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A generic clay database consisting of six parameters, including compression index ( Cc) and unloading–reloading index ( Cur), is compiled from 429 studies. This database, labeled as CLAY-Cc/6/6203, contains 6203 records. A data-driven approach of predicting Cc and Cur for a target site by combining sparse site-specific data with CLAY-Cc/6/6203 is illustrated. This data-driven approach consists of two steps. The first step is a learning step that adopts a hierarchical Bayesian model (HBM) to learn the prior information in CLAY-Cc/6/6203 (both inter-site and intra-site variabilities). The second step is a Bayesian inference step that updates the prior model into a posterior model. The inference outcome is a quasi-site-specific model. A real case study (Baytown, Texas, USA) is adopted to illustrate the application of the HBM-MUSIC-3X method in estimating and simulating the 3D spatially varying Cc and Cur profiles. The key conclusions are as follows: ( i) predictions from Big Indirect Data (BID) in the form of CLAY-Cc/6/6203 can be biased with large transformation uncertainty although data are abundant, ( ii) predictions from small (sparse) site-specific data are less biased but suffer from high statistical uncertainty although data are directly applicable, and ( iii) combining BID and site-specific data using an HBM learning strategy that accounts for site uniqueness is effective in terms of reducing prediction uncertainty.

Representative compression interpretation criteria were analysed to assess their relative merits and interrelationships when applied to drilled shafts socketed into rocks. Results of load tests around the world were gathered and collated into a database (CYCU/RockSocket/50) for the assessment. Each of the applied interpretation criteria was then evaluated and compared with one another and with the results of the interpretations of drilled shafts in various soil conditions and post-grouted drilled shafts. To assess the behaviour of drilled shafts socketed into rocks further, interpreted side and end bearing resistances were also determined. The mean interpreted capacities and displacements were higher for drilled shafts socketed into rocks when compared with drilled shafts in soils, but were comparable with those for tip post-grouted drilled shafts. On this basis, recommendations regarding specific interpretation criteria, which are advantageous for design displacement requirements under 12 mm for serviceability and displacements in the range of 53–71 mm for ultimate limit states, were established. Finally, behavioural assessments of the normalised load–displacement curves were extensively conducted using hyperbolic equations to test their effectivity to CYCU/RockSocket/50.

This study compiled a database called CYCU/RockTip/51 consisting of 51 rock socketed drilled shafts installed at different sites worldwide covering a wide variety of rock properties and shaft geometries. The tip resistances from seven representative prediction models are compared to the measured values. These measured values are obtained from the load-displacement curves of field load tests using three interpretation criteria. It was found that the prediction models of Teng, Coates, Rowe and Armitage, and ARGEMA over–predicted the measured capacity, while Zhang and Einstein, Vipulanandan et al., and Zhang are less biased. These tip prediction models also could be classified according to displacement requirements. The proposed tip prediction models of this study are presented based on different interpretation methods and the displacement ranges that they are mobilized. Finally, the normalized load displacement curve is fitted to hyperbolic curve with two model parameters (a and b). The a and b parameters define the reciprocal of the initial slope and the asymptotic resistance, respectively. The statistics of (b, a) for rock-socketed drilled shafts in CYCU/RockTip/51 are mean = (0.76, 1.09), COV = (0.13, 0.59), and a correlation coefficient = −0.79. These statistics are useful for reliability-based design.

The scale of fluctuation (SOF) is the critical parameter to describe the soil spatial variability, which significantly influences the embedded geostructures. Due to the limited data in the horizontal direction, horizontal SOF estimation is relatively challenging and not well studied yet. This paper aims to develop an efficient convolutional neural network (CNN)-based approach for estimating the horizontal SOF by coupling random field and limited CPT data. Two or three columns (i.e. pseudo-CPT) were selected from the simulated 2D random field with prescribed SOF at the same spacing and combined into a two-dimensional matrix as input data to train the CNN model, namely CNN2 and CNN3 models. The dataset of CNN2 and CNN3 models contains 196,670 and 149,420 samples. Results on the training and testing datasets show that the trained CNN model has a good estimation performance as the mean squared error value is less than 0.1 and the correlation coefficient value is larger than 0.99. The effectiveness of trained CNN models was further verified by the new simulated CPT data with untrained SOF from the random field and CPT data from real site in Hollywood, South Carolina. The excellent agreement indicates that the trained CNN model has the ability to capture the horizontal SOF for limited CPT data from the actual project. Finally, the collected CPT data from the Shanghai site was applied for application. The COV of the estimated results of CNN3 and CNN2 models for the Shanghai site is 0.09 and 0.40, indicating the estimation performance of the CNN3 model has less variability than the CNN2 model. The proposed method provides the potential to characterize the soil spatial variability using very limited CPT data.

This paper evaluates the effects of tip post-grouting on various capacity interpretation criteria for drilled shafts under compression loading. A wide array of load test data for drilled shafts constructed using three post-grouting methods, including tube-a-manchette, flat jack, and jet grouting, is utilized for the analysis. The load tests were divided based on the different tip post-grouting methods, then they were further divided based on the soil conditions (undrained or drained). The interpreted capacity and displacement at the interpreted capacity are examined for each interpretation criterion. Furthermore, the interpreted results were compared with current studies on drilled shafts that are not subjected to tip post-grouting techniques to determine the effects of post-grouting methods. Based on these analyses, the normalized load–displacement curves and the relationships between various interpretation criteria for drilled shafts with tip post-grouting are established. The drilled shafts subjected to any post-grouting method produced higher capacity and yield larger displacement with the same amount of normalized capacities for undrained and drained soils compared to drilled shafts not subjected to any post grouting procedures. Among the three grouting methods studied, the jet grouting method can produce a greater capacity than the other methods, especially for drained soil conditions. Finally, specific recommendations to guide the design of drilled shafts with tip post-grouting are provided.

Modelling and simulation of spatially or temporally varying geo-data play a pivotal role in the development of digital twins of civil infrastructures and smart cities. Measurements on geo-data are ...

The choice of the characteristic value of a material property is fundamental in all civil engineering design and critical in geotechnical engineering. Based on our tradition, we strive to look for a cautious value, whose evaluation includes our engineering judgement. While the definition of a characteristic value is often given with the aid of statistics as a fractile value, its determination includes considerations of mechanics because “value” refers to the relevant quantity affecting the limit state. Soils are complex, often spatially heterogeneous and our knowledge of them is typically based on sparse incomplete data. This makes the definition and determination of a characteristic value for soils more multifaceted than for structural materials. This paper discusses the choice of the characteristic value for soils from various perspectives (statistical, mechanistic and practical) and summarises some recent findings to clarify the limitations of existing practice. Overly simplified statistical approaches may lead to unsafe or overly conservative designs. The authors conclude that a balance between practicality and incorporating salient features are needed. By increasing the value of data in design decisions, engineers will be motivated to collect, share, and utilise data as much as possible and bring our practice closer to the digital economy. publishedVersion

The efficient propagation of imprecise probabilities through expensive simulators has emerged to be one of the great challenges for mixed uncertainty quantification in computational mechanics. An active learning method, named Collaborative and Adaptive Bayesian Optimization (CABO), is developed for tackling this challenge by combining Bayesian Probabilistic Optimization and Bayesian Probabilistic Integration. Two learning functions are introduced as engines for CABO, where one is introduced for realizing the adaptive optimization search in the epistemic uncertainty space, and the other one is developed for adaptive integration in the aleatory uncertainty space. These two engines work in a collaborative way to create optimal design points adaptively in the joint uncertainty space, by which a Gaussian process regression model is trained and updated to approach the bounds of model response moments with pre-specified error tolerances. The effectiveness of CABO is demonstrated using a numerical example and two engineering benchmarks.

Site characterisation is a cornerstone of geotechnical and rock engineering. “Data-driven site characterisation” refers to any site characterisation methodology that relies solely on measured data,...

Spatial variability in soil shear strength affects the occurrence of the ultimate limit state not only by the spatial averaging along the potential slip curve but also by seeking out mechanically a...

Various uncertainties arising during acquisition process of geoscience data may result in anomalous data instances (i.e., outliers) that do not conform with the expected pattern of regular data instances. With sparse multivariate data obtained from geotechnical site investigation, it is impossible to identify outliers with certainty due to the distortion of statistics of geotechnical parameters caused by outliers and their associated statistical uncertainty resulted from data sparsity. This paper develops a probabilistic outlier detection method for sparse multivariate data obtained from geotechnical site investigation. The proposed approach quantifies the outlying probability of each data instance based on Mahalanobis distance and determines outliers as those data instances with outlying probabilities greater than 0.5. It tackles the distortion issue of statistics estimated from the dataset with outliers by a re-sampling technique and accounts, rationally, for the statistical uncertainty by Bayesian machine learning. Moreover, the proposed approach also suggests an exclusive method to determine outlying components of each outlier. The proposed approach is illustrated and verified using simulated and real-life dataset. It showed that the proposed approach properly identifies outliers among sparse multivariate data and their corresponding outlying components in a probabilistic manner. It can significantly reduce the masking effect (i.e., missing some actual outliers due to the distortion of statistics by the outliers and statistical uncertainty). It also found that outliers among sparse multivariate data instances affect significantly the construction of multivariate distribution of geotechnical parameters for uncertainty quantification. This emphasizes the necessity of data cleaning process (e.g., outlier detection) for uncertainty quantification based on geoscience data.

A generic rock mass database consisting of nine parameters is compiled from 225 studies. The nine parameters are the deformation modulus, elastic modulus, dynamic modulus, rock quality designation, rock mass rating, Q-system, geological strength index of a rock mass, as well as intact-rock Young’s modulus and intact-rock uniaxial compressive strength. This generic database, labeled as ROCKMass/9/5876, consists of 5876 rock mass cases. The goal of this paper is to examine how an existing transformation model such as deformation modulus versus rock mass rating can be made more unbiased and more precise for a specific site by combining sparse site data with ROCKMass/9/5876 in a manner sensitive to site-specific differences. The outcome is a quasi-site-specific transformation model. Four methods are studied to construct a quasi-site-specific transformation model for the deformation modulus of a rock mass: probabilistic multiple regression (current state of practice), hybridization method, hierarchical Bayesian model, and similarity method. The results from two case studies in Turkey show that the hierarchical Bayesian model is the most effective.

The characterization of in situ ground conditions is essential for geotechnical practice. The probabilistic estimation of soil parameters can be achieved via updating with monitoring data within the Bayesian framework. The estimation of spatially varying soil parameters is seldom undertaken with time-variant monitoring data. In this study, an efficient Bayesian method is presented for the estimation of spatially varied saturated hydraulic conductivity ks of unsaturated soil slope with spatiotemporal monitoring data. The computationally cheap surrogate model of the adaptive sparse polynomial chaos expansion method is adopted to approximate the transient numerical model. Markov chain Monte Carlo method is used for the probabilistic estimation of basic random variables. Based on the hypothetical cases, the effects of monitoring frequency and stage are studied. The errors and the uncertainties of the estimated ks fields are increased with the decreasing monitoring frequency. Bayesian estimation of spatial variability is more accurate when using the later stage of monitoring data. The estimated method is further verified with a real case study by the comparison of borehole data, dynamic probe test (DPT) data, and field monitoring data. The distribution of the soil types acquired from boreholes is reflected in the estimated ks. The estimated field of ks has a certain agreement with the borehole log and DPT measurements and can reproduce the spatial variability of the site to an acceptable degree.

A hole-effect autocorrelation function is one that is non-monotonic or pseudo-periodic as defined in the geostatistics literature. This paper shows that such an autocorrelation function (AC...

In geotechnical engineering, it is challenging to construct a site-specific multivariate probability distribution model for soil/rock properties because the site-specific data are usually s...

An industry survey suggests an increasing application of high-displacement helical piles with greater shaft and helix diameters to support various structures. In this paper, a database of 84 static load tests is compiled and analyzed to evaluate the disturbance effect and characterize the model factors that can be used for reliability-based limit state design. The measured capacity is defined as the load at a pile head settlement equal to 5% of helix diameter. For similar helix configurations tested at the same site, the ratio of uplift to compression capacity indicates a low degree of disturbance for very stiff clay (0.8–1) and a medium degree of disturbance for dense sand (0.6–0.8). At the ultimate limit state, the model factor is defined as the ratio between measured and calculated capacity, where three design guidelines are considered. A hyperbolic model with two parameters is used to fit the load–displacement curves. At the serviceability limit state, the model factor can be defined with the hyperbolic parameters. Based on the database, probabilistic distributions of the capacity model factor and hyperbolic parameters are established. Finally, the capacity model statistics are applied to calculate the resistance factor in the load and resistance factor design.

The story of statistics in geotechnical engineering can be traced to Lumb’s classical Canadian Geotechnical Journal paper on “The Variability of Natural Soils” published in 1966. In parallel, the s...

In this study an effective stress model for cement-treated soil is employed to carry out a systematic study on cement-treated soil slab used to control the wall displacement in excavations with thick, soft clay layers. Deterministic analyses were first conducted to assess the drainage state of the treated soil slab. These indicate that, under timescales which are representative of those in actual construction, cement-treated soil slab conditions may range from nearly undrained to drained. Random finite-element analyses also show that the global undrained and drained behaviour of the treated soil slab differ significantly. Undrained loading leads to a rapid rise in stress with strain to a peak strength with subsequent softening. Drained behaviour, on the other hand, leads to a more compliant response, which suggests that the main issue in the drained condition is likely to be large displacement, rather than complete collapse. A rational design framework for cement-treated soil slab is proposed, which explicitly considers the distribution in global behaviours of the treated soil slab. This differs from current limit state approaches which are largely based on statistical properties of the input data, such as the unconfined compressive strength of sampled cores.

For steel H-piles under axial compression, 177 static load tests were used to evaluate the performance of the Chin-Davisson method to (1) interpret pile capacity and (2) characterise the statistics...