## 1 Introduction  
The past decades have witnessed rapid growth in the number and scale of deep foundation pit projects in subway constructions around the world. Once a foundation pit accident (e.g., collapse of retaining structures) occurs, the consequence is often catastrophic, with ripple effects to the safety of adjacent buildings and underground pipelines [1; 2; 3; 4]. In order to prevent such accidents, an important goal in the design and construction of foundation pits is to control the deformation of the soil and the retaining structures. Considering the uncertainties arising from the relevant parameters in the deformation process, the reliability approaches based on probability theory should be used to capture the randomness and variability of these parameters, yielding a probabilistic estimate of the safety level of the foundation excavations [5; 6; 7; 8; 9]. A significant number of studies are available in the literature regarding the deformation reliability assessment of retaining structures in foundation excavations. For example, [PERSON] et al. [10] investigated the influence of statistical parameter uncertainty on the probability of serviceability failure in braced excavations based on the Bootstrap method. [PERSON] et al. [11] conducted the probabilistic evaluation of serviceability failure in a braced excavation using the moment methods and the finite element platform PlaxisTM, and discussed the effect of spatial variability of soil parameters on the probability of serviceability failure. [PERSON] and [PERSON] [12] calculated the reliability index of braced retaining walls by approximating the nonlinear limit state surface through a neural network model. [PERSON] et al. [13] evaluated the lateral deformation of geosynthetic reinforced soil walls and abutments based on some selected methods. [PERSON] et al. [14] studied the reliability of reinforced retaining walls based on finite element modeling. The response surface approach was utilized to represent the performance function, coupling the first order reliability method to compute the reliability index. Many of the existing studies have performed reliability assessments of retaining structures in foundation pits based on finite element software, where the computational cost could be dramatically high. Another approach is to establish a relationship between the retaining structure deformation and some key factors such as the wall deformation mode, wall stiffness, soil properties, adjacent building characteristics, and others [15; 16; 17; 18]. However, these relationships are often empirically formulated and contain many unknown parameters to calibrate, which would become difficult in the presence of limited data and significant uncertainties. Alternatively, the direct use of in situ observed data could improve the accuracy and efficiency of structural reliability assessment [19; 20; 21; 22; 23; 24; 25]. For instance, [PERSON] et al. [22] investigated the impact of deep excavation on the adjacent metro shield tunnels using health monitoring data on the deformation. [PERSON] and [PERSON] [24] developed a procedure for the Bayesian back-analysis of retaining wall reliability, making use of the deflection data monitored at multiple locations. However, the incorporation of measurement error (ME) associated with data collection [26; 27] in the deformation reliability assessment of retaining structures has been limited discussed in previous studies. In fact, uncertain errors involved in the measurement of observations could deteriorate the quality of the data, and hence, the estimates of structural reliability [28; 29; 30]. This paper presents a method for deformation reliability analysis of retaining structures based on in situ monitoring data. The failure of a retaining structure is defined as a displacement at any depth exceeding the predefined threshold, which could differ from the engineering practice focusing on the deformations at the monitored depths only.