# Multifactor Uncertainty Analysis of Construction Risk for Deep Foundation Pits
## 4 Project Case Analysis
### Comprehensive Evaluation and Probability Analysis  
The risk grade of deep foundation pit construction was systematically and comprehensively evaluated. First, the results of the importance scoring of the evaluation indices were substituted into Equations (1)-(5) in order to calculate the degree of membership of each index to Gades I-V, and membership degree matrices \(\mathbf{R}(P)\) and \(\mathbf{R}(C)\) were constructed that are able to reflect the fuzzy relationship between the factor set and the evaluation set. Then, in combination with the results of the weight analysis obtained by FBWM, the fuzzy comprehensive evaluation vector \(B\) of the \(P\) and \(C\) of each index was calculated using Equation (14). Moreover, Equation (14) was used to calculate the weighted average of the risk grade of \(B\), from which the value of \(B^{*}\) was obtained, which represents the construction risk grade. Figures 6a and 7a show the triangular cloud model of risk grade, which obeys the triangular distribution and reflects the comprehensive evaluation results of the occurrence possibility (\(P\)) and loss (\(C\)) of all of the factors influencing risk in the project case (\(B^{*}(P)=2.500\), \(B^{*}(C)=2.6583\)), respectively. The triangular cloud model is well able to reflect the fuzzy uncertainty of the grade boundary and to represent the random uncertainty of the degree of membership of evaluation data to different risk grades under different circumstances. Since risk grade is a qualitative concept, the value of its quantification is uncertain, and its PDF is not unique. therefore, the occurrence probability of the risk grade corresponding to \(B^{*}\) also exists in many cases. Furthermore, the probability of risk at each grade changes in accordance with different data combinations, reflecting the random volatility of probability. As a result, this method generates the PDF of the evaluation data many times on the basis of randomly generated triangular cloud droplets (quantitative risk grade data). We substitute the values of \(B^{*}(P)\) and \(B^{*}(C)\) into the PDF to calculate the probability distribution results, and determine the risk grades of \(P\) and \(C\) of the project case. The comprehensive risk grade can be determined on the basis of a comparison with Table 1.  
Figure 5: Weight analysis results of primary indices. The results of multiple calculations show that the probability of the \(P\) of the project case being a member of level II is the highest, and the probability of the \(C\) of the project case being a member of level III is the highest (Figures 6b and 7b), on the basis of the probability distribution results (\(P_{\Pi}(P)=0.5537\), \(P_{\Pi}(P)=0.1838\); \(P_{\Pi}(C)=0.5537\), \(P_{\Pi}(C)=0.1838\)). Therefore, it can be seen from Table 1 that the construction risk grade of this deep foundation pit project is Grade II. According to the risk acceptance criteria in [16] the _Code for Risk Management of Underground Works in Urban Rail Transit_, risk management measures should be taken for the project, and risk treatment measures can be taken to strengthen daily management and monitoring. Combined with the actual situation of the project, the following treatment suggestions are presented: (1) harden the ground within the construction enclosure around the foundation pit, cut off the recharging of groundwater by surface water and atmospheric precipitation, and perform the drainage of the ground and the pit thoroughly and at the same time; (2) obey the rules of layer excavation, timely support, strictly prohibit overexcavation, and provide steel supports with anti-stripping and prestressed reinforcement measures; (3) during construction, perform monitoring of the foundation pit and the obser  
Figure 6: Comprehensive evaluation results (\(P\)). (**a**) Triangular cloud model, (**b**) probability density function (PDF). Figure 7: Comprehensive evaluation results (C). (**a**) Triangular cloud model, (**b**) probability density function (PDF).