Tunnel portal slope stability evaluation method based on combination of left and right half cloud asymmetric cloud model and Euclidean distance method
The integration of the left and right semi-cloud model with Euclidean distance enhances tunnel portal slope stability evaluation by addressing uncertainty and randomness, resulting in more accurate and objective stability assessments.
Patent Information
- Application Number
- CN202510480282.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-16
- Publication Date
- 2025-07-15
Smart Images

Figure CN120317136A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of tunnel portal slope stability analysis, and specifically relates to a method for evaluating the stability of tunnel portal slopes based on the combination of the left and right semi-cloud asymmetric cloud model and the Euclidean distance method. Background Technique
[0002] Mountain tunnel portals are often located on slopes with complex geological conditions. The instability of the portal slopes not only threatens the lives of construction workers but also seriously affects the project progress and construction costs. Therefore, reasonably evaluating the stability of tunnel portal slopes has become an urgent problem to be solved.
[0003] The instability mechanism of mountain tunnel portal slopes is complex and is affected by multiple factors, and it shows significant fuzziness and randomness in time and space. At present, there is no unified standard for the evaluation methods of tunnel portal slope stability at home and abroad. Traditional limit equilibrium methods and numerical simulation methods are also difficult to consider the uncertainty of evaluation indicators and are difficult to quickly and accurately determine the slope stability.
[0004] As an effective method for dealing with uncertainty problems, the cloud model can use the characteristics of normal distribution to better reflect the relationship between evaluation indicators and stability levels. At the same time, the Euclidean distance method can reduce the influence of subjective factors and improve the accuracy of evaluation results by quantitatively identifying stability levels.
[0005] Based on this, combining the two, a method for evaluating the stability of tunnel portal slopes is designed to solve the problems existing in the above-mentioned prior art. Summary of the Invention
[0006] The purpose of the present invention is to provide a method for evaluating the stability of tunnel portal slopes based on the combination of the left and right semi-cloud asymmetric cloud model and the Euclidean distance method to solve the problems raised in the background technique.
[0007] The present invention realizes the above purpose through the following technical solutions:
[0008] A method for evaluating the stability of tunnel portal slopes based on the combination of the left and right semi-cloud asymmetric cloud model and the Euclidean distance method includes the following steps:
[0009] S1. Determine the evaluation indicators and grading standards for the stability of tunnel portal slopes, and construct an evaluation index system for the stability of tunnel portal slopes;
[0010] S2. Collect the case index data and corresponding safety factors of tunnel portal slopes, and use the grey relational analysis method to determine the evaluation index weights;
[0011] S3. Determine the digital characteristics of each evaluation index with respect to the left - right semi - cloud asymmetric cloud model, generate cloud diagrams using MATLAB software, and determine the degree to which each evaluation index belongs to each level based on the left - right semi - cloud asymmetric cloud model;
[0012] S4. Multiply the membership degree of the evaluation index by the weight to obtain the membership degree of the tunnel portal slope corresponding to different levels;
[0013] S5. Use the Euclidean distance method to identify the stability level of the tunnel portal slope.
[0014] As a further optimization scheme of the present invention, in step S1, the determined evaluation indexes for the stability of the tunnel portal slope are respectively: slope height, slope gradient, tunnel burial depth ratio, [BQ] value, cohesion, internal friction angle, and daily maximum rainfall.
[0015] As a further optimization scheme of the present invention, in step S1, the index grading standard is based on the safety factor grading in the "Technical Code for Building Slope Engineering", and the slope stability level is divided into four levels, namely stable (Level I), basically stable (Level II), sub - stable (Level III), and unstable (Level IV).
[0016] As a further optimization scheme of the present invention, in step S2, the steps for determining the evaluation index weights using the grey relational analysis method include:
[0017] S2.1. Select the evaluation index as the comparison sequence X and the safety factor as the reference sequence Y. Suppose there are m tunnel portal slope case samples and n evaluation indexes, then the matrix forms of X and Y are as follows:
[0018]
[0019]
[0020] where, x ij represents the value of the j - th (j = 1, 2, …, n) index of the i - th (i = 1, 2, …, m) sample, and y i0 represents the safety factor of the i - th sample;
[0021] S2.2. Use the extreme - value method to perform dimensionless processing on the initial index data. For the indexes that are positively correlated with the stability of the portal slope, the following formula is used for calculation:
[0022]
[0023] For the indexes that are negatively correlated with the stability, the following formula is used for calculation:
[0024]
[0025] In the formula, xij represents the original value of the j-th index of the i-th sample, and min(x j ) represents the minimum value of the j-th index, and max(x j ) represents the maximum value of the j-th index. z ij represents the normalized value of the j-th index of the i-th sample;
[0026] S2.3. Calculate the difference between each normalized comparison sequence and the reference sequence using the following formula;
[0027] Δ ij = |y i0 - z ij |
[0028] S2.4. Calculate the correlation coefficient between each comparison sequence and the reference sequence according to the following formula:
[0029]
[0030] In the formula, ρ is the resolution coefficient, and its value range is (0, 1), generally taken as 0.5;
[0031] S2.5. Calculate the correlation degree of each index using the following formula;
[0032]
[0033] S2.6. Normalize the correlation degrees of each index using the following formula to obtain the weights.
[0034]
[0035] As a further optimization scheme of the present invention, in step S3, determining the digital characteristics of each evaluation index regarding the left and right semi-cloud asymmetric cloud model includes:
[0036] The cloud model combines fuzziness and randomness using three digital characteristics: expectation Ex, entropy En, and hyperentropy He, to realize the mapping between qualitative concepts and quantitative values. Let X be a quantitative domain represented by an exact value, and let be a qualitative concept on X. If the quantitative value x ∈ X and x is a random realization of the qualitative concept , then there exists a random number with a stable tendency which is the degree of determination of x for the qualitative concept . The distribution of x in the domain is called a cloud, and each (x, μ(x)) is called a cloud droplet. According to the "3En principle", about 99.74% of the quantitative values contributing to the qualitative concept in the domain fall within the interval [Ex - 3En, Ex + 3En]. According to this principle, En is calculated;
[0037] S3.2. For the intermediate-level clouds of the index (such as levels t = 2, 3, …, k - 1), it is considered that the upper and lower limit values of the cloud droplet distribution interval should be the Ex values of its adjacent evaluation levels. Also, since the distances between the Ex values of this evaluation level and those of its left and right adjacent evaluation levels may not be the same, the Ens of its left and right adjacent evaluation levels may not be the same either. Therefore, it is necessary to calculate the Ens of the left and right half-clouds of the intermediate levels separately:
[0038]
[0039] In the formula, a jt-1 and a jt are the lower and upper limit values of the boundary of the interval of evaluation index j for level t respectively, Ex jt , Ex jt-1 and Ex jt+1 are the expectations of index j for levels t, t - 1, and t + 1 respectively, En Ljt and En Rjt are the entropies of the left and right half-clouds of index j for level t respectively, He Ljt and He Rjt are the hyper-entsropies of the left and right half-clouds of index j for level t;
[0040] S3.3. For the leftmost-level cloud of the index (such as level t = 1), set Ex according to the critical value specified in the grading standard, that is, Ex is the upper limit value of this level interval, Ex j1 = a j1 . If the evaluation index value is less than Ex j1 , according to common sense, its membership degree should not be less than the membership degree when the index value is Ex j1 . Also, since the maximum value of the membership degree is 1, when the measured data of the evaluation index is less than Ex j1 , its membership degree should also be 1. The digital feature calculation formula of the leftmost-level cloud is as follows:
[0041]
[0042] In the formula, a j1 is the upper limit value of the boundary of the interval of evaluation index j for level t = 1, Ex j1 and Ex j2 are the expectations of index j for levels t = 1 and t = 2 respectively, En Lj1 and En Rj1 are the entropies of the left and right half-clouds of index j for level t = 1 respectively, He Lj1 and He Rj1 are the hyper-entsropies of the left and right half-clouds of index j for level t = 1;
[0043] S3.4. For the rightmost level cloud (e.g., level t = k), set Ex according to the critical value specified in the grading standard, that is, Ex is the lower limit value of the k-level interval, Ex jk = a jk-1 , then the digital feature calculation formula for the rightmost level cloud is as follows:
[0044]
[0045] In the formula, a jk-1 is the lower limit value of the evaluation index j with respect to the boundary of the k-level interval, Ex jk is the expectation of the index j with respect to level k, En Ljk and En Rjk are the entropies of the left half cloud and the right half cloud of the index j with respect to level k, He Ljk and He Rjk are the hyper entropies of the left half cloud and the right half cloud of the index j with respect to level k;
[0046] S3.5. Use MATLAB software to obtain the cloud diagram of the left and right half cloud asymmetric cloud model of the evaluation index.
[0047] As a further optimization scheme of the present invention, in step S3, determine the membership degrees of each evaluation index with respect to each level:
[0048] For the normal cloud model, if the index value x satisfies x ~ N(Ex, En' 2 ), En' ~ N(En, He 2 ), then the membership degree of x to the qualitative concept is shown in the following formula:
[0049]
[0050] Based on the left and right half cloud asymmetric cloud model, determine the degree to which each evaluation index belongs to each level, and form a matrix A
[0051]
[0052] In the formula, μ jt represents the membership degree of the index j to level t.
[0053] As a further optimization scheme of the present invention, in step S4, multiply the index weight by the matrix A to obtain the membership degree of the tunnel portal slope with respect to each evaluation level
[0054]
[0055] where μ t is the membership degree of the evaluation object with respect to each evaluation level t.
[0056] As a further optimized solution of the present invention, in step S5, the Euclidean distance method is used to identify the stability grade of the tunnel portal slope, and the specific formula is (taking 4 grades as an example):
[0057]
[0058] d t is the comprehensive measure μ t to the distance of grade t, and the minimum distance d t The corresponding grade is the stability grade of the object to be evaluated.
[0059] The beneficial effects of the present invention are as follows:
[0060] 1) The present invention uses the left-right semi-cloud asymmetric cloud model to determine the membership degree of the evaluation index for each grade, thereby effectively considering the randomness and fuzziness of the evaluation index, and more accurately reflecting the internal relationship between the evaluation index and the stability grade.
[0061] 2) The present invention uses the Euclidean distance method to objectively identify the stability grade, reduces the subjective influence, and improves the accuracy of the evaluation result. Description of the Drawings
[0062] Figure 1 is the flow chart of the tunnel portal slope stability evaluation method based on the combination of the left-right semi-cloud asymmetric cloud model and the Euclidean distance method of the present invention;
[0063] Figure 2 is the cloud diagram of the left-right semi-cloud asymmetric cloud model of the slope height.
[0064] Figure 3 is the cloud diagram of the left-right semi-cloud asymmetric cloud model of the slope gradient.
[0065] Figure 4 is the cloud diagram of the left-right semi-cloud asymmetric cloud model of the tunnel depth ratio.
[0066] Figure 5 is the cloud diagram of the left-right semi-cloud asymmetric cloud model of the [BQ] value.
[0067] Figure 6 is the cloud diagram of the left-right semi-cloud asymmetric cloud model of the cohesion.
[0068] Figure 7 is the cloud diagram of the left-right semi-cloud asymmetric cloud model of the internal friction angle.
[0069] Figure 8 is the cloud diagram of the left-right semi-cloud asymmetric cloud model of the maximum daily rainfall. Detailed Embodiments
[0070] To enable those of ordinary skill in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings. It is necessary to point out here that the following specific embodiments are only used to further illustrate the present invention and should not be construed as limiting the protection scope of the present invention.
[0071] Referring to the attached Figure 1 A method for evaluating the stability of a tunnel portal slope based on the combination of a left - right semi - cloud asymmetric cloud model and the Euclidean distance method is shown as follows:
[0072] S1. Determine the evaluation indexes and grading standards for the stability of the tunnel portal slope, and construct an evaluation index system for the stability of the tunnel portal slope;
[0073] S2. Collect the index data of tunnel portal slope cases and the corresponding safety factors, and use the grey relational analysis method to determine the weights of the evaluation indexes;
[0074] S3. Determine the digital characteristics of each evaluation index with respect to the left - right semi - cloud asymmetric cloud model, generate cloud diagrams using MATLAB software, and determine the degree to which each evaluation index belongs to each grade based on the left - right semi - cloud asymmetric cloud model;
[0075] S4. Multiply the membership degree of the evaluation index by the weight to obtain the membership degree of the tunnel portal slope corresponding to different grades;
[0076] S5. Use the Euclidean distance method to identify the stability grade of the tunnel portal slope.
[0077] In step S1 of this embodiment, the determined evaluation indexes for the stability of the tunnel portal slope are respectively: slope height, slope gradient, tunnel depth ratio, [BQ] value, cohesion, internal friction angle, and maximum daily rainfall.
[0078] The slope height and slope gradient are key parameters of the terrain characteristics. Generally speaking, as the slope height and slope gradient increase, the risk of instability of the tunnel portal slope also increases.
[0079] The [BQ] value is an important index for evaluating the quality of rock masses. The larger the [BQ] value, the better the quality of the rock mass, and the more stable the slope.
[0080] Different failure modes determine different focuses of the evaluation indexes. Since the rock and soil masses in the tunnel portal section under study usually have relatively developed joint fissures and severe weathering of the surrounding rock, landslide failures are particularly common. And the failure mechanism of landslides shows that the shear force on the sliding surface is the key factor leading to landslides. The magnitude of the shear force is mainly determined by the cohesion and internal friction angle of the sliding surface, and these two together reflect the shear strength characteristics of the rock and soil masses. Therefore, cohesion and internal friction angle are selected as the key indexes for evaluating slope stability.
[0081] Rainfall is the main external factor leading to slope instability. Heavy rainfall increases the pore water pressure inside the rock and soil mass, reducing the cohesion and internal friction angle, thus weakening the slope stability. Therefore, the daily maximum rainfall is selected as an important external factor affecting slope stability.
[0082] To further consider the influence of the tunnel on slope stability, the tunnel depth ratio (H0 / H) is introduced when selecting the stability evaluation index, where H0 is the tunnel depth and H is the tunnel height. The tunnel depth ratio can more accurately reflect the position characteristics of the tunnel relative to the slope. Compared with only using the tunnel depth index, it is more applicable to the stability assessment of tunnel portal slopes of different scales. For example, for a tunnel with a large height, even if the absolute depth is large, but if it is in a shallow burial state relative to the slope, the disturbance of the tunnel to the slope may be large. On the contrary, for a shorter tunnel, even if its absolute depth is small, but if it is in a deep burial state relative to the slope, the stability of the tunnel portal slope may be better.
[0083] In step S1 of this embodiment, referring to the safety factor classification in the "Technical Code for Building Slope Engineering" (GB50330-2013), the slope stability grade is divided into stable (Grade I), basically stable (Grade II), sub-stable (Grade III), and unstable (Grade IV). The specific classification criteria for the tunnel portal slope stability evaluation index are shown in Table 1.
[0084] Table 1 Classification Criteria for Tunnel Portal Slope Stability Evaluation Index
[0085] Furthermore, in step S2, the grey relational analysis method has advantages in dealing with system uncertainty and small sample problems. And this method determines the weight of each index by calculating the correlation degree between each evaluation index and the safety factor, which can not only reflect the change of index data but also establish the connection between the index and the safety factor, avoiding the limitations of simply relying on data. The steps of calculating the tunnel portal slope stability evaluation index weight by using the grey relational analysis method include:
[0086] S2.1. Select the evaluation index as the comparison sequence X and the safety factor as the reference sequence Y. Suppose there are m tunnel portal slope case samples and n evaluation indexes, then the matrix forms of X and Y are as follows:
[0087]
[0088]
[0089] Among them, x ij represents the value of the j-th (j = 1, 2,..., n) index of the i-th (i = 1, 2,..., m) sample, and y i0Denote the safety factor of the \(i\)-th sample;
[0090] Based on the case data of the tunnel portal slope collected in Table 2, substitute its index data and the corresponding case safety factor into the \(X\) and \(Y\) matrices.
[0091] Table 2 Case data of tunnel portal slope for calculating index weights
[0092] S2.2. Use the range method to dimensionless process the initial index data. For the indexes positively correlated with the stability of the tunnel portal slope (such as tunnel depth ratio, [BQ] value, internal friction angle, cohesion, safety factor), use the following formula for calculation:
[0093]
[0094] For the indexes negatively correlated with the stability (such as slope height, slope gradient, maximum daily rainfall), use the following formula for calculation:
[0095]
[0096] In the formula, \(x\) ij denotes the original value of the \(j\)-th index of the \(i\)-th sample, \(\min(x\) j ) denotes the minimum value of the \(j\)-th index, \(\max(x\) j ) denotes the maximum value of the \(j\)-th index, \(z\) ij denotes the standardized value of the \(j\)-th index of the \(i\)-th sample;
[0097] S2.3. Use the following formula to calculate the difference between each normalized comparison sequence and the reference sequence;
[0098] \(\Delta\) ij \(= |y\) i0 - z\) ij |\)
[0099] S2.4. Calculate the correlation coefficient between each comparison sequence and the reference sequence according to the following formula:
[0100]
[0101] In the formula, \(\rho\) is the resolution coefficient, and its value range is \((0, 1)\), generally taken as \(0.5\);
[0102] S2.5. Calculate the correlation degree of each index by the following formula;
[0103]
[0104] S2.6. Normalize the correlation degrees of each index using the following formula to obtain the weights.
[0105]
[0106] According to the above steps, the weights of each evaluation index of the tunnel portal slope are obtained, as shown in Table 3.
[0107] Table 3 Evaluation Index Weights
[0108] Furthermore, step S3 includes:
[0109] S3.1. The cloud model combines fuzziness and randomness using three numerical characteristics: expectation Ex, entropy En, and hyperentropy He, to achieve the mapping between qualitative concepts and quantitative values. Let X be a quantitative domain represented by an exact value, and let be a qualitative concept on X. If the quantitative value x ∈ X and x is a random realization of the qualitative concept , then there exists a random number with a stable tendency, which is the degree of determination of x for the qualitative concept . The distribution of x in the domain is called a cloud, and each (x, μ(x)) is called a cloud droplet. According to the "3En principle", about 99.74% of the quantitative values contributing to the qualitative concept in the domain fall within the interval [Ex - 3En, Ex + 3En]. Based on this principle, En is calculated;
[0110] S3.2. For the intermediate-level clouds of the index (such as levels t = 2, 3,... k - 1), it is considered that the upper and lower limit values of the cloud droplet distribution interval should be the Ex values of its adjacent evaluation levels. Also, since the distances between the Ex values of this evaluation level and its left and right adjacent evaluation levels may not be the same, the En values of the left and right half-clouds of the intermediate level must be calculated separately:
[0111]
[0112] In the formula, a jt-1 and a jt are the lower and upper limit values of the boundary of the interval of evaluation index j for level t, respectively. Ex jt , Ex jt-1 and Ex jt+1 are the expectations of index j for levels t, t - 1, and t + 1, respectively. En Ljt and En Rjt are the entropies of the left and right half-clouds of index j for level t, respectively. He Ljt and He Rjt are the hyperentropies of the left and right half-clouds of index j for level t;
[0113] S3.3. For the leftmost level cloud of the index (such as level t = 1), set Ex according to the critical value specified in the grading standard, that is, Ex is the upper limit value of this level interval, Ex j1 = a j1 , if the evaluation index value is less than Ex j1 , according to common sense, its membership degree should not be less than the membership degree when the index value is Ex j1 . Also, since the maximum value of the membership degree is 1, when the measured data of the evaluation index is less than Ex j1 , its membership degree should also be 1. The digital feature calculation formula of the leftmost level cloud is as follows:
[0114]
[0115] In the formula, a j1 is the upper limit value of the boundary of the interval of evaluation index j with respect to level t = 1, Ex j1 and Ex j2 are the expectations of index j with respect to levels t = 1 and t = 2, En Lj1 and En Rj1 are the entropies of the left half cloud and the right half cloud of index j with respect to level t = 1, He Lj1 and He Rj1 are the hyper entropies of the left half cloud and the right half cloud of index j with respect to level t = 1;
[0116] S3.4. For the rightmost level cloud (such as level t = k), set Ex according to the critical value specified in the grading standard, that is, Ex is the lower limit value of level k interval, Ex jk = a jk-1 , then the digital feature calculation formula of the rightmost level cloud is as follows:
[0117]
[0118] In the formula, a jk-1 is the lower limit value of the boundary of the interval of evaluation index j with respect to level k, Ex jk is the expectation of index j with respect to level k, En Ljk and En Rjk are the entropies of the left half cloud and the right half cloud of index j with respect to level k, He Ljk and He Rjk are the hyper entropies of the left half cloud and the right half cloud of index j with respect to level k;
[0119] According to the above formulas and grading standards, the digital features of each index with respect to each level are shown in Table 4;
[0120] Table 4 Digital Features of the Left - Right Asymmetric Cloud Model of Each Evaluation Index
[0121] S3.5. Obtain the left - right semi - cloud asymmetric cloud model cloud map of the evaluation index using MATLAB software, as shown Figures 2 to 8 below.
[0122] Furthermore, in step S3, determine the membership degree of each evaluation index with respect to each level:
[0123] For the normal cloud model, if the index value x satisfies x ~ N(Ex, En' 2 ), En′ ~ N(En, He 2 ), then the membership degree of x to the qualitative concept is shown as follows:
[0124]
[0125] Based on the left - right semi - cloud asymmetric cloud model, determine the degree to which each evaluation index belongs to each level, and form a matrix A
[0126]
[0127] where μ jt represents the membership degree of index j to level t.
[0128] Furthermore, in step S4, multiply the index weight by matrix A to obtain the membership degree of the tunnel portal slope with respect to each evaluation level
[0129]
[0130] where μ t is the membership degree of the evaluation object with respect to each evaluation level t.
[0131] Furthermore, in step S5, use the Euclidean distance method to identify the stability level of the portal slope. The evaluation level is set to four levels, and the specific formula is:
[0132]
[0133] Determine the minimum distance d t The corresponding level is the stability level of the object to be evaluated.
[0134] In this embodiment, according to the geological data and research results, the stability evaluation index data of a certain tunnel portal slope is shown in Table 5.
[0135] Table 5 Tunnel portal slope evaluation index data
[0136] Then, the membership degrees of the tunnel portal slope with respect to each level are 0, 0.4571, 0.1882, and 0.2949. According to the Euclidean distance method, the distances d1, d2, d3, and d4 are 1.1538, 0.6458, 0.9772, and 0.7416 respectively. According to the minimum distance principle, the stability level of the tunnel portal slope is Class II.
[0137] This method comprehensively considers many factors affecting the stability of the tunnel portal slope, uses the left and right semi-cloud asymmetric cloud model to determine the membership degree of each index with respect to each level, so as to consider the uncertainty of the evaluation index. The Euclidean distance method can quantitatively identify the stability level and avoid the influence of subjective judgment, thereby improving the accuracy of the evaluation results.
[0138] The above embodiments are only partial examples of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.
Claims
1. A method for evaluating the stability of a tunnel portal slope by combining a left-right semi-cloud asymmetric cloud model and the Euclidean distance method, characterized in that, It includes the following steps: S1. Determine the evaluation indexes and their grading standards for the stability of the tunnel portal slope, and construct an evaluation index system for the stability of the tunnel portal slope; S2. Collect the index data and corresponding safety factors of the tunnel portal slope cases, and use the grey relational analysis method to determine the weights of the evaluation indexes; S3. Determine the digital characteristics of each evaluation index with respect to the left-right semi-cloud asymmetric cloud model, generate cloud diagrams using MATLAB software, and determine the degree of membership of each evaluation index to each level based on the left-right semi-cloud asymmetric cloud model; S4. Multiply the membership degree of the evaluation index by the weight to obtain the membership degree of the tunnel portal slope corresponding to different levels; S5. Use the Euclidean distance method to identify the stability level of the tunnel portal slope.
2. A method for evaluating the stability of tunnel portal slopes based on the combination of left - right semi - cloud asymmetric cloud model and Euclidean distance method according to claim 1, characterized in that: In step S1, the determined evaluation indexes for the stability of the tunnel portal slope are respectively: Slope height, slope gradient, tunnel burial depth ratio, [BQ] value, cohesion, internal friction angle, and maximum daily rainfall.
3. A method for evaluating the stability of a tunnel portal slope based on the combination of a left-right semi-cloud asymmetric cloud model and the Euclidean distance method according to claim 1, characterized in that: In step S1, the index grading standard is based on the safety factor grading in the Technical Code for Building Slope Engineering. The slope stability level is divided into four levels, namely stable (Level I), basically stable (Level II), sub-stable (Level III), and unstable (Level IV).
4. A method for evaluating the stability of tunnel portal slopes based on the combination of left - right semi - cloud asymmetric cloud model and Euclidean distance method according to claim 1, characterized in that: In step S2, the steps for using the grey relational analysis method to determine the weights of the evaluation indexes include: S2.
1. Select the evaluation indexes as the comparison sequences X, and the safety factor as the reference sequence Y. Assuming there are m tunnel portal slope case samples and n evaluation indexes, the matrix forms of X and Y are as follows: where x ij represents the value of the j-th (j = 1, 2, …, n) index of the i-th (i = 1, 2, …, m) sample, and y i0 represents the safety factor of the i-th sample; S2.
2. Use the range method to perform dimensionless processing on the initial index data. For the indexes that are positively correlated with the stability of the portal slope, the following formula is used for calculation: For the indexes that are negatively correlated with the stability, the following formula is used for calculation: where x ij represents the original value of the j-th index of the i-th sample, min(x j ) represents the minimum value of the j-th index, max(x j ) represents the maximum value of the j-th index, and z ij represents the standardized value of the j-th index of the i-th sample; S2.
3. Use the following formula to calculate the difference between each normalized comparison sequence and the reference sequence; xxΔ ij = |y i0 - z ij | S2.
4. Calculate the correlation coefficients between each comparison sequence and the reference sequence according to the following formula: In the formula, ρ is the resolution coefficient, and its value range is (0, 1), generally taken as 0.5; S2.
5. Calculate the correlation degree of each index according to the following formula; S2.
6. Use the following formula to normalize the correlation degrees of each index, and then obtain the weights.
5. A tunnel portal slope stability evaluation method based on the combination of left-right semi-cloud asymmetric cloud model and Euclidean distance method according to claim 1, characterized in that: In step S3, the digital characteristics of each evaluation index with respect to the left-right semi-cloud asymmetric cloud model are as follows: S3.
1. The cloud model combines fuzziness and randomness using three numerical characteristics: expected value Ex, entropy En, and hyper-entropy He, to achieve the mapping between qualitative concepts and quantitative values. Let X be a quantitative domain represented by exact values. Let be a qualitative concept on X. If the quantitative value x ∈ X and x is a random realization of the qualitative concept , then there exists a random number with a stable tendency , which is the degree of determination of x for the qualitative concept . The distribution of x in the domain is called a cloud, and each (x, μ(x)) is called a cloud droplet. According to the "3En principle", about 99.74% of the quantitative values contributing to the qualitative concept in the domain fall within the interval [Ex - 3En, Ex + 3En]. Based on this principle, En is calculated; S3.
2. For the cloud of the middle level of the index (such as level t = 2, 3,... k - 1), it is considered that the upper and lower limit values of the cloud droplet distribution interval should be the Ex values of its adjacent evaluation levels. Also, because the distance between the Ex values of this evaluation level and its left and right adjacent evaluation levels may not be the same, the En values of its left and right adjacent evaluation levels may not be the same either. Therefore, it is necessary to calculate the En values of the left and right semi-clouds of the middle level separately: where a jt-1 and a jt are the lower and upper limit values of the evaluation index j with respect to the interval boundary of the grade t, respectively, Ex jt , Ex jt-1 and Ex jt+1 are the expectations of the index j with respect to the grades t, t - 1, and t + 1, respectively, En Ljt and En Rjt are the entropies of the left half-cloud and the right half-cloud of the index j with respect to the grade t, respectively, He Ljt and He Rjt are the hyper- entropies of the left half-cloud and the right half-cloud of the index j with respect to the grade t; S3.
3. For the leftmost level cloud of the index (such as level t = 1), set Ex according to the critical value specified in the grading standard, that is, Ex is the upper limit value of this level interval, Ex j1 = a j1 . If the evaluation index value is less than Ex j1 , according to common sense, its membership degree should not be less than the membership degree when the index value is Ex j1 . Also, since the maximum value of the membership degree is 1, when the measured data of the evaluation index is less than Ex j1 , its membership degree should also be 1. The digital feature calculation formula of the leftmost level cloud is as follows: where a j1 is the upper limit value of the evaluation index j with respect to the interval boundary of level t = 1, Ex j1 and Ex j2 are the expectations of index j with respect to levels t = 1 and t = 2, En Lj1 and En Rj1 are the entropies of the left half-cloud and the right half-cloud of index j with respect to level t = 1, He Lj1 and He Rj1 are the hyper-entropies of the left half-cloud and the right half-cloud of index j with respect to level t = 1; S3.
4. For the rightmost level cloud (e.g., level t = k), set Ex according to the critical value specified by the grading standard, that is, Ex is the lower limit value of the k-level interval, Ex jk = a jk-1 , then the digital feature calculation formula for the rightmost level cloud is as follows: where a jk-1 is the lower limit of the interval boundary of evaluation index j with respect to level k, Ex jk is the expectation of index j with respect to level k, En Ljk and En Rjk are the entropies of the left and right half-clouds of index j with respect to level k, He Ljk and He Rjk are the hyper-entropies of the left and right half-clouds of index j with respect to level k; S3.
5. Use MATLAB software to obtain the cloud diagrams of the left-right semi-cloud asymmetric cloud model of the evaluation indexes.
6. The slope stability evaluation method for tunnel portal based on the combination of left - right semi - cloud asymmetric cloud model and Euclidean distance method according to claim 1, wherein: In step S3, the membership degrees of each evaluation index to each level are as follows: For the normal cloud model, if the index value x satisfies x ~ N(Ex, En '2 ), En' ~ N(En, He 2 ), then the membership degree of x to the qualitative concept is shown as follows: Determine the degree of membership of each evaluation index to each level based on the left-right semi-cloud asymmetric cloud model, and form matrix A where μ jt represents the membership degree of index j to level t.
7. A method for evaluating the stability of tunnel portal slopes based on the combination of left and right semi-cloud asymmetric cloud models and Euclidean distance method, characterized in that: In step S4, multiply the index weights by matrix A to obtain the membership degrees of the tunnel portal slope to each evaluation level, that is where μ t is the membership degree of the evaluation object with respect to each evaluation level t.
8. A method for evaluating the stability of tunnel portal slopes based on the combination of left and right semi-cloud asymmetric cloud models and the Euclidean distance method, characterized in that: In step S5, the Euclidean distance method is used to identify the stability grade of the tunnel entrance slope, and the specific formula is as follows (taking four grades as an example): d t To comprehensively measure the distance from μ t to level t and determine the minimum distance d t The corresponding level is the stability level of the object to be evaluated.
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