# Multifactor Uncertainty Analysis of Construction Risk for Deep Foundation Pits
## 1 Introduction  
Deep foundation pit engineering is engineering of a complex system that is prone to accidents during construction [1]. Risk evaluation in deep foundation pit engineering is a necessary step in order to predict the risk level, and it is also an important means for reducing the probability of accidents occurring. However, risk is inevitably associated with uncertainty, which includes the fuzzy and random uncertainty involved in risk evaluation. The uncertainty increases the difficulty of accurately predicting risk in deep foundation pit construction [2]. Therefore, it is both important and difficult to carry out research on the uncertainty in deep foundation pit construction risk evaluation. The quantitative characterisation and treatment of risk uncertainty is still a research focus in the field of risk analysis [3]. In recent years, to analyse the impact of uncertainty on risk evaluation results in deep foundation pit construction, many scholars have proposed a series of valuable evaluation methods based on fuzzy analysis, probability, Bayesian networks, and other theories. These methods include a fuzzy comprehensive evaluation method [2], a risk analysis method based on evidence theory [4], a risk coupling evaluation method [5], a fuzzy entropy and cloud theory evaluation method [6], an improved riskmatrix analysis method [7], a stepwise weight evaluation ratio analysis and comprehensive risk evaluation method [8], a fuzzy comprehensive evaluation method based on a C-OWA operator [9], a dynamic risk evaluation method based on risk decomposition structure matrix and particle swarm optimisation [10], etc. Most of these evaluation models represent improvements with respect to traditional risk evaluation methods, and solve the problems of risk identification, risk analysis [11], index weight determination, fuzzy uncertainty, and risk membership encountered in risk evaluation. However, there are still some problems that need to be resolved with respect to the following aspects: (1) Generally, the indicators used to measure the nature of the evaluation object are fuzzy, but the existing weight determination methods lack consideration of the indicators' fuzzy uncertainty. (2) The fuzzy and random uncertainties of risks are not fully considered. For example, the membership function in fuzzy mathematics can only reflect the fuzziness of the evaluation system but cannot consider the randomness of the system, which reduces the accuracy of the risk evaluation results. As an extension of classical set theory, fuzzy set theory can solve practical problems in uncertain environments [12]. Triangular fuzzy numbers can transform uncertain evaluation language into definite values. Therefore, using a triangular fuzzy number to determine the index weight can solve the fuzzy uncertainty problem when the evaluation index is described by a natural evaluation language. The cloud model [13] is an uncertainty model for realising qualitative and quantitative transformation. The cloud model can not only solve fuzzy uncertainty problems caused by the fuzzy boundary of risk grade using natural language, it can also solve the random uncertainty problem caused by the transformation of risk grade natural language and its definite values [14]. At the same time, the cloud model can be applied to realise the visualisation of risk evaluation results and improve the intuitiveness of evaluation. The triangular membership function is the simplification of the standard normal membership function, which is simple to calculate and is often used in fuzzy control. This can be extended to triangular membership clouds by using fuzzy set theory, and provides a solution for fuzzy control problems. As a result, aiming at the construction risk of deep foundation pit subway stations, this study establishes a general engineering risk analysis method in the field of engineering risk analysis.