Keywords

1 Introduction

A large number of diseases have been found in the completed loess tunnels, such as inverted arch cracking, excessive surface deformation, and lining failure [1]. Considering the characteristics of loess itself, the strength loss of the surrounding rock of the basement is large in the case of water ingress during the operation period, so the reinforcement of the loess tunnel foundation has always been a key research direction.

At present, high pressure jet grouting pile [2] are well used in loess tunnels due to their advantages of high strength, simple construction equipment, small floor area, fast construction speed, and good reinforcement effect on high compressibility and strong collapsible loess.

Some scholars at home and abroad have conducted a lot of researches on the high pressure jet grouting pile method, and Li Xiaojie et al. [3] compared and analyzed the measured and calculated values of the bearing capacity and settlement of the composite foundation of the high pressure jet grouting pile with the background of engineering practice. Lai Jingxing et al. [4] used numerical simulation combined with field measurements to analyze the consolidation of the foundation of the loess tunnel reinforced by high pressure jet grouting pile. Xuan Loi Nguyen et al. [5] took the Zhonghua Tunnel project in Vietnam as an example to study the principle and application effect of high pressure jet grouting pile in underground engineering reinforcement in Vietnam by comparing two methods: theoretical calculation formula and on-site monitoring and measurement.

To sum up, although a lot of research has been done by scholars at home and abroad, it is impossible to carry out research on tunnel water intake during the operation period due to the operation control of expressways, and the current research in this area is also very lacking. In this paper, the research is carried out by numerical simulation, and the correctness of the model is demonstrated by the monitoring data during the construction period, so as to ensure the reliability of the research.

2 Project Overview

The relying project is located in Ning Jiaping Village, Qing Shuiyi Township, Yuzhong County, Lanzhou City, with a total length of 674 m, a maximum buried depth of 97.0 m, an excavation width of 12 m, and a tunnel longitudinal section as shown in Fig. 1. Tunnel profile (Source: Rely on engineering design documents). The strata in the area where the tunnel is located can be divided into three layers, from top to bottom, the Quaternary Upper Pleistocene aeolian slightly dense loess (\({\text{Q}}_{3}^{\text{eol}}\)), the Quaternary Upper Pleistocene aeolian meso-dense loess (\({\text{Q}}_{3}^{\text{eol}}\)) and the Cretaceous Lower Cretaceous estuarine group 1 (K1hk1) sandstone. In addition, the collapsibility grade of the loess is grade 4, which has serious collapsibility, and the natural bearing capacity of the surrounding rock at the bottom of the tunnel cannot meet the design requirements, so the tunnel bottom must be reinforced to ensure the stability of excavation and the safety of the operation period.

Fig. 1.
figure 1

(Source: Rely on engineering design documents)

Tunnel profile

Full size image

3 Substrate Reinforcement Scheme and Tunnel Monitoring Scheme

3.1 Reinforcement Schemes

The tunnel reinforcement scheme and the parameters of the high pressure jet grouting pile are shown in Fig. 2

Fig. 2.
figure 2

(Source: Rely on engineering design documents)

Tunnel reinforcement scheme

Full size image

3.2 Tunnel Monitoring Program

In this paper, a total of 8 earth pressure cells are buried at the monitoring section, which are respectively buried at the vault, spandrel, side wall, arch foot and inverted arch center, and the supporting automatic acquisition system is used to collect data at 1 h intervals, please see Fig. 3 for details.

Fig. 3.
figure 3

(Source: Design documents and picture taken by the author)

Pictures of the tunnel monitoring site

Full size image

4 Numerical Simulation Under Water Ingress Conditions During the Operation Period of the Tunnel Bottom

4.1 Selection of Vehicle Loads and Pavement Loads

According to the design documents, the pavement load acting on the inverted arch is calculated by gravity of the surface course. In the design of underground structures, the vehicle load is often treated according to the uniform load, and the road design code is treated according to the concentrated force, and these two treatment methods can not well reflect the vibration effect of the vehicle load. In this paper, the dynamic load coefficient is introduced to convert the dynamic load into a quasi-static load [6], and it is found that the dynamic load coefficient of the vehicle reaches 0.1–0.4 in the many researches [7].

In the conventional vehicle moving dead load method, considering the high-frequency characteristics of the vehicle load, the vehicle load is simplified into a uniform load distributed along the road surface in a strip, the width is taken as the width of the standard contact surface b of the front wheel of the vehicle, and the value of b is not changed by the vehicle overload, and the length of action is taken as the length d of the vehicle, and the moving load is distributed on the two contact surfaces, and the calculation diagram is shown in Fig. 4. The vehicle moves the dead load \(\text{P}=\left(1+\upmu \right){\text{P}}_{0}\), \({\text{P}}_{0}\) is the load of the standard vehicle. The backing project is a highway-I. class. The vehicle gravity standard value is 550 kN, the left and right wheel tracks of the vehicle are 1.8 m, the wheelbase is 3 + 1.4 + 7 + 1.4 m, the front wheel landing length and width is 0.3 m × 0.2 m, the middle and rear wheel landing length and width are 0.6 m × 0.2 m, the vehicle dimensions are 15 m × 2.5 m, and the vehicle dynamic load coefficient is 0.4. The calculated vehicle load is 128 Kpa, taking into account the most unfavorable scenario, according to the two-lane arrangement.

Fig. 4.
figure 4

(Source: Technical standards for highway engineering)

Vehicle load layout (axle load unit: kN; Size unit: m)

Full size image

4.2 Parameter Selection of Inlet Layer at the Bottom of the Tunnel

Jian Tao et al. [8] analyzed the shear modulus of undisturbed loess with different moisture content under different confining pressures, and found that when the confining pressure is constant, the higher the moisture content, the smaller the shear modulus, and when the moisture content increases from 3% to 18%, the shear modulus decreases between 13%–60%. There are many scholars at home and abroad who have found the same law. In addition, a large number of experiments show that when the elastic modulus of loess is determined, its physical parameters have a clear value range, and the current physical parameters of loess have been obtained through experiments, and the attenuation degree of elastic modulus of 15%, 30%, 45% and 60% is used to reflect the degree of water inflow at the bottom of the tunnel.

4.3 Establishment of Finite Element Modeling

Basic Assumptions

The rock mass material is assumed to be homogeneous and isotropic, and the more applicable Drucker-Prager criterion is used for the constitutive relationship of rock and soil, which overcomes the Mohr-Coulomb criterion by considering the influence of the medium principal stress compared with the Moore-Coulomb criterion The main drawback of the Coulomb criterion. The shotcrete and micro anchor pipes in the supporting structure are regarded as linear elastic materials, and nonlinearity is not considered. The initial stress field of the rock mass only considers the self-weight stress, the effect of the grouting of the advanced small conduit is simulated by improving the physical parameters of the reinforcement layer, and the supporting effect of the steel arch and the reinforcement mesh is converted to the shotcrete, and the elastic modulus and gravity of the second-lined reinforcement mesh are also converted to the second-lined concrete.

Although the model based on the above assumptions is different from the actual situation, these assumptions have been verified by time, and it can effectively reflect the law of force and deformation, and it is convenient to operate, which is a powerful tool for scientific researchers.

Model Parameters

The parameters of the surrounding rock material and high pressure jet grouting pile are shown in Table 1.

Table 1. Material parameters
Full size table

Model Building

The three-dimensional model is established in strict accordance with the relying project, and the stratum is divided into two layers, the upper layer is a slightly dense loess layer with a depth of 0–20 m, and the lower layer is a medium-dense loess layer with a depth of more than 20 m, see Fig. 5. The normal stiffness modulus (\({\text{K}}_{\text{n}}\)) and shear stiffness modulus (\({\text{K}}_{\text{t}}\)) of the pile interface unit are automatically calculated by the software interface assistant, and the final shear force and pile end bearing capacity are related to the ultimate side friction resistance of the pile and the ultimate end resistance of the pile, according to the “Technical Code for Building Pile Foundation” JGJ94-2008 and considering the effect of the rotary grouting pile gourd-like pile body on the improvement of bearing capacity, the pile end spring stiffness can be taken according to the previous experience [9], and the specific parameters are shown in Table 2.

Table 2. 1D pile element parameters
Full size table
Fig. 5.
figure 5

(Source: The author built the model by himself)

3D FEM model

Full size image

5 Calculation Results and Analysis

In order to analyze the variation law of tunnel bottom stress and displacement with the construction stage, five transverse analysis points were selected at the monitoring section, which were located on the surrounding rock at the tunnel bottom below the “inverted arch initial lining-40” (longitudinal center section of the tunnel), and the analysis points were numbered from left to right as point C’ at the foot of the left wall, point B’ in the middle of the left half of the inverted arch, point A in the center of the tunnel, Point B in the middle of the right half of the inverted arch and point C at the foot of the right wall, see Fig. 6. Analysis points position.

Fig. 6.
figure 6

(Source: Author's drawing)

Analysis points position

Full size image

5.1 Analysis of Soil Displacement Between Piles

As can be seen from Fig. 7, the vertical settlement at the analysis point becomes larger and larger with the decrease of the elastic modulus of high pressure jet grouting pile. The vertical settlement of the analysis points on the left and right arch feet is close to linear growth, and the growth rate of the vertical settlement of the analysis points in the middle of the inverted arch and the left and right halves of the inverted arch (the slope of the vertical displacement connection line of the adjacent two working conditions) gradually decreases with the decrease of the elastic modulus of the inlet layer, because the vertical displacement at the analysis point of the surrounding rock of the inverted arch is an absolute displacement, which is the difference between the overall settlement of the structure at the inverted arch and the uplift of the inverted arch under the action of load.

When there is no high pressure jet grouting pile at the bottom of the tunnel, the vertical displacement at the analysis point when the elastic modulus is not attenuated under the load is larger than that when there is a jet grouting pile at the bottom of the tunnel. Until “E decreases by 15%”, the displacement growth rate at the analysis point is positive. After the “E decreases by 15%”, except for the left arch foot, the displacement growth rate of the rest of the positions turns negative, that is, the uplift begins to rise, and with the continuous decrease of the elastic modulus, the uplift growth rate decreases continuously (the absolute value gradually increases), because the elastic modulus of the inlet layer continues to decrease without the reinforcement of the jet grouting pile, and the ability to resist the uplift of the surrounding rock at the bottom of the tunnel is getting worse and worse. And because the buried depth at the left arch foot is much greater than that of other positions, the phenomenon of bulge only occurs after “E is reduced by 45%”.

It can be seen that the high pressure jet grouting pile is very important for the reinforcement of the tunnel base, which can effectively increase the ability to resist deformation after the water ingress at the tunnel bottom, and prevent the uplift phenomenon (relative displacement) caused by the softening of the surrounding rock at the tunnel bottom, and its most unfavorable position is at the center of the inverted arch.

Fig. 7.
figure 7

(Source: The author draws according to the calculation results of the model)

Displacement of tunnel basement with attenuation of elastic modulus of submerged layer

Full size image

5.2 On-Site Measurement and Analysis

The number and position of the earth pressure cell at the monitoring section are shown in Fig. 8 (Source: Author's drawing). Figure 9 (Source: The author draws according to monitoring results) shows the variation of earth pressure over time, due to the impact of the epidemic, it was not possible to inspect the equipment on site in time. After the earth pressure cell is buried for 4 h, the data acquisition equipment is powered off, and the data acquisition equipment is re-powered at 1080 h, but does not affect the overall distribution law of the radial earth pressure of the surrounding rock, in the 8 earth pressure cells, the data is not collected for 523955 damage, and 523960 is damaged at the 3283 h, but its data has been stabilized. The rest of the earth pressure cell data is normal, and its pattern is gradually increasing with time until it is stable. As can be seen from Table 3, the surrounding rock is mainly subjected to compressive stress, with the pressure at the arch foot being the largest, followed by the spandrel and the lowest pressure at the center of the inverted arch. Although there is a certain deviation between the measured values and the numerical simulation results, they are within a reasonable range, and the basic law of the distribution of surrounding rock and soil pressure is consistent, which shows that the calculation results are credible.

Fig. 8.
figure 8

Earth pressure cells arrangement

Full size image
Fig. 9.
figure 9

Earth pressure monitoring data

Full size image
Table 3. Radial pressure of the surrounding rock after the tunnel is completed
Full size table

6 Conclusion

After the high pressure jet grouting pile reinforces the tunnel bottom, the uplift phenomenon caused by the softening of the surrounding rock at the tunnel bottom can be effectively inhibited when the water enters the tunnel bottom during the operation period, so that the initial lining of the inverted arch is in a state of compression, and the monitoring results also prove that the model calculation results are reasonable.

It can be seen that the bottom of the tunnel reinforced by the high pressure jet grouting pile is different from the natural foundation, which not only has to resist the settlement of the inverted arch surrounding rock under the load, but also resists the uplift of the inverted arch surrounding rock when the tunnel bottom enters the water, and the pile body stress is very complex in this process, and it should be considered in the design, in addition, the drainage must be done in the tunnel maintenance.