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The probability analysis of ground deformation is becoming a trend to estimate and control the risk brought by shield tunnelling. The gap parameter is regarded as an effective tool to estimate the ground loss of tunnelling in soft soil. More specifically, ω, which is a gap parameter component defined as the over (or insufficient) excavation due to the change in the posture of the shield machine, may contribute more to the uncertainty of the ground loss. However, the existing uncertainty characterization methods for ω have several limitations and cannot explain the uncertain correlations between the relevant parameters. Along these lines, to better characterize the uncertainty of ω, the multivariate probability distribution was developed in this work and a dynamic prediction was proposed for it. To attain this goal, 1 523 rings of the field data coming from the shield tunnel between Longqing Road and Baiyun Road in Kunming Metro Line 5 were utilized and 44 parameters including the construction, stratigraphic, and posture parameters were collected to form the database. According to the variance filter method, the mutual information method, and the value of the correlation coefficients, the original 44 parameters were reduced to 10 main parameters, which were unit weight, the stoke of the jacks (A, B, C, and D groups), the pressure of the pushing jacks (A, C groups), the chamber pressure, the rotation speed, and the total force. The multivariate probability distribution was constructed based on the Johnson system of distributions. Moreover, the distribution was satisfactorily verified in explaining the pairwise correlation between ω and other parameters through 2 million simulation cases. At last, the distribution was used as a prior distribution to update the marginal distribution of ω with any group of the relevant parameters known. The performance of the dynamic prediction was further validated by the field data of 3 shield tunnel cases.

We consider a discrete search problem to detect a hidden target on one of the M-intersected real lines at the origin. The target position is a vector of independent random variables with a known multivariate probability distribution that is symmetric around the origin. From the available information about the probability of the target, we can consider one bounded interval as a search space on each line. To maximize the detection probability, we divide each interval into a number of small subintervals. Some subintervals have low target probabilities; thus, we delete them and distribute their probabilities among the searched subintervals. The problem has a discrete version where each line contains a set of independent search subintervals. The search effort is bounded by a normal distribution. More than obtaining the maximum detection probability, we also need to get the minimum search effort to detect the target. After studying the stability of the minimum search effort, we present an illustrative example to show the effectiveness of our model. [ABSTRACT FROM AUTHOR]

Probabilistic site characterization is the cornerstone of data-centric geotechnics, which underpins the digitalization in geotechnical engineering. The essential aspect of probabilistic site characterization is to reasonably infer the probability density distributions of geotechnical parameters, based on field and laboratory data. In this paper, a clay property database, SZ-CLAY/11/5130, was established by collecting geotechnical investigation reports from 52 engineering projects in Shenzhen city. This SZ-CLAY/11/5130 database was first compared with the global clay database CLAY/10/7490 and the Shanghai clay database SH-CLAY/11/4051, in terms of their sample ranges, correlations, and scatter plots. Then, the multivariate probability distribution of eight clay parameters was established using the training records selected from SZ-CLAY/11/5130, to characterize the generic correlations between multiple clay parameters. Based on Bayesian theory, the posterior distributions of clay mechanical parameters from a construction site in Shenzhen city were updated using both the site-specific correlations and the generic correlations given by SZ-CLAY/11/5130. The constructed multivariate probability density distribution is necessary for this updating step. [ABSTRACT FROM AUTHOR]