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During the construction of the tunnel, there may be water-bearing anomalous structures such as fault fracture zone. In order to ensure the safety of the tunnel, it is necessary to carry out advanced tunnel detection. The traditional linear inversion method is highly dependent on the initial model in the tunnel resistivity inversion, which makes the inversion results falling into the local optimal optimum rather than the global one. Therefore, an inversion method for tunnel resistivity advanced detection based on ant colony algorithm is proposed in this paper. In order to improve the accuracy of tunnel advanced detection of deep anomalous bodies, an ant colony optimization (ACO) inversion is used by integrating depth weighting into the inversion function. At the same time, in view of the high efficiency and low cost of one-dimension inversion and the advantages of L1 norm in boundary characterization, a one-dimensional ant colony algorithm is adopted in this paper. In order to evaluate the performance of the algorithm, two sets of numerical simulations were carried out. Finally, the application of the actual tunnel water-bearing anomalous structure was carried out in a real example to evaluate the application effect, and it was verified by excavation exposure.

Geophysical inversion is an effective method to find a model with a response similar to the actual measured values. All inversion methods are essential to determine the underground model whose response is consistent with the measured data within certain restrictions and acceptable limits [

In particular, great progress has been made in non linear inversion methods in the field of tunnel detection. For example, Nguyen et al. [

Ant colony optimization was introduced in the early 1990s by Marco Dorigo and colleagues [

The common approach in the regularization optimization method is the smoothness-constrained or L2 norm method [

The rest of the article is arranged as follows. We first briefly introduce the ACO inversion with L1 norm or L2 norm. We also describe the procedures for ACO inversion in advanced tunnel detection. We illustrate the effectiveness of this inversion method by applying it to synthetic examples and field survey in a tunnel environment. The field data were collected from the water conveyance project from Songhua River in the middle of Jilin province.

The ant colony algorithm is a method that ants find the shortest path from their nest to a food source. The core of this behavior is the indirect communication between ants through chemical pheromone trails. When the ants are looking for food, they will initially explore the area around the nest in a random manner. During exploring, ants will leave chemical pheromone on the ground. Once an ant finds a food source, it evaluates the quantity and quality of the food and brings some back to the nest. The amount of pheromones ants left on the ground during the return depends on the quantity and quality of food. Pheromone will guide other ants to find a food source [

The objective function of resistivity inversion based on the

As the electrode spacing increases, the sensitivity of the observed data to the deep also increases. The data weighting factor is introduced into the inversion problem to increase the weight of effective observed data. Therefore, the objective function of the ACO algorithm based on the L1 norm is expressed as follows [

The probability of ants transferring from one cell to another is determined by pheromone intensity and visibility. The transition probability is expressed as follows [

At the beginning,

To solve the problem of normal L1 norm inversion, the main methods include the iterative shrinkage thresholding/shaping method [

First, the 3D induced polarization method was used for forward modeling of advanced detection in tunnel [

Schematic diagram for induced polarization advanced prediction in the tunnel. The position of electrodes B and N are at a remote distance from tunnel face.

For 3D resistivity forward tunnel modeling problems, the finite element method is used in this paper. In particular, as for the model grid division, the inversion area in front of the tunnel is divided into 10 layers, and each layer is 3 m.

Finally, the ACO algorithm for inversion is used, and the process is as follows:

Initializing the parameters: input number of a group ant, upper limits of iteration, and other parameters.

Ants choose paths based on the transition probability

Calculate objective function value

Update pheromone intensity _{i}, the final result will be outputted.

To illustrate the efficiency of the ACO algorithm based on the L1 norm in the 1D layered stratum inversion of the tunnel, the algorithm was tested using two synthetic examples to simulate the water-bearing fault.

The first model example is shown in Figure _{0} and _{0} are both 1 in the L1 norm and 1.8 and 1 in the L2 norm, respectively. An anomalous layer is located 12 m ahead of the tunnel face, and its thickness is 3 m. The background resistivity of the model is 1000 Ωm, and the anomalous layer with a resistivity of 400 Ωm.

Inversion results for two models with low resistivity. (a) True resistivity of model 1. The results obtained after inversion of model 1 are shown in (b) using L1 norm and (c) using L2 norm. (d) Sketch of model 2. The results obtained after inversion of model 2 are shown in (e) using L1 norm and (f) using L2 norm. The black dotted frame represents the actual location of the low resistivity layer set by the model.

Figures

The second model consists of one anomalous layer with a low resistivity value (400 Ωm), which is located at 21 m along

From the two numerical simulations, the inversion results show that the L1 norm is more effective than the L2 norm in reflecting the position and resistivity of the low resistivity layer ahead of the tunnel face. These results will be verified in the field data.

To examine the efficiency of the inversion algorithm on the tunnel detection, we inverted 1D resistivity data from the water conveyance project from Songhua River in the middle of Jilin province. The No.4 contract section of the main line construction is located between the Chalu River and Yinma River sections in Jilin City, the survey area at the tunnel mileage of 64 + 728 – 64 + 698 m. According to the geological reconnaissance, the surrounding rock in this section is mainly limestone, and the integrity of the rock mass is poor. Moreover, this section is with the scope of the fault.

We adopted the induced polarization method proposed by Li et al. [

Inversion results for field data. (a) L1 norm inversion imaging. (b) L2 norm inversion imaging. The black dotted frame represents the low resistivity anomalous body.

According to the tunneling exposures shown in Figure ^{3} per hour at 64 + 727. The excavation result is consistent with the result obtained by L1 norm inversion. On the whole, the ACO inversion algorithm based on the L1 norm could better estimate the low resistivity anomalous bodies than the L2 norm.

The complete section projection drawing of the geologic sketch and the excavation mileage is from 64 + 728 m to 64 + 698 m.

The excavation results at 64 + 727.

In this paper, an ACO algorithm based on the L1 norm is proposed for advanced tunnel detection. The key component of this approach is using the 3D induced polarization method to collect and process the data in the forward modeling. The inversion adopts the data weighting L1 norm ACO, which can increase the weight of effective data in the deep, so as to locate the deep anomalous bodies.

The proposed method provides an ACO algorithm using the L1 norm for tunnel advance detection. Compared to the L2 norm method, the developed method produces a better effect in identifying the sharp boundary of low resistivity anomalous bodies.

The developed method was tested using the two low resistivity models to simulate the water-bearing fault, and the 1D distribution of low resistivity body can be recovered by this inversion method. The method was applied to the field detection of the water conveyance project from Songhua River in the middle of Jilin province, which was verified through tunnel excavation.

The data used to support the findings of the study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by the Science & Technology Program of Department of Transport of Shandong Province under Grant no. 2019B47_2.