KEYWORDS: empirical models, Bayesian framework, fall cone test, undrained shear strength, liquidity index, debris flow

Empirical models are routinely used in the geotechnical engineering field for gross estimation of soil properties, because most of the tests, both in-site and laboratory, are either time-consuming or cost inefficient, inconvenient for preliminary design. However, the applicability of the empirical model to a specific site is questionable, since it does not necessarily contain the site information. Thus, in this study, the objective is to apply a Bayesian framework to incorporate the local data in model selection process to ensure a more suitable model; furthermore, a parameter updating process is followed to make the model more suitable for the site condition.

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KEYWORDS: empirical models, Bayesian framework, fall cone test, undrained shear strength, liquidity index, debris flow

Empirical models are routinely used in the geotechnical engineering field for gross estimation of soil properties, because most of the tests, both in-site and laboratory, are either time-consuming or cost inefficient, inconvenient for preliminary design. However, the applicability of the empirical model to a specific site is questionable, since it does not necessarily contain the site information. Thus, in this study, the objective is to apply a Bayesian framework to incorporate the local data in model selection process to ensure a more suitable model; furthermore, a parameter updating process is followed to make the model more suitable for the site condition.

Specifically, two widely used form of empirical models are considered. One is the regression model, another one is the probabilistic model. For the regression model, the relationship between the undrained shear strength (S_u) and liquidity index (LI) is used as a demonstration example. A thorough literature review is conducted to find out the existing relationships between the two variables. Moreover, since the local data is needed, several fall cone tests and Atterberg limit tests on artificially composed CDG soil are performed.

For the probabilistic model, the distribution of two important parameters for a debris flow, the maximum impact pressure (P) and total discharge (Q) is studied. Since there is no existing study regarding the correlation of the two parameters, the copula theory is used to construct the first empirical distribution model of the two parameters. The selection of the copula function is also completed through the Bayesian framework, and the resulted histogram showed satisfactory similarity.

Following the development of the joint model, it is updated by another 20 data, which is randomly selected from a group of 118 continuous debris flows. Owing to the multidimensional characteristic of the joint model, the Markov Chain Monte Carlo method is used to update the function. After updating, the prediction histogram presented a trend more similar to the continuous debris flow data, indicating the Bayesian framework indeed can improve the applicability of the model in this case.

The key contributions of this study includes the followings: firstly, the most suitable Su­-LI model for CDG soil in Hong Kong is determined with limited project-specific data. Secondly, with the Bayesian updating, a final best-fit model is proposed. Thirdly, a similar Bayesian updating is proved workable for a higher-order system, in estimating the five model parameters of the P-Q joint distribution in debris flows.