, which results in a decrease in acceleration amplitude. The restrained effect decreases as the distance between the accelerometer and the underground structure increases.

3.3 Arias intensity

The acceleration amplitude is not the sole factor influencing the intensity of a given earthquake motion; the duration also plays a crucial role. Arias intensity (I_A) [29] is defined as the cumulative energy per unit weight absorbed by an infinite set of undamped single-degree-of-freedom oscillators at the end of an earthquake. I_A could be calculated by

(8)I_{\mathrm{A}}= \frac{\text{π}}{2g}{\int }_0^{T_{\mathrm{d}}}{a}^2\left(t\right) \mathrm{d}t,

where a\left(t\right) is the acceleration of the observed site, g is the gravitational acceleration, and T_{\mathrm{d}} is the duration of the ground motion. Arias intensity can simultaneously capture the impact of ground motion amplitudes and durations, rendering it a valuable indicator of ground motion destructiveness.

Fig.9 shows Arias intensities of SA0, SA1, SA2, and SA3 during the synthetic earthquake motion with the peak acceleration amplitude of 0.1g. SA0 consistently exhibits higher I_A values than the other accelerometers. I_A of SA2 is greater than that of SA1 and SA3. I_A of SA3 is the least of those of the four observed sites. Notably, with respect to a specific earthquake motion, the more seismic energy absorbed by the field and the underground structure during transfer, the less I_A of the site surface becomes. Thus, the reduce of I_A may result from the restrained effects of box frames to surrounding soil. SA2 is 2000 mm away from both Part A and Part C, while SA1 and SA3 is 500 mm away from Part A and Part C, respectively. The difference in the distance to box frames results in varying degrees of restrained effects on SA1, SA2, and SA3. According to the difference between I_A of SA1 and SA3, the restrained effect from Part C is greater than that from Part A in I_A.

3.4 Peak ground acceleration amplification factor

A considerable quantity of studies point out that soil nonlinearity has a significant effect on the ground acceleration response [30–32]. The restrained effect of the underground structure to surrounding soil results in a change in the soil nonlinearity of the site, which in turn affects the ground acceleration response. The difference in the soil nonlinearity effect of the four observed sites is discussed in the following using PGA.

PGA serves as a common metric for quantifying the amplitude of specific ground motions. The acceleration amplification factor (β_A) [32] is formally defined as the ratio of the peak acceleration recorded at the measuring point to the input peak acceleration, which could be calculated by

(9){\beta }_{\mathrm{A}}= \frac{\mathrm{m}\mathrm{a}\mathrm{x}\left(a\left(t\right)\right)}{\mathrm{m}\mathrm{a}\mathrm{x}\left(a_{\mathrm{i}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}}\left(t\right)\right)},

where a\left(t\right) and a_{\mathrm{i}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}}\left(t\right) are accelerations of the observed site and input, respectively.

Fig.10 depicts PGA amplification factors of the four observation accelerometers, namely SA0, SA1, SA2, and SA3, subjected to synthetic earthquake motions with varying amplitudes. In SEM-0.1g, SA1 exhibits the highest β_A among the four accelerometers, while SA3 displays the lowest. This is consistent with the result of acceleration amplitudes in Fig.8. As the intensity of the input motion increases, β_A of SA0 decreases significantly from 2.60 (SEM-0.1g) to 1.66 (SEM-0.6g) for the effect of soil nonlinearity. However, β_A of SA1, SA2, and SA3 show different tendencies. β_A of SA1 decreases from 1.95 (SEM-0.1g) to 1.83 (SEM-0.6g), which compared with that of SA0, is less sensitive to the input motion intensity. In other words, the soil nonlinearity effect of SA1 is weaker than that of SA0. β_A of SA2 decreases from 1.95 (SEM-0.1g) to 1.42 (SEM-0.6g), while that of SA3 increases from 1.37 (SEM-0.1g) to 1.74 (SEM-0.6g).

β_A of SA0 decreases with increasing input motion intensity, which shows the nonlinearity of the soft soil. While β_A of SA1 and SA3 show different tendencies due to the restrained effects from Part A and Part C, respectively. Compared with SA1 and SA3, SA2 has the greatest distance from the adjacent box frame. Owing to the distance, SA2 is subjected to the least restrained effect from box frames. Thus, the site of SA2 has a similar nonlinearity with that of SA0, which results in a similar tendency in β_A.

4 Seismic responses of the underground structure

Part A, Part B, and Part C differ in the stiffness and the quality, which leads to different seismic responses for each. Acceleration responses and joint extensions are discussed in the following to evaluate the dynamic characteristics of jacked culverts and box frames. The interaction between the culvert and the box frame is investigated.

4.1 Acceleration Fourier spectrum

White noise is adopted to present dynamic characteristics of jacked culverts and box frames in terms of the spectrum. As shown in Fig.5, A1–A12 are all on jacked culverts; FA1 and FA2 are in Part A and Part C, respectively. These accelerometers are in close depths where the soil accelerometer SA4 locates. The Fourier spectra of A1–A12, FA1, and FA2 are presented in Fig.11(a). Fig.11(b) is the Fourier spectrum of SA4 Since the underground structure mainly follows the movements of surrounding soil during seismic excitation [33], the accelerometers on jacked culverts and in box frames are more sensitive to acceleration components of the dominant frequency where the Fourier spectrum of SA4 reaches the peak amplitude.

4.2 Acceleration amplitude

Fig.12 displays the acceleration time histories of accelerometers situated on box frames and culverts in SEM-0.1g, SEM-0.2g, SEM-0.4g, and SEM-0.6g. In every test case, the accelerograms have little or no phase difference, indicating the consistency of underground structure movements during the earthquake motions. In SEM-0.1g and SEM-0.2g, acceleration amplitudes of frames and culverts are close to the input excitations. While in SEM-0.4g and SEM-0.6g, acceleration amplitudes of frames and culverts are much less than the input excitations. Considering the nonlinearity effect of the model soil, frames and culverts are influenced by the surrounding soil and their acceleration responses exhibit similar nonlinearity effects. The peak accelerations of frames (FA1 and FA2) are much smaller than those of the culverts in SEM-0.4g and SEM-0.6g, because of the difference in dynamic characteristics between frames and culverts.

4.3 Correlation coefficient of acceleration

To quantify the similarity among the acceleration responses of culverts and box frames, the correlation coefficients [22] of their acceleration records are calculated.

(10)r\left(A_{\text{m}},A_{\text{n}}\right)=\frac{\text{Cov}\left(A_{\text{m}},A_{\text{n}}\right)}{\sqrt{\text{Var}\left[A_{\text{m}}\right]\text{Var}\left[A_{\text{n}}\right]}},

where A_{\mathrm{m}} and A_{\mathrm{n}} are acceleration records of accelerometers to analysis; r\left(A_{\mathrm{m}},A_{\mathrm{n}}\right) is the correlation coefficient of A_{\mathrm{m}} and A_{\mathrm{n}}; \mathrm{C} \mathrm{o}\mathrm{v}\left(A_{\mathrm{m}},A_{\mathrm{n}}\right) is the covariance of A_{\mathrm{m}} and A_{\mathrm{n}}; \mathrm{V} \mathrm{a}\mathrm{r}\left[A_{\mathrm{m}}\right] and \mathrm{V}\mathrm{a}\mathrm{r} \left[A_{\mathrm{n}}\right] are variances of A_{\mathrm{m}} and A_{\mathrm{n}}, respectively.

Correlation coefficients of accelerometers (FA1, FA2, and A1–A12) in SEM-0.1g, SEM-0.2g, SEM-0.4g, and SEM-0.6g are shown in Fig.13. For instance, the element at the second line and the third column of each matrix is the correlation coefficient of the accelerometers of A1 and A2. According to the definition of the correlation coefficient, the matrixes are symmetric, and the main diagonal elements are equal to 1. The other elements of the matrixes range from −1 to 1, where 1 means a complete positive linear correlation, and −1 means a complete negative linear correlation.

In SEM-0.1g, elements in the matrixes vary from 0.16 to 1, which means the culvert and the box frame have different acceleration responses. Elements of the first and last rows (or columns) are the correlation coefficients of FA1 and FA2 with respect to the other accelerometers, respectively. Elements in first row are generally smaller than those in the last row. This means that the acceleration responses of the culvert are closer to Part C than to Part A. A1, A6, A7, and A12 are at the transition zone from box frames to culverts. Thus, the four accelerometers are affected by the responses of the box frame and the adjacent culvert. The accelerometers at more central position (A2–A5, and A8–A11) have obviously bigger correlation coefficients between each other. The correlation coefficients of Case1 prove that the culvert and the box frame have different acceleration responses originating from their different dynamic characteristics. Acceleration responses of culverts are affected by box frames to varying degrees depending on the distance from the box frame.

In SEM-0.2g, SEM-0.4g, and SEM-0.6g, the correlation coefficients of FA1 subjected to the other accelerometers are obviously larger than those in SEM-0.1g. The correlation coefficients of FA1 remain smaller than those of FA2 in the four test cases. This means that FA1, recording the acceleration response of Part C, has records of acceleration response that more closely match those of the culvert in cases with high amplitude inputs. FA2, recording the acceleration response of Part A, is consistently better matched up to the culvert in the accelerogram than FA1. Accelerograms of the box frame and the culvert tend to be close in cases with high amplitude inputs.

4.4 Joint extension

Since input motions are in the longitudinal direction, discrepant acceleration responses of culverts result in longitudinal deformations. Owing to the significant difference in the tensile stiffness between culvert rings and joints, longitudinal deformations are mainly demonstrated by extensions and closures of joints. The 160 joint extension transducers can be divided into four groups, which are placed on both sides of the twin culverts, respectively. As depicted in Fig.4, every joint has two joint extension transducers on both sides. Joint extensions and closures of the twin jacked culverts in SEM-0.1g are presented by a series of animated GIF (graphics interchange format) images in Supplementary materials. The GIF images change over the time of input motions.

To reveal the characteristics of joint extensions and closures, presenting the joint extensions and closures during a period corresponding to the dominant frequency is a proper method. The Fourier spectra of A1–A12 in SEM-0.1g are depicted in Fig.14. The dominant frequency is 9.64 Hz and the corresponding period T_0 is 0.104 s. In SEM-0.1g, the joint extension of OJ34 at t=1.105 s is 0.1783 mm, which is the maximum extension of all joints in this case. Thus, t=1.105 s is set as the midpoint of the representative period (1/2T_0). Nine representative moments (0T_0, 1/8T_0, 1/4T_0, 3/8T_0, 1/2T_0, 5/8T_0, 3/4T_0, 7/8T_0, 1T_0) of the period T_0 corresponding to the dominant frequency can be derived.

The joint extensions and closures at the nine moments are depicted in Fig.15. A negative joint extension means that the joint is closing at this time. The joint deformations exhibit cyclic variation in the given period. The characteristics of the distribution of the joint extensions are summarized as follows. 1) The distribution of the joint extensions is spiky, meaning that several joints have much larger extensions than the surrounding ones. As depicted in Fig.15(e), OJ34 have a joint extension of 0.1783 mm, while the average of OJ1–0J40 at this moment is 0.0115 mm. 2) The locations of joints with larger extensions are inherited during the input motion. For instance, OJ23 and OJ34 have joint extensions much larger than the average joint extension in the nine moments.

To compare the joint extensions of both sides of jacked culverts, joint extension differences between the two sides of each culvert at the nine moments are depicted in Fig.16. The extension differences which change over time of input motions in SEM-0.1g are presented in Supplementary materials. The extension difference is calculated by subtracting the extension of one side from that of the other side.

The distribution of joint extension differences is spiky and inherited just like the distribution of joint extensions depicted in Fig.15. The locations where larger joint extension differences occur always correspond to the locations where extensions are significantly larger than average such as OJ23 and OJ34. The joints with large joint extensions are all on the part of jacked culverts near Part C. Part C is of greater stiffness and quality comparing with Part A, which results in greater stiffness mutation at the transition zone from Part C to Part B. The stiffness mutation results in complex seismic responses in terms of greater joint extension differences.

5 Conclusions

This paper has presented an experimental study of the seismic performance of C-FCUS in soft soil. By comparing site characteristics and responses of the underground structure, this study investigated the restrained effects of the underground structure to surrounding soil and the interaction between culverts and box frames. Notably, the excitations in this present study are all in longitudinal direction, and the jacked culverts are rigidly connected to the box frames by combining epoxy resin and carbon fiber cloth. The seismic responses in other cases will be discussed in future studies. The following conclusions of this present study are drawn.

1) The underground structure has varying degrees of restrained effects on surrounding soil. Ground surface accelerations at different locations show good agreement in the dominant frequency where amplitudes vary due to the restrained effects. Local sites near box frames have smaller PGAs compared with the sites relatively far away from box frames. The underground structure has similar restrained effects on the Arias intensity of local sites. Increasing the intensity of the input motion, β_A of SA1 has a slight decrease while β_A of SA2 decreases similarly to that of SA0. The increasing distance from box frames to the site soil leads to a weakening of the restrained effect.

2) The jacked culverts and box frames mainly follow the movements of surrounding soil during seismic excitation. The transition zone from box frames to jacked culvert shows dynamic characteristics closer to those of the adjacent box frame, comparing with the middle part of culverts. Part A and Part C show different characteristics in both the amplitude and the spectrum.

3) The distribution of joint extensions and joint extension differences is spiky and inherited. The difference in dynamic characteristics between jacked culverts and box frames could result in greater joint extension differences in longitudinal excitations.

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