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The Research on Tunnel Surrounding Rock Classification Based on Geological Radar and Probability Theory

In order to effectively classify the surrounding rock types of tunnels, a multi-factor tunnel surrounding rock classification method based on GPR and probability theory is proposed. Geological radar was used to identify the geology of the surrounding rock in front of the face and to evaluate the quality of the rock face. According to the previous survey data, the rock uniaxial compressive strength, integrity index, fissure and groundwater were selected for classification. The related theories combine them into a multi-factor classification method, and divide the surrounding rocks according to the great probability. Using this method to classify the surrounding rock of the Ma’anshan tunnel, the surrounding rock types obtained are basically the same as those of the actual surrounding rock, which proves that this method is a simple, efficient and practical rock classification method, which can be used for tunnel construction.


Introduction
Different geological conditions have some connection with the stability of surrounding rock. The different stability (fully stable, basically stable, temporarily stable, unstable, etc.) correspond to the grade of surrounding rock. There are many geological factors that affect the grading of surrounding rock, such as stratigraphic lithology, rock mass structure, structural fracture, elegance status, integrity, groundwater, etc. Not only are the factors independent of each other, but also the quality of the surrounding rock and the various factors are highly nonlinear relationship. Therefore, how to select independent factors and reasonable evaluation methods is a challenge faced by geoengineering workers. Many new methods have been introduced into the classification of surrounding rocks (Zhang Lewen, 2011;Fu Zhengfei, 2006;Wang Huafeng, 2016) At present, the classification method of tunnel surrounding rock mainly comes from various industry norms. Generally speaking, there are single factor method and multi-factor method. The single factor method refers to the grading of the surrounding rock by means of a single comprehensive index, which is related to the development of survey technology, and its adaptability is not too high. The multi-factor method has strict requirements for the selection and combination of indexes and is relatively complicated. In traditional engineering, according to the specification, the surrounding rock mass of the tunnel is geologically graded to measure the rock mass strength Rc, the rock mass integrity coefficient Kv, the state of the structural plane and the basic mass index BQ of the surrounding rock According to the rock strength Rc and rock mass integrity coefficient Kv obtained from the previous survey data and combined with the geologic radar electromagnetic wave method used in construction, the development of the fractures, structural planes and groundwater of the surrounding rock in front of the working face is graded. And then using the theory of probability to get a new method of surrounding rock classification, and this method is applied to the Ma An Shan tunnel.

The Role of Geological Radar in Prediction
The advanced geological forecast of the tunnel refers to the combination of the various signals and waveform features reflected by the geophysical technology during the tunnel excavation and the disclosed geological phenomena to make the forward prediction of the surrounding rock of the working face. On the basis of previous surveys, the influence of the tunnel scale, structure type and construction method on the surrounding rock, we can further ascertain the geological conditions in a certain section ahead of the working face.
Ground penetrating radar (GPR), as a detection method of advanced geological forecasting of tunnels, has very high accuracy and can identify the basic engineering geological problems of rock and soil within a certain range around and in front of the working face, such as discontinuous interface, broken zone, caverns and filling conditions can affect the safe construction of the tunnel (Xu Jia, 2008;Pawlak Z, 2002).
In the tunneling project, the development of fractures, faults and groundwater in front of the rock face plays an important role in the stability of the surrounding rock. By analyzing the image of the geological radar, according to the structure plane, the degree of fracture development, groundwater content, we can grade the surrounding rock, grading and classification is shown in Table 1:

3.1.The expression of the value
According to the theory of probability theory, if event A and event B are mutually exclusive events, the probability that at least one event A and event B occur must be the sum of the two probabilities, and the probability of the two occurring separately is two separately The product of probability, that is, (Huang Kun, 2005).
Further more, for such linear continuous variables that may appear, the mathematical expectation in this interval is its average value, that is, In the formula, a and b are the values of the two endpoints in a section respectively. Assuming that any one signal value represents a random event, the classification level of the surrounding rock is used as an interval segment. To determine which interval the signal is most likely to appear in (corresponding to which level), it is necessary to calculate and compare the probability that it appears at each level . The level of maximum probability appears is the surrounding rock level at which the numerical signal is located.
Where, L is the total length of the segment, L = | d-a |, E is the expected number.

3.2.Surrounding rock classification with single factor
Taking the rock uniaxial uniaxial compressive strength Rc as an example, when Rc is used as a singlefactor index to classify the surrounding rock, the range of Rc is: Class I is very hard rock range (60,120 MPa), the expected number is 90 MPa, Class II is hard rock range (30,60) MPa, the expected number is 45 MPa, III is soft rock range (15, according to the principle of probability theory, according to Eq. (2), the probability that the surrounding rock will obtain the final result in these three kinds of classification is the product of the probability of pre-evaluating the surrounding rock in each classification. The upper limit of saturated uniaxial compressive strength of rock is 120 Mpa and the lower limit is 0. The upper limit of integrity index Kv is 1 and the lower limit is 0. The upper limit of crack and groundwater W is 1 and the lower limit is 0, According to the formula (4), respectively, the expected value of each level, see Table 4.
According to the principle of probability theory, the rock mass of each kind of tunnel under the influence of three kinds of factors, the probability calculation method belonging to a surrounding rock type is shown in Eqs. (6) According to the theory of probability theory, among the many independent events, the event with the highest probability is most likely to occur. Therefore, by calculating the probability of the surrounding rock type, it can be determined that the type with the highest probability is the most probable surrounding rock type of the rock to be determined, that is, the most probable rock mass is max {PⅠ, PⅡ, PⅢ, PⅣ , PV} corresponding to the rock category. Based on the rock hardness and rock mass integrity, and groundwater and initial stress is used to amendment.
Ⅰ-Ⅳ (good-bad) 5 《Standard for engineering classification of rock masses》 《Code for investigation of geotechnical engineering》 The basic mass index of rock mass is BQ.And groundwater, weak structural surface and initial stress is used to correction Ⅰ-Ⅴ (good-bad)

Engineering Applications
We take 4 sections of the Ma An Shan tunnel for example. The uniaxial compressive strength Rc of rock mass and the representative wave velocity of each surrounding rocks are gotten from the rock samples tested by drilling sampling. Comprehensive determination of the core to take, can get the integrity coefficient Kv. Based on the result of GPR, the structural surface state and groundwater condition of the surrounding rock of the target section can be gotten. Take section 1 as an example, the image of the GPR is shown in Figure 1. Fig.1 Geological radar image of hole 1# The results of the previous survey show that the No. 1 section is the weathered dolomitic limestone, the rock mass is relatively broken and the integrity is better. The uniaxial compressive strength Rc is 27.19 and the integrity coefficient Kv is 0.15. In some regions of the GPR images, the amplitudes significantly increase and vary greatly, the energy clusters are unevenly distributed, the waveforms are disorderly distributed, the events of the faults are intricate, and even the images are blurred in the deep areas. Combined with the geology of the face, the forward joints Fissures are more developed, weathered heavily, the rock is more broken, score 0.3.
The four sections of the index value of the statistics shown in Table 5  The above parameters substitute into the formula (6) ~ (10), respectively, calculate the probability of the corresponding category, the results shown in Table 6 to Table 9. Table 6 The grading results are shown in Table 10. The probability of wall rock of No. 2 section in grade III is 0.636253 and the grade of grade is 0.623625, which is close to each other, indicating that the surrounding rock of this section is between the two and the actual excavation result also proves This point; the basic quality of rock mass in section 4 is better, but because of the presence of more fractures in front of the geologic radar response, the comprehensive evaluation result is level II, which is consistent with the actual results.
The evaluation results in Table 10 show that the evaluation results of the surrounding rock grade of this model are basically consistent with the actual situation. Therefore, it is feasible to apply this method to the stability evaluation of the surrounding rock of the tunnel.

Conclusion
(1) In the process of investigation, due to the restriction of practical conditions, the classification of surrounding rock of tunnel may not be so accurate. With the use of geological radar in the construction of the front of the working face, we can know the rock fractures and groundwater conditions, and evaluat it. This is operable.
(2) Three indexes of rock mass saturated uniaxial compressive strength, integrity coefficient and development of fissure groundwater are selected. The probabilistic method is used to evaluate the three indexes comprehensively. The evaluation results are in good agreement with the actual ones, which shows that the method is practicable and provides a new idea for the stability evaluation of the surrounding rock of the tunnel. It has played a good guiding role in the construction.