In summary, the above research mainly focused on the performance of the rectangular freezing soil mass, and there is little research on the trapezoidal freezing soil mass for tunnel portal reinforcement. For the rectangular freezing soil mass, the differences in soil load between the top and bottom of the large-diameter tunnel were not taken into account, and the top and bottom of the tunnel were reinforced in the same way. This caused a huge economic waste.
In this paper, trapezoidal freezing soil mass was proposed to reinforce the soil at the tunnel’s initial end. Based on the Wuhu River-Crossing Tunnel, the relationship between the longitudinal length of trapezoidal freezing soil mass and portal stability is established according to the tunnel portal damage mode. Then, the numerical simulation method is applied to study the influences of the length of the upper and lower sides of the trapezoidal freezing soil mass on the displacement of the tunnel portal. Finally, the trapezoidal freezing soil mass was applied in the Wuhu River-Crossing Tunnel and the reinforcement effects were analyzed. This study provides an optimized solution for the soil reinforcement of shield tunnel portals in the water-rich sand layer, which has important engineering significance.
3. Theoretical Analysis of Tunnel Portal StabilityThe soil body of the tunnel portal is subjected to the upper soil body load and ground load P. When the sealing door is removed, the tunnel portal soil body equilibrium is broken and a sliding surface may be formed. Thus, damage occurs, as shown by the dashed line in Figure 4. This sliding surface is assumed to be a circular arc, with the top of the tunnel portal as the center and the diameter D1 of the tunnel portal as the radius. The sliding moment is greater than the resistance moment on the circular arc surface. To enhance the stability of the soil body in the tunnel portal area, it is necessary to reinforce the soil body and enhance the resistance moment on the sliding surface. The sliding moment of the soil body consists of three parts, which are the sliding moment caused by the ground load P, the sliding moment caused by the self-weight of the upper soil body, and the sliding moment caused by the self-weight of the sliding soil body. The resistance moment of the soil body is composed of the resistance moment of the soil body before reinforcement and the increasing resistance moment after reinforcement of the soil body. The increased resistance moment after reinforcement of the soil body is especially critical for tunnel portal stability. These expressions can be computed as followed.Sliding moment M, M=M1+M2+M3
(1)
M1(kN·m) is the sliding moment due to ground load P;
M2(kN·m) is the sliding moment caused by the self-weight of the upper soil;
M3(kN·m) is the sliding moment caused by the sliding soil body.Sliding resistance moment Md, Md=Mr+ΔMr
(2)
Mr(kN·m) is the resistance moment before soil reinforcement;
∆Mr(kN·m) is the increased resistance moment after soil body reinforcement.
Increased resistance moment after soil body reinforcement ΔMr:ΔMr=Δc⋅θ⋅D12=Δc⋅arcsinLD1⋅D12
(3)
∆c(kPa) is the increased value of cohesion after soil body reinforcement;
θ is the center angle of the circle corresponding to the reinforcement body, θ≤π/2;
D1(m) is the diameter of the tunnel portal;
L(m) is the longitudinal length of the rectangular freezing soil mass.
The equilibrium condition for the stable soil mass:K is the slip stability coefficient.
The relationship between slip stability coefficient K and θ is as follows.K=MrM+Δc⋅D12M⋅θ
(5)
When the rectangular freezing soil mass longitudinal length L is smaller than the diameter of tunnel portal D1, i.e., θ≤π/2, the center angle of circle θ increases with the increase in longitudinal length L. According to Equation (5), the stability coefficient of the tunnel portal also increases with increase in the center angle of the circle θ. When the longitudinal length L is greater than the diameter of tunnel portal D1, the center angle of circle θ equal π/2 and the slip stability coefficient will be constant.
From the Equations (3) and (5), it is known that with the reinforcement width increasing, the resistance moment of the soil body will not increase, and the stability coefficient of the tunnel portal will remain unchanged. Compared with the freezing soil mass length L, the influences of freezing soil mass width on the resistant moment are very small. The influences of freezing soil mass width were ignored, and the width was kept the same in the paper.
From the above analysis, it is clear that the magnitude of the sliding resistance moment is determined by the central angle θ. In addition, the angle affects the stability coefficient of the tunnel portal. Figure 5 and Figure 6 show the theoretical calculation model diagram and the trapezoidal freezing soil mass local enlargement diagram, respectively. The effects of upper side L1 and lower side L2 of trapezoidal freezing soil mass on the central angle θ are analyzed as follows.The trapezoidal freezing soil mass, which is shown in Figure 6a, is separated from Figure 5. The dimensions in Figure 6a have the following relationship. Substitute Equation (6) into Equation (7), the Equation (10) can be gained. Substitute Equation (8) into Equation (9), the Equation (11) can be gained.b−a=D1(L2−L1)2d+D1
(12)
The part in the red box of Figure 6a was isolated, as shown in Figure 6b. The tunnel portal with trapezoidal freezing soil mass was analyzed separately. The dimensions in Figure 6b have the following relationship.(b−a)2+D12=D1sinθ1
(13)
D1sin(π−θ1)=asinθ2
(14)
θ=π/2−[π−θ2−(π−θ1)]
(15)
Substitute Equations (13) and (14) into Equation (15), Equation (16) is obtained.θ=π2−arcsinD1(b−a)2+D12+arcsina(b−a)2+D12
(16)
Substitute Equations (10), (11), and (12) into Equation (16), the center angle of the circle can be computed by Equation (17).θ=π2−arcsin2d+D1(L2−L1)2+(2d+D1)2+arcsinL1D1+dL1+dL2D1(L2−L1)2+(2d+D1)2
(17)
L1(m) is the upper side length of the trapezoidal freezing soil mass;
L2(m) is the lower side length of the trapezoidal freezing soil mass;
d(m) is the length from upper side of the trapezoidal freezing soil mass to the top of the tunnel;
D1(m) is the diameter of the tunnel portal, D1 = 14.5 m.
Firstly, the lower side’s length L2 of the trapezoidal freezing soil mass is 4 m, while the upper side’s length L1 ranges from 2 m to 4 m. The upper side length of the trapezoidal soil mass is 2 m, while the lower side’s length L2 ranges from 2 m to 4 m. Figure 7 shows the value of the central angle θ for different L1, and L2. The relationship between θ and L1 can be obtained by linear fitting with θ=0.012105L1+0.23107 when the correlation coefficient is above 0.99. The relationship between θ and L2 can be obtained by linear fitting with θ=0.05845L2+0.02143, and the correlation coefficient is also above 0.99.From the above fitting formulas, it can be seen that the central angle θ increases with the increase in L1 and L2, respectively. The increasing ratio of θ with the L2 increasing is 4.83 times greater than that with the L1 increasing. It means that the central angle θ is more sensitive to L2 than to L1, and that L2 has greater influences on the central angle θ. From Equation (5), it is known that the tunnel portal stability coefficient is proportional to the central angle θ. Therefore, increasing L2 is more effective than increasing L1 for tunnel portal stability. To improve the reinforcement effect, the upper side length of the freezing soil mass can be reduced and the lower side length can be increased. Thus, the trapezoidal freezing soil mass can be used to reinforce the tunnel portal, and its reinforcement effects are superior to the rectangular freezing soil mass.
From the above analysis, it is known that the freezing reinforcement scheme of the Wuhu River-Crossing Tunnel can be optimized. The optimized scheme is as follows. The upper side length of the freezing soil mass is reduced (from 3 m to 2 m), while the lower side length freezing soil mass is increased (from 3 m to 4 m). The freezing soil mass transverse dimensions remain unchanged. The optimized freezing reinforcement body profile is shown in Figure 8. 5. The Application of Trapezoidal Freezing Soil Mass in the Wuhu River-Crossing TunnelIn order to verify the reinforcement effects of the trapezoidal freezing soil mass, it was applied in the Wuhu River-Crossing Tunnel. As mentioned in Section 3, the optimized freezing soil mass dimensions are as follows. The upper and lower side lengths of the trapezoidal freezing soil mass were 2 m and 4 m, respectively. The height and width of the freezing soil mass were unchanged. The mixing pile dimensions were also the same as those in real engineering. The portal displacement was analyzed by the numerical simulation method.Figure 16 shows the displacement contour of the tunnel portal with the optimization scheme. Figure 16a shows that x-direction displacement is relatively larger on the left and right sides of the portal. The maximum x-direction displacements are −1.09 mm and 1.14 mm, respectively, on the left and right sides of the tunnel portal. Figure 16b shows that the z-direction displacement is relatively larger on the top and bottom of the tunnel portal. The maximum z-direction displacements of the portal are −1.12 mm and 1.14 mm, respectively, on the top and bottom of the tunnel portal.Figure 17 is the y-direction displacement contour on the longitudinal section of the tunnel with the optimization scheme. From the figure, it can be seen that the portal’s central displacement is the highest. The maximum y-direction displacement is −5.66 mm. The maximum displacement value is much less than the allowable value of 15 mm [24,25]. This means the optimized scheme can also meet the safety requirements of real engineering.Figure 18 shows the monitoring point displacement of the tunnel portal with the optimization scheme or the original scheme. From the figure, it can be seen that the displacement of the portal with the optimization scheme is always lower than that of the portal with the original scheme. The maximum reduction ratio is 37.4% and the minimum reduction ratio is 14.2%.The portal’s central displacement was 9.91 mm for the original scheme, while it was 5.56 mm for the optimization scheme. The reduction rate was 42.9%. This means that the optimization scheme is more effective than the original scheme in controlling the portal displacement. It can be concluded that the trapezoidal freezing soil mass is more effective for the tunnel end soil reinforcement compared with the rectangular freezing soil mass.
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