**3. Evaluation of Social Stability Risk Coupling for Major Projects**

### *3.1. Construction of Risk Evaluation Index System for Social Stability for Major Projects*

Based on the identification of social stability risk factors of major projects and the Bow-tie model, this paper constructs the dimensions of the social stability risk evaluation index system of major projects, including government risk, public risk, economic risk, social risk, and natural environmental risk; comprehensively analyzes the internal uncertain factors of the local government and the surrounding residents, as well as the exogenous uncertain factors such as "economic-social-natural environment" produced by the external environment, dynamically and dialectically considers the risk factors, and summarizes them; and selects 12 program layer indicators according to the principles of comprehensiveness, science, maneuverability, and humanization, as shown in Table 1.

**Table 1.** Indicators at the program level.



**Table 1.** *Cont.*

#### *3.2. Coupling Evaluation of Social Stability Risks of Major Projects Based on N-K Model*

The N-K model [14,15] is a general model used to study complex dynamic systems, including two parameters: N is the number of constituent elements of the system, and K is the number of interdependencies in the network. If there are N elements in the system, and each element has n different states, then there are N kinds of possible combinations. The elements of the system are combined in a certain way, that is, a network is formed. The minimum value of K is 0 and the maximum value is N-1.

The steps of using the N-K model to measure the social stability risk coupling of major projects include: major project coupling risk classification, data statistics, and coupling probability calculation.

According to the number of risk factor coupling, the social stability risk coupling of major projects is divided into the following three categories:

(1) Single factor coupling risk: A single risk factor affecting the social stability of major projects will contain multiple risk factors, and each risk factor will interact with each other. Single factor coupling risk includes government (abbreviated G, Code a) factor risk, public (abbreviated P, Code b) factor risk, economic (abbreviated E, Code c) factor risk, social (abbreviated S, Code d) factor risk and natural environmental (abbreviated NE, Code e) factor risk, are recorded as *T*<sup>10</sup> (*a*), *T*<sup>11</sup> (*b*), *T*<sup>12</sup> (*c*), *T*<sup>13</sup> (*d*), *T*<sup>14</sup> (*e*), respectively, and the total value of coupling risk is recorded as T1. The single factor coupling risk is shown in Table 2.

**Table 2.** Single factor coupling risk.


(2) Two-factor coupling risk: Includes 10 types of two-factor coupling risk, and the total value of coupling risk is recorded as *T*2. The two-factor coupling risk is shown in Table 3.


(3) Multi-factor coupling risk: Refers to the interaction of three or more risk factors affecting the social stability of major projects, and the total value of coupling risk is recorded as *T*3. The multi-factor coupling risk is shown in Table 4.


**Table 4.** Multi-factor coupling risk.

In this paper, by calculating the interactive information among five types of social stability risk factors of major projects, the coupling effect is evaluated to form a new risk state. The probability that this type of coupling occurs is measured in terms of the number of times that it occurs more rapidly. The coupling risk magnitude and the accident probability are measured in terms of the coupling value magnitude, i.e., if the resulting value healed with some form of coupling, then the coupling risk healed with the resulting probability healed.

Firstly, the calculation formula of single factor coupling is shown in Formula (1).

$$T(a, b, c, d, e) = \sum\_{h=1}^{H} \sum\_{i=1}^{I} \sum\_{j=1}^{K} \sum\_{k=1}^{L} \left[ P\_{hijkl} \times \log\_2(\frac{P\_{hijkl}}{P\_{h\dots} \times P\_{j\dots} \times P\_{\dots k\dots} \times P\_{\dots k\dots} \times P\_{\dots l}}) \right] \tag{1}$$

where *a*, *b*, *c*, *d* and *e* represent five coupling element numbers (where a represents government risk, *b* represents public risk, *c* represents economic risk, *d* represents social risk, and *e* represents natural environmental insurance); *T* represents the coupling value, and the larger the coupling value is, the more likely the risk accident caused by this method is; *h*, *i*, *j*, *k*, *l* represent the state of the five factors respectively; *Phijkl* represents the probability of the coupling of the five factors; *Ph* ... . represents when the government risk factor is in the h state, the single factor coupling probability; *P*.*<sup>i</sup>* ... represents the probability of single factor coupling when the public risk factor is in the *i* state; *P*.*.j*.. represents the probability of single factor coupling when the economic risk factor is in the *j* state; *P*...*k*. represents the probability of single factor coupling when the social risk factor is in *k* state; *P* ... .*<sup>l</sup>* represents the probability of single factor coupling when the natural environmental risk factor is in the *l* state.

Two-factor coupling refers to a form of pairwise coupling among the risk coupling factors of social stability in major projects. The two risk couplings will produce 10 cases; taking *T*<sup>20</sup> (*a*, *b*) as an example, its calculation formula is shown in Formula (2).

$$T\_{21}(a,b) = \sum\_{h=1}^{H} \sum\_{i=1}^{I} \left[ P\_{hi\dots} \times \log\_2(\frac{P\_{hi\dots}}{P\_{h\dots} \times P\_{i\dots}}) \right] \tag{2}$$

Multi-factor coupling refers to the interaction of more than two factors in the coupling factors that affect the social stability risk of major projects, with a total of 13 cases; taking *T*<sup>30</sup> (*a*, *b*, *c*) as an example, its calculation formula is shown in Formula (3).

$$T\_{31}(a,b,c) = \sum\_{h=1}^{H} \sum\_{i=1}^{I} \sum\_{j=1}^{J} \left[ P\_{hij.} \times \log\_2(\frac{P\_{hij.}}{P\_{h...} \times P\_{j...} \times P\_{...j...}}) \right] \tag{3}$$

Finally, according to the order of each coupling value, the conclusion of coupling evaluation is drawn.

#### **4. Example**

#### *4.1. Example Statistics of Social Stability Risk Events in Major Projects*

This paper collected from website news reports, papers, paper press publications at home and abroad to analyze the cases of stable risk events of major engineering societies at home and abroad, and counted 108 risk events occurring at home and abroad between 2000 and 2020, including 72 risk events at home and 36 risk events abroad; the major engineering social stability risk events are shown in Table 5.


**Table 5.** Information on social stability risk events of major projects.

In the model, 1 and 0 are used to indicate whether each factor is in an unsafe state, 1 indicates occurrence, and 0 indicates that the risk occurrence probability is not present and the coupling value is used to quantify the risk occurrence probability (as shown in Table 6). The coupling factors with a frequency (frequency) of 0 on the way are not marked.

**Table 6.** Statistics of social stability risk events of major projects under different coupling modes.


In Table 3, 00000 of the single factor coupling indicated that none of the five coupling factors had an impact on the social stability risk of major projects, 10,000 said that only government factors had an impact on the social stability risk of major projects, and there were three such accidents with a frequency of 0.028; 11,000 in the two factor coupling indicates that the risk is the result of the coupling of government factors as well as social public factors, and there are seven such accidents with a frequency of 0.065; 11,010 of the

multi-factor coupling indicates that the risk is the result of the coupling of government factors, social public factors, and social factors, and there are four such accidents with a frequency of 0.037.
