There are few studies on the dynamic-response mechanism of near-fault and far-field ground motions for large underground structures, especially for the branch joint of a utility tunnel (UT) and its internal pipeline. Based on the theory of a 3D viscous-spring artificial boundary, this paper deduced the equivalent nodal force when a P wave and an SV wave were vertically incident at the same time and transformed the ground motion into an equivalent nodal force using a self-developed MATLAB program, which was applied to an ABAQUS finite element model. Based on near-fault and far-field ground motions obtained from the NGA-WEST2 database, the dynamic responses of a utility tunnel and its internal pipeline in different input mechanisms of near-fault and far-field ground motions were compared according to bidirectional input and tridirectional input, respectively. Generally, the damage to the utility tunnel caused by the near-fault ground motion was stronger than that caused by the far-field ground motion, and the vertical ground motion of near-fault ground motion aggravated the damage to the utility tunnel. In addition, the joint dislocation of the upper and lower three-way joints of the pipeline in the branch system under the seismic action led to local stress concentrations. In general, the branch system of the utility tunnel had good seismic performance to resist the designed earthquake action and protect the internal pipeline from damage during the rare earthquake.
Currently, traffic jams and the lack of public space caused by the old urban form have greatly restricted the development of cities. Among the numerous reconstruction schemes, the urban underground space has been considered to play an effective role in urban renewal [
Seismic analysis methods of underground structures can be divided into quasi-static analyses and time-history analyses [
In recent years, research on the dynamic response of near-fault earthquakes and far-field earthquakes has mainly focused on the above-ground structure [
Based on the popularization of utility tunnels in the urban underground space and many damage cases of utility tunnels due to earthquakes, the seismic performance of utility tunnels has attracted the attention of scholars. The current seismic research on utility tunnels has mainly focused on the standard segment of the utility tunnel. Through time-history analysis, Jiang et al. [
At present, the seismic research on utility tunnels is mostly concentrated on the standard section, and the related research on pipelines in the tunnels is less common. Additionally, the research form is relatively narrow, which is not enough to meet the development trend of the diversified structure of utility tunnels, the integrated construction of underground spaces, and the changing social needs [
To study the seismic response of complex underground structures such as the branch system, an input model of the ground motion is explained in
To ensure the calculation accuracy of the soil-structure interaction, a viscous-spring artificial boundary was used to simulate the infinite field. This was achieved using a parallel system of spring-dampers on the intercepted soil boundary nodes, which were used to simulate the elastic-recovery capacity of a semi-infinite medium, consume the ground-motion energy, and overcome the low-frequency global drift [
where
According to the elastic formula, the shear modulus
The velocities of the P and S waves are defined as follows:
For node
This paper refers to the method of Liu et al. [
where
Since the incident angle of the seismic wave is nearly perpendicular to the surface when it reaches the ground surface, according to the geometric and physical equations of elastic mechanics:
The free-field stress tensor can be obtained as follows:
where
In this paper, the P wave and SV wave are vertically incident at the same time;
We can obtain:
When node
When node
where
The branch system is the part where the internal pipeline and external pipeline of a utility tunnel are connected. The tunnel section is partially expanded, and either the roof is partially raised or the floor is lowered locally. In this paper, the branch system of a utility tunnel in Nanjing was taken as the research object, and nonlinear dynamic-response analysis was carried out to study the seismic characteristics of the branch system in different ground-motion input mechanisms.
Due to the large scale of the utility tunnel in the longitudinal direction, in order to save calculation costs, the 3D time-history analysis cannot be modeled completely according to the original longitudinal dimension. In fact, when the longitudinal dimension is larger than a certain length (75–100 m), the influence of the longitudinal boundary condition on the structural response is weakened [
The pipeline route is shown in
The plastic-damage model [
where
The stress-strain relations can be expressed by stiffness degradation and the elastic part of the strain tensor:
where
For any section, (1 –
The equivalent plastic strain
where
In this paper, C35 concrete was used for the main structure and piers of the utility tunnel, a concrete casing was set at the branch-joint opening, and C40 concrete was used for simulation. From the Chinese Code [
According to the report of the geotechnical investigation, the soil in this area is mainly silty clay. The Drucker–Prager failure criterion was used for the soil, Q235 steel was used for the pipe, and HRB400 steel was used for the steel bar. The specific properties are presented in
Material | C35 | C40 |
---|---|---|
Dilation angle (°) | 31 | 31 |
Eccentricity | 0.1 | 0.1 |
Stress ratio | 1.16 | 1.16 |
2/3 | 2/3 | |
Viscosity parameter | 1E-5 | 1E-5 |
Compressive yield stress (MPa) | 23.4 | 26.8 |
Tensile yield stress (MPa) | 2.2 | 2.39 |
Mass density (kg/m3) | 2390 | 2400 |
Elastic modulus (GPa) | 31.5 | 32.5 |
Poisson’s ratio | 0.2 | 0.2 |
Material | Soil | Steel bar | Pipe |
---|---|---|---|
Elastic modulus (GPa) | 0.025 | 206 | 206 |
Poisson’s ratio | 0.3 | 0.28 | 0.3 |
Mass density (kg/m3) | 1880 | 7800 | 7850 |
Yield stress (MPa) | – | 400 | 235 |
Dilation angle (°) | 40 | – | – |
Cohesion (kPa) | 31.9 | – | – |
Shear wave velocity (m/s) | 101.14 | – | – |
In this paper, ABAQUS software was used for modeling. To ensure the accuracy of the ground-motion input, the size of the finite element mesh was limited to a certain extent. However, the finer the mesh is, the higher the cost of the calculation will be. Element mesh size is generally determined by the seismic wavelength, such that
The soil was simulated by a solid element (C3D8R), and the mesh size was 1 m × 1 m × 1 m, which was refined near the branch joint and the buried pipeline. For the utility tunnel, this paper mainly studied the branch joint. Therefore, the branch joint was divided by the solid element (C3D8R), and the standard segments on both sides of the branch joint were divided by the continuous shell element (SC8R). At the same time, the steel bars were embedded in the concrete without considering their bonding slip. The pipe was simulated by a shell element (S4R), and the piers were poured with plain concrete, which was divided by solid elements.
In practical engineering, the pipe is completely fixed on the piers by a steel hoop; so, in the simulation, the pipe was fixed by tie constraints on the contact surface. In the simulation of the soil-structure interaction, general contact was used to simulate the contact relationship between the soil-tunnel, soil-pipe, and pipe-tunnel. The tangential behavior was defined as a penalty contact, and the friction coefficient was 0.3 [
A self-developed MATLAB program was used to realize the batch implementation of the viscous-spring artificial boundary and equivalent node force on the boundary nodes. The flowchart is shown in
The finite element model is shown in
Step 1: The static model is established to balance the initial ground stress until the vertical displacement of the site is less than 10-4 m. At this time, four lateral boundaries and one bottom boundary are used as normal fixed constraints, and the support reaction on the boundary is extracted.
Step 2: Before dynamic analysis, the boundary constraints need to be removed to ensure the seismic input. At this time, the support reaction extracted from the static model should be applied to each boundary in the form of a concentrated force to ensure that the stress field remains unchanged.
Step 3: In the dynamic-analysis step, the boundary condition is changed to viscous-spring artificial boundary to ensure the equivalent nodal-force input.
There have been 32 destructive earthquakes in Nanjing and its surrounding areas, recorded in history. These areas are likely to encounter near-fault earthquakes of magnitude over 6.0 and far-field earthquakes of magnitude 7.0–7.5 [
The Northridge earthquake in 1994, the Erzincan earthquake in 1992, and the Kocaeli earthquake in 1999 were selected as the excitations for near-fault ground motion. Similarly, the Taft earthquake in 1952, the Landers earthquake in 1992, and the Loma Prieta earthquake in 1989 were selected as the excitations for far-site ground motion, as shown in
Number | Event | Station | Magnitude (Mw) | Rupture distance (km) |
---|---|---|---|---|
1 | Northridge | Newhall-W Pico Canyon Rd. | 6.69 | 5.48 |
2 | Erzican | Erzincan | 6.69 | 4.38 |
3 | Kocaeli | Yarimca | 7.51 | 4.83 |
4 | Kern County | Taft Lincoln School | 7.36 | 38.89 |
5 | Landers | Desert Hot Springs | 7.28 | 21.78 |
6 | Loma Prieta | Hollister City Hall | 6.93 | 27.60 |
The mean acceleration response-spectrum values in the three directions are shown in
In this paper, the amplitude of the ground-motion acceleration was adjusted. The horizontal ground motion was input according to the peak accelerations of 0.2 and 0.4 g, considering an earthquake intensity of VIII in the Chinese Code [
The results showed that the damage to the tunnel under a seismic intensity of 0.2 g was relatively light; so, only the damage to the tunnel under a seismic intensity of 0.4 g was counted. The locations of serious damage in the tunnel are shown in
Taking Erzincan as an example, it was assumed that the elements with a damage variable greater than 0.5 failed to bear any load, and the red region shown in
Some representative sampling points were set on the pipe to extract the pipe stress, as shown in
The maximum stress of the pipeline sampling points under 0.4 and 0.2 g seismic intensities is shown in
Under 0.4 g seismic intensity, the near-fault seismic response (
In this paper, the dynamic responses of the branch joint and inner pipelines of the urban-underground utility tunnel of Nanjing under near-fault and far-field earthquakes were studied according to bidirectional and tridirectional input. A viscous-spring artificial boundary was used to solve the semi-infinite space problem and simulate the energy dissipation. The equivalent nodal-force input method was deduced when a P wave and SV wave were incident vertically at the same time and was realized by the finite element method in ABAQUS software.
According to the dynamic-response results, near-fault and far-field earthquakes had significant influence on the structural response under different input mechanisms. The following conclusions were obtained:
The influence of the vertical component of near-fault ground motion on the damage to the utility tunnel cannot be ignored, causing 20% more damaged elements in the tridirectional input than in the bidirectional input. The connection between the branch joint of the utility tunnel and the standard segment is the most seriously damaged part under an earthquake, which can easily cause tensile fracture under strong ground motion. Due to the existence of the concrete casing, the damage to the concrete main structure around the opening of the branch joint is very small. With the increase of the ground motion intensity, the pipe stress under the near-fault ground motion is significantly higher than that under far-field ground motion. For rare earthquakes, the pipe stress under a near-fault earthquake is 20%–50% higher than that under a far-field earthquake. The stress level of the straight or curved pipeline in the tunnel under ground motion is smaller than that of the general buried pipeline. However, for the dislocation between the special joints such as the three-way pipeline and the contact point between the pipe and the casing in the tunnel under ground motion, the stress level will rise sharply, being 2–3 times higher than the stress of the general pipe in the tunnel. In general, the branch system of the utility tunnel has as good a seismic performance as the traditional underground structure. Owing to its good mechanical properties, it can resist design earthquakes. Only the roof at the connection between the branch joint of the utility tunnel and the standard segment is damaged under a rare earthquake action, and the internal pipe stress does not reach the yield limit of the material.