# Evaluation of the Engineering Geology Practice Route Based on Multifactor Reliability Analysis

Authors: Xiaoming Zhao; Binbin Yang; Dongqi Tang
Journal: Geofluids
 (2022)

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## Abstract

Engineering geological practice and investigation are important measures for geological fluid and engineering geological research; the practice route has an important impact on the achievement of research objectives. In this study, the practice route is mainly affected by four primary indicators: abundance of geological resources, rationality of the practice route, effect of practice, and the accommodation conditions. The four primary indicators include 13 secondary indicators, and each secondary indicator can be divided into positive and negative random variables, which is the specific content of the evaluation. In order to collect the feedback data of participants on the practice route, a questionnaire was constructed based on indicators at all levels. According to the results of the questionnaire, the mean and standard deviation of each random variable are counted and the distribution law of probability density is fitted. A performance function is constructed to represent the approval status of participants for each indicator. Considering the influence of 26 random variables, a multifactor evaluation method for the engineering geology practice route is proposed based on the reliability analysis method. This method can be used to analyze the approval status of random factors, search for the shortcomings of the route, and provide an effective method to improve the rationality of the route. The conclusion shows that this study provides a solution to evaluate fuzzy problems in engineering geological practice, especially if the problems are difficult to be quantified through experiment or measurement.


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## Body

## 1. Introduction

Geology is a natural science that studies the earth and its evolution. It is a knowledge system about the material composition, internal structure, external characteristics, interaction between spheres, and evolution history of the earth. Engineering geology is a branch of geology, which studies the interaction between human engineering activities and geological environment. Engineering geology practice is an effective way to understand engineering geological conditions and engineering geological problems. It is the prerequisite for scientific and reasonable engineering geological survey and lays a foundation for discovering and preventing adverse geological phenomena. During the practice, some field geological phenomena are understood through direct observation, which not only increases the trainees’ perceptual knowledge of geological phenomena, expands their vision, and cultivates the ability to recognize the essence of things through phenomena but also improves their observation and hands-on ability.In order to achieve the best practice effect, it is necessary to evaluate the practice route scientifically, find out the shortcomings, and improve the rationality of the route continuously. There are two kinds of methods for making decisions or evaluating the reliability of a structure: theoretical approximate analysis and numerical calculation. In theoretical analysis, the performance function is constructed to express the relationship between different factors or the influencing factors are divided into multilevel indicators for research. A simple method is presented for a second-order structural reliability approximation by Kiureghian et al. The method is based on an approximating paraboloid which is fitted to the limit state surface at discrete points around the point with minimal distance from the origin. An expression for the second-order error in the approximation is derived, and the error is shown to be small, even for large dimensions and dispersed curvatures. In comparison to the existing approximation method, the proposed method is simpler and requires less computation. It is insensitive to noise in the limit state surface, approximately accounts for higher-order effects, and facilitates the use of an existing formula for the probability content of parabolic sets [1]. The response-surface approach can be used for the analysis of structural and mechanical systems whose geometrical and material properties have spatial random variability. The method utilizes a polynomial expansion of the numerical nonlinear structural operator, the polynomial form is then modified by suitable error factors, and each error factor is due to the deviations of the single property from its spatial average in the different finite elements [2]. An approximate method for solving the structural reliability of uncertain systems is developed by combining the response surface method with the fast integration method. This method is especially suitable for the sensitivity analysis of the failure probability of uncertain systems under the influence of the parameter distribution law [3]. A simple approximate method is used to improve the second-order reliability analysis, which improves the calculation efficiency and maintains the calculation accuracy [4]. The response surface method is further utilized to investigate physicochemical multifactor coupling effects on UHPC crack resistance. Based on the obtained results, it shows that using low cement content, adding steel fibers and adding expansive agent all can effectively improve crack resistance of UHPC [5]. The analytic hierarchy process decomposes decision-making problems into different hierarchical structures according to the order of general objectives, subobjectives of each level, evaluation criteria, and specific alternatives. Then, the priority weight of each element of each level to an element of the upper level is obtained by solving the eigenvector of the judgment matrix; finally, the weighted sum method is used to merge the final weight of each alternative scheme to the overall goal and the best scheme is the one with the largest final weight [6, 7].The analytic hierarchy process is suitable for decision-making problems with hierarchical and staggered evaluation indexes, and the target value is difficult to describe quantitatively. Analytic hierarchy process is also widely used in decision-making in architecture, mathematics, medicine, management, education, and other disciplines to help managers make the most scientific decisions [8–14]. The role of the analytic hierarchy process is to select the better from of the alternatives. When applying analytic hierarchy process, there may be a situation that our own creativity is not enough, resulting in that although we choose the best of many schemes that we think of, the effect is still not good enough for the enterprise. For most decision makers, if an analysis tool can analyze the best one in my known scheme for me, then, point out the shortcomings of the known scheme or even put forward the improvement scheme; such an analysis tool is more perfect. But obviously, the analytic hierarchy process has not been able to do this. The regression model [15, 16], maximum entropy model [17, 18], ant colony theory [19], factor space theory [20–22], and other theories or models are not suitable to evaluate the engineering geological practice route due to their own characteristics.The improved center point method is suitable for solving the structural reliability index when the probability density function of random variables is arbitrary distribution. This method is called the JC method because it was adopted by the International Joint Committee on Structural Safety (JCSS) established in 1970; Rackwitz and Flessler [23] developed an improved checking point method to solve the structural reliability under complex loads. In this method, various loads in the system are regarded as independent random variables and the distribution law of probability density function of random variables can be considered. Hasofer and Lind [24] improved the solution process of the JC method in 1974. In order to simplify the equation form in actual calculation, the assumption of small variance is approximately introduced. For different problems, the algebraic expression and physical mechanism of failure criterion are different. When using the improved solution method, the formula form in the solution process is fixed, which brings great convenience to solve different types of problems. The principles of correct modeling and analysis for solving uncertain problems, as well as the influencing factors related to safety and design, are proposed. Under the condition of uncertainty, the safety of the structure can only be ensured according to or failure probability. Therefore, the security level is explicitly expressed as a function of uncertainty [25]. The Monte Carlo method and importance sampling method are commonly used numerical calculation methods for system decision-making or evaluation. As a special technique of Monte Carlo probability integration, importance sampling has been proved to be an efficient and unrestricted method. An alternative method is proposed to guide and correct the important sampling function. It is relatively easy to deal with random variables which is the Gaussian uncorrelation and nonlinear limit functions and has a reasonable convergence speed [26]. Dey and Mahadevan [27] proposed an adaptive importance sampling method for estimating the reliability of time-varying systems of brittle structures. This method eliminates the idealized simplified hypothesis in the early research, is convenient to add the reliability analysis module to the structural analysis, and provides a fast and accurate estimation of failure probability.Several routes with rich typical geological phenomena were selected for engineering geological practice in Dengfeng city. The purpose of practice is to understand the engineering geological characteristics of rock strata in this area, including the occurrence of rock strata, the types of folds, the properties, distribution and development of faults and joints, the development conditions and laws of landslide and collapse, and their impact on engineering construction [28, 29]. The selection of the engineering geology practice route is very important, which should at least meet the following conditions: understand enough typical engineering geological phenomena, ensure the safety and timeliness of practice, meet the practice requirements, and have sufficient rest and health. The combination of the questionnaire and reliability analysis is used to evaluate the practice route, search for the shortcomings of the route, and provide an intuitive and effective technical technique to improve the rationality of the route.


## 2. Engineering Geology Practice Route

There are 5 routes for engineering geology practice; we choose the Junji peak route for evaluation, which is the longest and most difficult route. Figure1 shows the location of the Junji peak route, which is composed of route ABCDE. Route ABC is an urban road, route CD is a mountain road with a certain slope, and route DE is composed of climbing steps. The total length of the route is about 20 km, and the elevation difference is about 900 m, and it takes 13 hours to complete this practice route by walking.Figure 1
Location of the Junji peak practice route.Site A is the Zhongyue Hotel, where the students start their practice in the morning and have rest in the evening. Site B is a famous tourist attraction called Qimuque, which was built in memory of Qi’s mother. A large-scale geological disaster occurred more than 4000 years ago, and the falling stones are called Qimu stones. Therefore, the geological disaster has a historical and cultural background. Here, the students observe the collapse, learn the geological causes of the collapse, and use the compass to measure the occurrence of the rock stratum. Collapse is the phenomenon that the rock mass on the steep slope suddenly breaks away from the parent body and rolls downward under the action of gravity. Site C is a small village called Fanjiazhuang village at the foot of Songshan Mountain, where a geological phenomenon alluvial fan is developed. Here, students learn about the causes of the alluvial fan, material composition, and the impact of the alluvial fan on the engineering. We started to climb the mountain from site C to site D which followed the path in the mountain village. Site D is called Xianyou Bridge, where geological phenomenon rock walls are developed. Students learn about the formation conditions and morphological characteristics of rock walls here. Site E is located on the hillside of Songshan Mountain, where the world-famous Songyang movement in geological history is developed. Here, students learn the time, process, and characteristics of the formation of Songyang movement, as well as the formation process and structure of sedimentary rocks and metamorphic rocks. After learning the Songyang movement, the students returned to Zhongyue Hotel at site A. Usually, the practice starts from point A at 7:00 a.m. and returns at 20:30. Due to the huge amount of activities, the students need enough supplement, while there are few shops in the mountains. They need to carry enough water and food in their backpacks for a day, which increases the burden on the students.


## 3. Multifactor Evaluation Method Based on Reliability Theory

### 3.1. Reliability Theory

Reliability refers to the ability of a system or structure composed of many factors to play a preset role and complete a predetermined function within a specified time and under specified conditions. It includes the evaluation of structural safety, applicability, and durability. When this ability is measured by probability, it is called reliability. For a system with positive factorR, the sum of external load or negative factors is S, assuming that its safety factor F can be expressed as equation (1):
(1)F=R−S.Obviously, as long asR>S is satisfied, that is, the resistance of the structure itself is greater than the total load, the safety of the structure can be guaranteed. However, in practice, if the safety factor F is greater than 0, the structure will still be damaged. The reason for this phenomenon is that when analyzing the stability of the structure, the resistance and load are known or calculated and they are determined values. In this case, the safety factor f obtained is the solution of the deterministic method, which ignores many randomness of the structure in practice. While considering the randomness of the structure, in order to facilitate calculation, statistics such as mean and standard deviation are often used to express its randomness.Assuming that its probability density function obeys the Gaussian distribution, as shown in Figure2, if the deterministic method is used to analyze the reliability of the structure, the means of random variables R and S are μR and μS, respectively, and the structural safety factor can be expressed as equation (1). Obviously, the safety factor is greater than 0, and the structure is safe in this case. However, when random variables are distributed in the overlapping interval of probability density function fR and fS, the situation of R<S generally exists, the safety factor f<0, and the structure has serious instability risk and is unsafe.Figure 2
Probability density function of structural resistanceR and total load S.


### 3.2. JC Method for Evaluating System Reliability

The JC method can be used to solve the reliability of the system under the action of multiple random variables. The basic principle is that the system random variablex obeying any probability density function is transformed into the random variable y obeying normal distribution through normal transformation and the calculation space is also transformed from the X space to the Y space. When the equivalent normalization method is used for normal transformation, equation (2) shall be satisfied.
(2)fXxi∗=fYxi∗,FXxi∗=FYxi∗,where fX is the original probability density function value, fY is the equivalent normal distribution probability density function value, FX is the original probability distribution function value, and FY is the equivalent normal function probability distribution function value. Suppose that X1∗,X2∗,⋯,Xn∗ are n-independent random variables affecting system reliability, with a mean value of μ and standard deviation of ν.DefineS as the checking point, expand the performance function into Taylor series at checking point S, and retain the first-order term. At this time, the performance function Z can be expressed as equation (3):
(3)Z≈gX1∗,X2∗,⋯,Xn∗+∑i=1n∂g∂Xi∗S=S∗Xi−Xi∗=0.Set random variableY as shown in equation (4).
(4)Yi=Xi−μXiσXi,Xi~N0,1,i=1,2,⋯,n.Then, the random variable is transformed from theX space to the Y space and the original verification point S is transformed into a new verification point S∗. In this case, the performance function Z′ can be expressed as equation (5).
(5)Z′≈fY1∗,Y2∗,⋯,Yn∗+∑i=1n∂f∂YiS=S∗Yi−Yi∗=0.The mathematical expectation and variance of the performance functionZ′ can be expressed as equation (6).
(6)EZ′=∑i=1n∂f∂YiS=S∗EYi−Yi∗,σZ′=∑i=1n∂f∂YiS=S∗2.Considering that the random variableY follows the standard normal distribution, the system reliability index β can be expressed as equation (7):
(7)β=∑i=1n∂f/∂YiS=S∗EYi−Yi∗∑i=1n∂f/∂YiS=S∗2=−∑i=1n∂f/∂YiS=S∗Yi∗∑i=1n∂f/∂YiS=S∗2.Then, the directional cosine of each random variable can be expressed as equation (8):
(8)cosθYi∗=−∑i=1n∂f/∂YiS=S∗∑i=1n∂f/∂YiS=S∗2.Equation (9) can be obtained by substituting (8) into equation (7).
(9)β=∑i=1ncosθYi∗Yi∗,∑i=1ncos2θYi∗=1.Using equation (10), the random variable can be converted from the Y space to the X space.
(10)Xi=μXi+cosθYi∗⋅β⋅σXi.At this time, the directional cosine of the random variable can be expressed as a function of the random variable in theX space, as shown in equation (11).
(11)cosθYi∗=−∑i=1n∂g/∂XiS=S∗σXi∑i=1n∂g/∂XiS=S∗σXi2.Obviously, for the check points, equation (12) is satisfied.
(12)gX1∗,X2∗,⋯,Xn∗=0.Through the iterative operation of equations (10)–(12), multiple system reliability indexes β can be obtained. When the difference between the β values obtained in the last two iterations meets the condition of equation (13), the calculation converges and the iteration ends.
(13)Δβ=βn−βn−1≤ε,where ε is a sufficiently small value given according to the accuracy requirements, and then, the failure probability Pf is calculated, as shown in equation (14):
(14)Pf=1−Φβn.The calculation process of system failure probability is shown in Figure3.Figure 3
Flow chart of system failure assessment.


## 3.1. Reliability Theory

Reliability refers to the ability of a system or structure composed of many factors to play a preset role and complete a predetermined function within a specified time and under specified conditions. It includes the evaluation of structural safety, applicability, and durability. When this ability is measured by probability, it is called reliability. For a system with positive factorR, the sum of external load or negative factors is S, assuming that its safety factor F can be expressed as equation (1):
(1)F=R−S.Obviously, as long asR>S is satisfied, that is, the resistance of the structure itself is greater than the total load, the safety of the structure can be guaranteed. However, in practice, if the safety factor F is greater than 0, the structure will still be damaged. The reason for this phenomenon is that when analyzing the stability of the structure, the resistance and load are known or calculated and they are determined values. In this case, the safety factor f obtained is the solution of the deterministic method, which ignores many randomness of the structure in practice. While considering the randomness of the structure, in order to facilitate calculation, statistics such as mean and standard deviation are often used to express its randomness.Assuming that its probability density function obeys the Gaussian distribution, as shown in Figure2, if the deterministic method is used to analyze the reliability of the structure, the means of random variables R and S are μR and μS, respectively, and the structural safety factor can be expressed as equation (1). Obviously, the safety factor is greater than 0, and the structure is safe in this case. However, when random variables are distributed in the overlapping interval of probability density function fR and fS, the situation of R<S generally exists, the safety factor f<0, and the structure has serious instability risk and is unsafe.Figure 2
Probability density function of structural resistanceR and total load S.


## 3.2. JC Method for Evaluating System Reliability

The JC method can be used to solve the reliability of the system under the action of multiple random variables. The basic principle is that the system random variablex obeying any probability density function is transformed into the random variable y obeying normal distribution through normal transformation and the calculation space is also transformed from the X space to the Y space. When the equivalent normalization method is used for normal transformation, equation (2) shall be satisfied.
(2)fXxi∗=fYxi∗,FXxi∗=FYxi∗,where fX is the original probability density function value, fY is the equivalent normal distribution probability density function value, FX is the original probability distribution function value, and FY is the equivalent normal function probability distribution function value. Suppose that X1∗,X2∗,⋯,Xn∗ are n-independent random variables affecting system reliability, with a mean value of μ and standard deviation of ν.DefineS as the checking point, expand the performance function into Taylor series at checking point S, and retain the first-order term. At this time, the performance function Z can be expressed as equation (3):
(3)Z≈gX1∗,X2∗,⋯,Xn∗+∑i=1n∂g∂Xi∗S=S∗Xi−Xi∗=0.Set random variableY as shown in equation (4).
(4)Yi=Xi−μXiσXi,Xi~N0,1,i=1,2,⋯,n.Then, the random variable is transformed from theX space to the Y space and the original verification point S is transformed into a new verification point S∗. In this case, the performance function Z′ can be expressed as equation (5).
(5)Z′≈fY1∗,Y2∗,⋯,Yn∗+∑i=1n∂f∂YiS=S∗Yi−Yi∗=0.The mathematical expectation and variance of the performance functionZ′ can be expressed as equation (6).
(6)EZ′=∑i=1n∂f∂YiS=S∗EYi−Yi∗,σZ′=∑i=1n∂f∂YiS=S∗2.Considering that the random variableY follows the standard normal distribution, the system reliability index β can be expressed as equation (7):
(7)β=∑i=1n∂f/∂YiS=S∗EYi−Yi∗∑i=1n∂f/∂YiS=S∗2=−∑i=1n∂f/∂YiS=S∗Yi∗∑i=1n∂f/∂YiS=S∗2.Then, the directional cosine of each random variable can be expressed as equation (8):
(8)cosθYi∗=−∑i=1n∂f/∂YiS=S∗∑i=1n∂f/∂YiS=S∗2.Equation (9) can be obtained by substituting (8) into equation (7).
(9)β=∑i=1ncosθYi∗Yi∗,∑i=1ncos2θYi∗=1.Using equation (10), the random variable can be converted from the Y space to the X space.
(10)Xi=μXi+cosθYi∗⋅β⋅σXi.At this time, the directional cosine of the random variable can be expressed as a function of the random variable in theX space, as shown in equation (11).
(11)cosθYi∗=−∑i=1n∂g/∂XiS=S∗σXi∑i=1n∂g/∂XiS=S∗σXi2.Obviously, for the check points, equation (12) is satisfied.
(12)gX1∗,X2∗,⋯,Xn∗=0.Through the iterative operation of equations (10)–(12), multiple system reliability indexes β can be obtained. When the difference between the β values obtained in the last two iterations meets the condition of equation (13), the calculation converges and the iteration ends.
(13)Δβ=βn−βn−1≤ε,where ε is a sufficiently small value given according to the accuracy requirements, and then, the failure probability Pf is calculated, as shown in equation (14):
(14)Pf=1−Φβn.The calculation process of system failure probability is shown in Figure3.Figure 3
Flow chart of system failure assessment.


## 4. Case Study

### 4.1. Random Variables in the Questionnaire

In this study, four primary indicators that have a significant impact on the engineering geological practice route are selected to form the content of the questionnaire. Table1 lists the main contents of the questionnaire, in which the four primary indicators include 13 secondary indicators and each secondary indicator can be divided into positive (R) and negative (S) variables. Participants can give positive or negative comments on each secondary indicators.Table 1
The main contents of the questionnaire for evaluating engineering geological practice route.
Primary indicatorsSecondary indicatorsAbundance of geological resources1. Development of the typical geological phenomena:R1: developed; S1: undeveloped2. Correlation of the geological phenomena:R2: correlated; S2: uncorrelated3. Ornamental of the geological phenomena:R3: ornamental; S3: not ornamental4. Cultural of the geological phenomena:R4: cultural background; S4: no cultural backgroundRationality of the engineering geology practice route5. Safety of the practice route:R5: safe; S5: unsafe6. Traffic condition of the practice route:R6: convenient; S6: inconvenient7. Physical fatigue during practice:R7: normal; S7: fatigue8. The difficulty of practice supply:R8: normal; S8: difficultEffect of engineering geology practice9. Understanding of the practice content:R9: understand; S9: confuse10. Ability of identifying geological hazards scientifically:R10: capable; S10: incapable11. Ability of completing practice report independently:R11: capable; S11: incapable12. The basic survival skills in the wild:R12: capable; S12: incapableAccommodation conditions13. Accommodation conditions:R13: good; S13: poorFor example, the abundance of geological resources includes the development, correlation, ornamental, and cultural evaluation of the typical geological phenomena. The positive part (R2) of correlation of the geological phenomena is that geological phenomena are interrelated and the negative variable (S2) is that there is no correlation between different geological phenomena. Therefore, in general, the evaluation of the engineering geological practice route is affected by 26 random variables.In order to obtain effective evaluation data, a questionnaire was conducted in all the students participating in engineering geology practice and students can evaluate the value of each random variable according to their practice. A total of 194 valid questionnaires were received in this survey, and the distribution law and mean and standard deviation of each random variable were obtained through statistical analysis.Table2 lists the mean and standard deviation of 26 random variables, in which R1–R13 are positive random variables and S1–S13 are negative random variables. The mean value represents the students’ overall evaluation of the practice content, and the standard deviation reflects the dispersion degree of the evaluation value. According to the scores of all participants on the random variable R1, the mean value is obtained, which represents that the overall cognition of participants on R1 is 61.26 and the standard deviation is 4.89, which shows that almost all students’ evaluation of R1 is not discrete and tends to be consistent. The mean of random variable S11 is 18.62 and the standard deviation is 12.21, indicating that the overall evaluation of S1 by participants is 18.62; however, there is a large cognitive deviation among different individuals. Some participants evaluate S11 much higher than 18.62, while some participants believe that the random variable S11 is far less than 18.62.Table 2
Mean and standard deviation of random variables in the questionnaire.
Positive random variableNegative random variableRi (i = 1, 13)MeanStandard deviationSi (i = 1, 13)MeanStandard deviationR161.264.89S139.798.47R260.269.38S240.9311.86R373.8210.28S327.7212.27R453.1414.75S443.5616.73R579.9812.55S518.4210.55R667.2015.63S633.7916.17R775.7613.74S724.4313.96R874.019.18S826.119.32R982.049.99S918.9313.78R1067.6111.41S1034.6612.73R1181.2611.42S1118.6212.21R1258.0817.07S1243.8117.94R1327.4512.02S1372.9311.67Figure4 shows the frequency distribution of 8 random variables contained in abundance of geological resources; it can be seen that the probability density functions of random variables R1–R4 and S1–S3 approximately obey the Gaussian distribution and the probability density functions of S4 approximately obey the lognormal distribution. Based on the above analysis, the performance function of geological resource abundance can be expressed as equation (15).
(15)g1R,S=∑i=14Ri−Si.Figure 4
Probability density distribution of the random variables in abundance of geological resources (R1–R4, S1–S4).Figure5 shows the frequency distribution of 8 random variables contained in the rationality of the engineering geology practice route. It can be seen that the probability density functions of random variables R5, R8, S5, and S8 approximately obey the Gaussian distribution and the probability density functions of R6, R6, S7, and S7 approximately obey the lognormal distribution. Based on the above analysis, the performance function of the rationality of the practice route can be expressed as equation (16).
(16)g2R,S=∑i=58Ri−Si.Figure 5
Probability density distribution of the random variables in the rationality of the engineering geology practice route (R5–R8, S5–S8).Figure6 shows the frequency distribution of 8 random variables contained in the effect of the engineering geological practice. It can be seen that the probability density functions of random variables R9–R12 and S9–S12 approximately obey the Gaussian distribution. Based on the above analysis, the performance function of the engineering geology practice effect can be expressed as equation (17).
(17)g3R,S=∑i=912Ri−Si.Figure 6
Probability density distribution of the random variables in effect of the engineering geology practice (R9–R12, S9–S12).Figure7 shows the frequency distribution of two random variables contained in the accommodation conditions for engineering geological practice. It can be seen that the probability density function of random variable R13 approximately obeys the lognormal distribution and the probability density function of S13 approximately obeys the Gaussian distribution. Based on the above analysis, the performance function of the accommodation conditions can be expressed as equation (18).
(18)g4R,S=R13−S13.Figure 7
Probability density distribution of the random variables in accommodation conditions for engineering geology practice (R13, S13).Considering the influence of all random variables, the performance function of the overall evaluation of the engineering geological practice route can be expressed as equation (19).
(19)gR,S=∑i=113Ri−Si.


### 4.2. Results and Discussion

Firstly, only the influence of two random variables contained in each secondary indicator, such asR13 and S13, is considered to study the weight of different secondary indicators in the evaluation of the practice route. Table 3 lists the negative evaluation probability of the engineering geological route under the action of 13 independent secondary indicators. It can be seen that the probability of negative evaluation of accommodation conditions is the largest, reaching 99.0596%, which is the most important factor affecting the evaluation of the engineering geological route. It implies that almost all students believe that the accommodation conditions of engineering geological practice are poor, which far deviates from their psychological expectations. For the cultural evaluation of the geological phenomena and evaluation of basic survival skills in the wild, the probability of negative evaluation reaches 28.5486% and 28.2222%, respectively, indicating that these two options are secondary factors affecting the evaluation. The probability of negative evaluation of two secondary indicators: the correlation evaluation of the geological phenomena and traffic condition evaluation of the practice route are 10.0562% and 6.6540%, respectively, which is the third factor affecting the evaluation. The impact of other secondary indicators is less than 5%, and the impact on the evaluation of the engineering geological practice route is almost positive, indicating that students generally believe that these factors have high quality and meet their psychological expectations.Table 3
Negative evaluation probability of engineering geology practice route with single secondary indicator.
Secondary indicatorsRandom variablePfDevelopment of the typical geological phenomena.R1, S11.4073%Correlation of the geological phenomena.R2, S210.0562%Ornamental of the geological phenomena.R3, S30.1989%Cultural of the geological phenomena.R4, S428.5486%Safety of the practice route.R5, S50.0087%Traffic condition of practice route.R6, S66.6540%Physical fatigue during practice.R7, S71.2557%The difficulty of practice supply.R8, S80.0125%Understanding of practice content.R9, S90.0104%Ability of identifying geological hazards scientifically.R10, S102.6961%Ability of completing practice report independently.R11, S110.0090%The basic survival skills in the wild.R12, S1228.2222%Accommodation conditions.R13, S1399.0596%Table4 lists the probability of negative evaluation of the engineering geological practice route under the action of primary indicators. It can be seen that the overall negative impact probability of the abundance of geological resources is 0.2726%. It can be seen in Table 3 that the negative impact probabilities of the four secondary indicators are 1.4073%, 10.0562%, 0.1989%, and 28.5486%. The maximum probability is 28.5486%, 107.7 times of the overall negative impact probability, and the minimal probability is 0.1989%, approaching 0, which is a very small value. The negative impact probability of this primary indicator is close to the minimum probability of the secondary indicator, indicating that the satisfaction of this indicator is very high, and this indicator plays a leading role in the evaluation. It implies that if participants generally like one factor of engineering geological practice, their tolerance to other adverse factors is greatly improved.Table 4
Negative evaluation probability of engineering geology practice route with primary indicator.
Primary indicatorsRandom variablePfAbundance of geological resources.R1, S1, R2, S2, R3, S3, R4, S40.2726%Rationality of engineering geology practice route.R5, S5, R6, S6, R7, S7, R8, S80.0013%Effect of engineering geology practice.R9, S9, R10, S10, R11, S11, R12, S120.0003%Accommodation conditions.R13, S1399.0596%The first three primary indicators.Ri, Si, (i = 1, …, 12)1.6656e-7%All primary indicators.Ri, Si, (i = 1, …, 13)0.0466%The overall negative impact probability of route rationality is 0.0013%, while the impact probabilities of four secondary indicators are 0.0087%, 6.6540%, 1.2557%, and 0.0125%, respectively. Obviously, the total probability is close to the minimum probability of a secondary indicator, indicating that the minimum probability has a great impact on the total probability. It implies that if a certain factor is generally affirmed in the practice, it will play an important role in the overall evaluation.It can be seen in Table4 that the negative impact probability of accommodation conditions is 99.0596%, which means that students generally feel that accommodation conditions are very poor. The negative evaluation probability of the first three primary indicators is less than 1%; it implies that the students generally recognize the first three primary indicators of engineering geological practice. Considering the total influence of the first three primary indicators, the negative probability of practice route evaluation is 1.6656e−7%, approaching 0. The negative evaluation of the engineering geological route with all of the primary indicator is 0.0466%. Compared with the first three primary indicators, the probability of negative evaluation has been significantly improved, indicating that a primary indicator with generally low recognition will greatly increase the probability of the overall negative evaluation in practice. Targeted adjustment should be made according to the actual situation to make the practice route recognized by the students and improve the effect of engineering geology practice.


## 4.1. Random Variables in the Questionnaire

In this study, four primary indicators that have a significant impact on the engineering geological practice route are selected to form the content of the questionnaire. Table1 lists the main contents of the questionnaire, in which the four primary indicators include 13 secondary indicators and each secondary indicator can be divided into positive (R) and negative (S) variables. Participants can give positive or negative comments on each secondary indicators.Table 1
The main contents of the questionnaire for evaluating engineering geological practice route.
Primary indicatorsSecondary indicatorsAbundance of geological resources1. Development of the typical geological phenomena:R1: developed; S1: undeveloped2. Correlation of the geological phenomena:R2: correlated; S2: uncorrelated3. Ornamental of the geological phenomena:R3: ornamental; S3: not ornamental4. Cultural of the geological phenomena:R4: cultural background; S4: no cultural backgroundRationality of the engineering geology practice route5. Safety of the practice route:R5: safe; S5: unsafe6. Traffic condition of the practice route:R6: convenient; S6: inconvenient7. Physical fatigue during practice:R7: normal; S7: fatigue8. The difficulty of practice supply:R8: normal; S8: difficultEffect of engineering geology practice9. Understanding of the practice content:R9: understand; S9: confuse10. Ability of identifying geological hazards scientifically:R10: capable; S10: incapable11. Ability of completing practice report independently:R11: capable; S11: incapable12. The basic survival skills in the wild:R12: capable; S12: incapableAccommodation conditions13. Accommodation conditions:R13: good; S13: poorFor example, the abundance of geological resources includes the development, correlation, ornamental, and cultural evaluation of the typical geological phenomena. The positive part (R2) of correlation of the geological phenomena is that geological phenomena are interrelated and the negative variable (S2) is that there is no correlation between different geological phenomena. Therefore, in general, the evaluation of the engineering geological practice route is affected by 26 random variables.In order to obtain effective evaluation data, a questionnaire was conducted in all the students participating in engineering geology practice and students can evaluate the value of each random variable according to their practice. A total of 194 valid questionnaires were received in this survey, and the distribution law and mean and standard deviation of each random variable were obtained through statistical analysis.Table2 lists the mean and standard deviation of 26 random variables, in which R1–R13 are positive random variables and S1–S13 are negative random variables. The mean value represents the students’ overall evaluation of the practice content, and the standard deviation reflects the dispersion degree of the evaluation value. According to the scores of all participants on the random variable R1, the mean value is obtained, which represents that the overall cognition of participants on R1 is 61.26 and the standard deviation is 4.89, which shows that almost all students’ evaluation of R1 is not discrete and tends to be consistent. The mean of random variable S11 is 18.62 and the standard deviation is 12.21, indicating that the overall evaluation of S1 by participants is 18.62; however, there is a large cognitive deviation among different individuals. Some participants evaluate S11 much higher than 18.62, while some participants believe that the random variable S11 is far less than 18.62.Table 2
Mean and standard deviation of random variables in the questionnaire.
Positive random variableNegative random variableRi (i = 1, 13)MeanStandard deviationSi (i = 1, 13)MeanStandard deviationR161.264.89S139.798.47R260.269.38S240.9311.86R373.8210.28S327.7212.27R453.1414.75S443.5616.73R579.9812.55S518.4210.55R667.2015.63S633.7916.17R775.7613.74S724.4313.96R874.019.18S826.119.32R982.049.99S918.9313.78R1067.6111.41S1034.6612.73R1181.2611.42S1118.6212.21R1258.0817.07S1243.8117.94R1327.4512.02S1372.9311.67Figure4 shows the frequency distribution of 8 random variables contained in abundance of geological resources; it can be seen that the probability density functions of random variables R1–R4 and S1–S3 approximately obey the Gaussian distribution and the probability density functions of S4 approximately obey the lognormal distribution. Based on the above analysis, the performance function of geological resource abundance can be expressed as equation (15).
(15)g1R,S=∑i=14Ri−Si.Figure 4
Probability density distribution of the random variables in abundance of geological resources (R1–R4, S1–S4).Figure5 shows the frequency distribution of 8 random variables contained in the rationality of the engineering geology practice route. It can be seen that the probability density functions of random variables R5, R8, S5, and S8 approximately obey the Gaussian distribution and the probability density functions of R6, R6, S7, and S7 approximately obey the lognormal distribution. Based on the above analysis, the performance function of the rationality of the practice route can be expressed as equation (16).
(16)g2R,S=∑i=58Ri−Si.Figure 5
Probability density distribution of the random variables in the rationality of the engineering geology practice route (R5–R8, S5–S8).Figure6 shows the frequency distribution of 8 random variables contained in the effect of the engineering geological practice. It can be seen that the probability density functions of random variables R9–R12 and S9–S12 approximately obey the Gaussian distribution. Based on the above analysis, the performance function of the engineering geology practice effect can be expressed as equation (17).
(17)g3R,S=∑i=912Ri−Si.Figure 6
Probability density distribution of the random variables in effect of the engineering geology practice (R9–R12, S9–S12).Figure7 shows the frequency distribution of two random variables contained in the accommodation conditions for engineering geological practice. It can be seen that the probability density function of random variable R13 approximately obeys the lognormal distribution and the probability density function of S13 approximately obeys the Gaussian distribution. Based on the above analysis, the performance function of the accommodation conditions can be expressed as equation (18).
(18)g4R,S=R13−S13.Figure 7
Probability density distribution of the random variables in accommodation conditions for engineering geology practice (R13, S13).Considering the influence of all random variables, the performance function of the overall evaluation of the engineering geological practice route can be expressed as equation (19).
(19)gR,S=∑i=113Ri−Si.


## 4.2. Results and Discussion

Firstly, only the influence of two random variables contained in each secondary indicator, such asR13 and S13, is considered to study the weight of different secondary indicators in the evaluation of the practice route. Table 3 lists the negative evaluation probability of the engineering geological route under the action of 13 independent secondary indicators. It can be seen that the probability of negative evaluation of accommodation conditions is the largest, reaching 99.0596%, which is the most important factor affecting the evaluation of the engineering geological route. It implies that almost all students believe that the accommodation conditions of engineering geological practice are poor, which far deviates from their psychological expectations. For the cultural evaluation of the geological phenomena and evaluation of basic survival skills in the wild, the probability of negative evaluation reaches 28.5486% and 28.2222%, respectively, indicating that these two options are secondary factors affecting the evaluation. The probability of negative evaluation of two secondary indicators: the correlation evaluation of the geological phenomena and traffic condition evaluation of the practice route are 10.0562% and 6.6540%, respectively, which is the third factor affecting the evaluation. The impact of other secondary indicators is less than 5%, and the impact on the evaluation of the engineering geological practice route is almost positive, indicating that students generally believe that these factors have high quality and meet their psychological expectations.Table 3
Negative evaluation probability of engineering geology practice route with single secondary indicator.
Secondary indicatorsRandom variablePfDevelopment of the typical geological phenomena.R1, S11.4073%Correlation of the geological phenomena.R2, S210.0562%Ornamental of the geological phenomena.R3, S30.1989%Cultural of the geological phenomena.R4, S428.5486%Safety of the practice route.R5, S50.0087%Traffic condition of practice route.R6, S66.6540%Physical fatigue during practice.R7, S71.2557%The difficulty of practice supply.R8, S80.0125%Understanding of practice content.R9, S90.0104%Ability of identifying geological hazards scientifically.R10, S102.6961%Ability of completing practice report independently.R11, S110.0090%The basic survival skills in the wild.R12, S1228.2222%Accommodation conditions.R13, S1399.0596%Table4 lists the probability of negative evaluation of the engineering geological practice route under the action of primary indicators. It can be seen that the overall negative impact probability of the abundance of geological resources is 0.2726%. It can be seen in Table 3 that the negative impact probabilities of the four secondary indicators are 1.4073%, 10.0562%, 0.1989%, and 28.5486%. The maximum probability is 28.5486%, 107.7 times of the overall negative impact probability, and the minimal probability is 0.1989%, approaching 0, which is a very small value. The negative impact probability of this primary indicator is close to the minimum probability of the secondary indicator, indicating that the satisfaction of this indicator is very high, and this indicator plays a leading role in the evaluation. It implies that if participants generally like one factor of engineering geological practice, their tolerance to other adverse factors is greatly improved.Table 4
Negative evaluation probability of engineering geology practice route with primary indicator.
Primary indicatorsRandom variablePfAbundance of geological resources.R1, S1, R2, S2, R3, S3, R4, S40.2726%Rationality of engineering geology practice route.R5, S5, R6, S6, R7, S7, R8, S80.0013%Effect of engineering geology practice.R9, S9, R10, S10, R11, S11, R12, S120.0003%Accommodation conditions.R13, S1399.0596%The first three primary indicators.Ri, Si, (i = 1, …, 12)1.6656e-7%All primary indicators.Ri, Si, (i = 1, …, 13)0.0466%The overall negative impact probability of route rationality is 0.0013%, while the impact probabilities of four secondary indicators are 0.0087%, 6.6540%, 1.2557%, and 0.0125%, respectively. Obviously, the total probability is close to the minimum probability of a secondary indicator, indicating that the minimum probability has a great impact on the total probability. It implies that if a certain factor is generally affirmed in the practice, it will play an important role in the overall evaluation.It can be seen in Table4 that the negative impact probability of accommodation conditions is 99.0596%, which means that students generally feel that accommodation conditions are very poor. The negative evaluation probability of the first three primary indicators is less than 1%; it implies that the students generally recognize the first three primary indicators of engineering geological practice. Considering the total influence of the first three primary indicators, the negative probability of practice route evaluation is 1.6656e−7%, approaching 0. The negative evaluation of the engineering geological route with all of the primary indicator is 0.0466%. Compared with the first three primary indicators, the probability of negative evaluation has been significantly improved, indicating that a primary indicator with generally low recognition will greatly increase the probability of the overall negative evaluation in practice. Targeted adjustment should be made according to the actual situation to make the practice route recognized by the students and improve the effect of engineering geology practice.


## 5. Conclusion

In this study, the engineering geological practice route is evaluated, 13 secondary indicators closely related to the practice are selected, and the feedback data is obtained by the questionnaire. Based on the reliability theory, the influence of each primary indicator and secondary indicator is analyzed. The main conclusions are as follows:(1)
Considering the impact of a single secondary indicators, when the negative evaluation probability of the route is extremely small, the mean value of positive random variables is much greater than the mean value of negative random variables, indicating that questionnaire participants generally have a high evaluation of this secondary indicators, such as the ornamental of the geological phenomena, the safety of the practice route, and ability of completing practice report independently. When the negative evaluation probability of the route is extremely high, the mean value of positive random variables is much smaller than the mean value of negative random variables, indicating that the questionnaire participants generally do not recognize this secondary indicators, such as accommodation conditions, cultural of the geological phenomena, and basic survival skills in the wild(2)
If the negative evaluation probability of the route is high under the influence of a single secondary indicator, it indicates that this factor has obvious deficiencies and further investigation and research on this factor can be carried out to improve shortcomings and reduce negative evaluation, such as cultural of the geological phenomena, basic survival skills in the wild, and other secondary indicators(3)
For primary indicators, if the negative evaluation probability of the route is very small, this secondary indicator will play a leading role in the evaluation of the route and reduce the negative evaluation probability of the route significantly, which means that when students generally like a certain factor of engineering geological practice, their tolerance to other unfavorable factors has been greatly improved. In contrast, when the negative evaluation probability of the route is large, it will also play a leading role, significantly increasing the negative evaluation probability of the route, which means that when students generally do not recognize a certain factor, it will seriously affect the overall evaluation(4)
Considering the influence of all secondary indicators, the negative evaluation probability of accommodation conditions reaches 99.0596%, almost 100%, which is a large value. Since there are many small values in the evaluation of other factors, the negative evaluation probability of the engineering geological practice route is still very low, indicating that the quality of this route is very high and can meet the requirements of practice



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