3.2.1. Static Loads for New Tunnel Excavation
1). Basic parameters
The paper uses three-dimensional four-sided structural units to simulate mudstones and malmstones using the Drucker-Prager model.Mudstone and malmstone samples were taken from the typical Class IV rock section of Shiqian Wanshoushan Highway Tunnel, and density test, uniaxial compression and deformation test, and triaxial compression test were carried out with reference to the national standards of "Rock Testing Procedures for Water Conservancy and Hydropower Engineering" (SL264-2020) and "Standard of Testing Methods for Engineering Rocks" (GB/T50266-2013).
Table 1 shows the parameters of peripheral rock support of Shiqian Wanshoushan Highway Tunnel.
As shown in
Figure 5, the peripheral rock support of Shiqian Wanshoushan highway tunnel is shown. Anchor support is discounted to the modulus of elasticity of the rock body in the reinforced area by stiffness, and steel frame and grid support is discounted to the initial lining of sprayed concrete by stiffness, and the reinforced area of rock anchors is estimated according to Duraksha's formula [
28]: steel frame or grid discounting formula:
where:
E_{c} - modulus of elasticity of spray concrete after conversion (MPa);
E_{c}_{0} - modulus of elasticity of original spray concrete (MPa);
S_{g} --Steel frame or grille frame cross-sectional area (m2);
E_{g} - modulus of elasticity of steel frame or grill (MPa);
S_{c} - cross-sectional area of concrete (m
^{2}).
Anchor support discount formula:
where:
E_{r} - modulus of elasticity of the rock mass after conversion (MPa);
E_{r}_{0} - modulus of elasticity of original spray concrete (MPa);
V_{b} - volume of anchor rods in the support area (m
^{3});
E_{b} - modulus of elasticity of anchor rod (MPa);
V_{r} - volume of rock body in the support area (m
^{3}).
The parameters of the mudstone and malmstone rock mass and the discounted anchor support and steel-frame grating support are shown in
Table 2.
2) Numerical simulation process
- (1)
The corresponding rock properties are assigned to the strata and the initial ground stress field is balanced. There is no influence of tectonic joints in the cross-section tunnel project, and the ground stress is considered according to the initial self-gravitational stress field.
- (2)
Simulate the excavation of the whole section of the existing railroad tunnel, apply initial support and secondary lining, and zero the displacement field.
- (3)
Excavation of new highway tunnel. Tunnel each excavation footage of 2m, after excavation for the initial support and secondary lining, in order to facilitate data analysis for multiple excavation steps as a whole encapsulated into different data results extracted when the step Si. set the left side of the tunnel for the first excavation of the tunnel, from the inlet (left) to the exit (right) excavation, the right side of the tunnel for the excavation after the front and back of the tunnel difference of 3 Si, Si No. for the S1, S2, S3. S20, ......S20. The left hole S1 and S17, the right hole S4 and S20 are the time step of going to the boundary effect, which is 90m respectively. left hole S2=S3=S15=S16=50m,S4=S5=S6=S7=S8=S9=S10=S11=S12=S13=S14=20m.right hole S5=S6=S18=S19=S14=20m. S6=S18=S19=50m, S7=S8=S9=S10=S11=S12=S13=S14=S15=S16=S17=20m as shown in
Figure 6.
- (4)
Layout of monitoring points in existing tunnels. Along the Hurong Tunnel floor layout measurement points, tunnel left and right intersection of the center of the line is set as 0 measurement points, to the left hole extension line layout 0 ~ 61 measurement points, to the right hole extension line layout 0 ~ -61 measurement points measurement point interval distance of 3m, the 7th measurement point for the left line of the intersection, the -7th measurement point for the right line of the intersection.
3.2.2. Dynamic Blasting Loads for New Tunnels
1) Eigenvalue analysis (general formula, refer to established running literature [A])
Eigenvalue is used to analyze the inherent dynamic characteristics of the structure, which is an important parameter for the design of the structure subjected to dynamic loads. Through the eigenvalue analysis [
37], the dynamic characteristics of the structure such as vibration shape, self-oscillation period, and vibration parameter coefficients can be obtained.
The characteristic equations for the calculation of vibration shape and intrinsic period are as follows:
where K is the stiffness matrix of the structure; M is the mass matrix of the structure; "ω" _"n" ^ "2" is the eigenvalue of the nth vibration mode; "Ф"
̅_"n" is the eigenvector of the nth vibration mode, and the spatial iterative method is used to calculate the eigenvectors to converge [
41].
- (1)
Boundary conditions
According to the literature [
31,
38], the elastic boundary is defined by the curved surface spring and the spring coefficient is calculated according to the foundation reaction coefficient of the road design code.
Vertical rock formation reaction force coefficient:
Horizontal rock formation reaction factor:
where
k_{v}_{0} =
k_{h}_{0} =
E_{0}/30,
B_{v} =
A_{v}^{1/2},
B_{h} =
A_{h}^{1/2}, Av is the vertical cross-section area of the rock layer, Ah is the horizontal cross-section area of the rock layer, and E0 is the elastic modulus of the rock layer.
After extracting the cross-sectional area in each direction based on the 3D solid model (
Figure 4), the vertical and horizontal foundation reaction coefficients are calculated by Eqs. 4 and 5, as shown in
Table 3.
- (2)
Analysis of results
As shown in
Figure 7, the calculation is carried out through Equation 1, and the comprehensive comparison of the eigenvalue results of the mass participation coefficients and periods of different vibration modes, and the final determination of the period values of vibration modes 6 and 7, 1.085584 and 1.031460, are used as the basis data for the calculation of damping of vibration modes of the time-range analysis.
- (3)
Time course analysis
Time-course analysis is the process of calculating the dynamic characteristics of the structure and the structural response (displacement, internal force, velocity, etc.) at any moment in time.According to the literature [
39,
40,
41], the power balance equations used are as follows:
where M is the total mass matrix of the finite element system; C is the total damping matrix of the finite element system; K is the total stiffness matrix of the finite element system; ("u")
̈"(t)", ("u")
̇"(t)", and "u(t)" are the acceleration, velocity, and displacement vectors of each node of the system; and "p(t)" is the dynamic load.
- (1)
Boundary conditions
Define the viscous boundary through the surface spring [
31,
38], the P-wave and S-wave damping calculations in the X, Y and Z directions of the rock layer required to establish the viscous boundary are shown in Equations (7) and (8).
P-wave damping calculation formula:
S-wave damping formula:
where
ρ is the density, kg/m
^{3};
γ is the bulk weight, t/m
^{3};
λ = vE/[(1+
v)(1-2
v)], the bulk modulus, t/m
^{2};
G =
E/2(1+
v), the shear modulus, t/m
^{2};
E is the modulus of elasticity, t/m
^{2};
v is the Poisson's ratio;
g is the acceleration of gravity;
A is the cross-sectional area of the boundary rock layer, m
^{3};
c_{p} is the P-wave damping constant;
c_{s} is the S-wave damping constant.
When inputting damping in GTS NX, only
c_{p} and
c_{s} can be input because the program automatically calculates the cross-sectional area of each unit. According to Eqs. (7) and (8) combined with the mechanical parameters of the rock formation, the results of cp and cs are shown in
Table 4.
- (2)
Dynamic load
Blasting load parameters include loading waveform, peak stress, location and direction of action, loading and unloading time, total vibration time and loading boundary.
The blast load waveform adopts the triangular load waveform, the peak load is reached quickly in 10 ms, and the unloading time is 100 ms. The peak load is determined by the empirical formula according to the literature [
42], and the empirical formula is as follows:
where
Z is the proportional distance;
R is the distance from the gun hole to the loading surface, m;
Q is the gun hole charge.
Under the tunnel blasting excavation of existing railroad tunnels mass vibration velocity requirements do not exceed 2cm / s, according to the literature [
43], a one-time detonation of the maximum allowable amount of drug formula:
where
V is the existing tunnel media mass vibration velocity;
Q is a one-time permitted under the tunnel detonation of the total charge, kg;
R is the center of the source of self-explosion to the distance of the protected building, m;
K is the medium factor;
a for the blasting vibration coefficient.
According to new tunnels and existing tunnels engineering geological conditions,
K take 250,
a take 1.5, through the formula (11) calculations, the existing tunnel floor from the center line of different distances from the maximum amount of detonation charge and mass vibration velocity, see
Table 5
The maximum charge of 8.0 kg was selected as the base data for calculating the peak blasting load in conjunction with the spatial relationship of the cross tunnels. According to the maximum charge requirements for the upper and lower steps of the excavation section blasting design, the design of the shell hole section shown in
Figure 8, blasting parameters are shown in
Table 6.
Combined with the excavation section blasting design, the distance from the gun hole to the load surface is 1.0 m, based on the formula (7) and (8) to obtain the peak blasting load of 20.89 MPa. Blasting load in the form of pressure applied to the tunnel excavation boundary rock layer, the direction of action for the perimeter of the tunnel vertical direction.
3.2.3. Existing Tunnel Operational Loads
- (1)
Train dynamic load
The dynamic load of each wheel during train operation is simplified into a series of vertical concentrated forces whose size changes dynamically with time, and the artificial excitation function method is utilized to determine the train vibration load. The excitation function consists of a static load and a series of sinusoidal functions superimposed on the dynamic load [
44,
45], whose expression is:
where
${P}_{0}$ is the static wheel load;
${P}_{1}$、
${P}_{2}$、
${P}_{3}$ are the peak loads corresponding to smoothness of travel, line power additional load, and waveform wear;
${M}_{0}$ is the mass of the train under the springs;
${L}_{i}$ is the uneven vibration wavelengths of the smoothness of travel, line power additional load, and waveform wear control conditions;
${a}_{i}$ is the lost height corresponding to the uneven vibration wavelength of the three control conditions;
v is the train speed.
According to the existing tunnel train operation information, comprehensively considering the relevant parameters of CRH series trainsets, the train parameters are selected as eight cars, length 200m, speed 200km/h (55.5m/s), axle weight 19t, unsprung mass 2t, and static wheel weight 95kN on one side. According to the track unevenness laying accuracy standard (
Figure 9) mentioned in the literature [
32], the uneven wavelength and vector height are determined under three control conditions:
L_{1}=10 m,
a_{1}=3.5 mm;
L_{2}=2 m,
a_{2}=0.4 mm;
L_{3}=0.5 m,
a_{3}=0.1 mm. According to the formulae (12)~(13) to get the train dynamic loading time curve, as shown in
Figure 10.