Influence of Spatial Variability on the Uniaxial Compressive Responses of Rock Pillar Based on 3D Random Field

Author(s):  
Fuyong Chen ◽  
Wengang Zhang
Author(s):  
Recep M. Gorguluarslan ◽  
O. Utku Gungor

Abstract In this study, the influence of the spatial variability of geometric uncertainties on the strut members of the lattice structures fabricated by additive manufacturing is investigated. Individual struts are fabricated with various printing angles and diameters using a material extrusion process and PLA material. The diameter values of the fabricated samples are measured along the printing and radial directions at each layer under an optical microscope. Spatial correlations are characterized based on the measurements using the experimental autocorrelation function. Candidate autocorrelation functions are fitted to the measured data to identify the best fitted one for each diameter parameter and the corresponding correlation lengths are evaluated for random field. The applicability of the Karhunen-Loeve expansion (KLE) is investigated to reduce the dimensionality of the random field discretization. The results show that the diameters of the strut members at each layer are spatially dependent and the KLE method was found to give a good representation of the random field.


2019 ◽  
Vol 56 (8) ◽  
pp. 1169-1183 ◽  
Author(s):  
M.K. Lo ◽  
Y.F. Leung

This paper introduces an approach that utilizes field measurements to update the parameters characterizing spatial variability of soil properties and model bias, leading to refined predictions for subsequent construction stages. It incorporates random field simulations and a surrogate modeling technique into the Bayesian updating framework, while the spatial and stage-dependent correlations of model bias can also be considered. The approach is illustrated using two cases of multi-stage braced excavations, one being a hypothetical scenario and the other from a case study in Hong Kong. Making use of all the deflection measurements along an inclinometer, the principal components of the random field and model bias factors can be updated efficiently as the instrumentation data become available. These various sources of uncertainty do not only cause discrepancies between prior predictions and actual performance, but can also lead to response mechanisms that cannot be captured by deterministic approaches, such as distortion of the wall along the longitudinal direction of the excavation. The proposed approach addresses these issues in an efficient manner, producing prediction intervals that reasonably encapsulate the response uncertainty as shown in the two cases. The capability to continuously refine the response estimates and prediction intervals can help support the decision-making process as the construction progresses.


2019 ◽  
Vol 36 (9) ◽  
pp. 2929-2959
Author(s):  
Hui Chen ◽  
Donghai Liu

Purpose The purpose of this study is to develop a stochastic finite element method (FEM) to solve the calculation precision deficiency caused by spatial variability of dam compaction quality. Design/methodology/approach The Choleski decomposition method was applied to generate constraint random field of porosity. Large-scale laboratory triaxial tests were conducted to determine the quantitative relationship between the dam compaction quality and Duncan–Chang constitutive model parameters. Based on this developed relationship, the constraint random fields of the mechanical parameters were generated. The stochastic FEM could be conducted. Findings When the fully random field was simulated without the restriction effect of experimental data on test pits, the spatial variabilities of both displacement and stress results were all overestimated; however, when the stochastic FEM was performed disregarding the correlation between mechanical parameters, the variabilities of vertical displacement and stress results were underestimated and variation pattern for horizontal displacement also changed. In addition, the method could produce results that are closer to the actual situation. Practical implications Although only concrete-faced rockfill dam was tested in the numerical examples, the proposed method is applicable for arbitrary types of rockfill dams. Originality/value The value of this study is that the proposed method allowed for the spatial variability of constitutive model parameters and that the applicability was confirmed by the actual project.


Author(s):  
Zhimin Xi ◽  
Byeng D. Youn

So far manufacturing tolerance variability over samples has been widely considered in many engineering design problems. Traditionally the tolerance variability is modeled as a spatially independent random parameter although the variability is a function of spatial variables (x, y, and z) in many engineering applications. Little attention has been paid to spatial variability (or random field) in manufacturing and operational conditions, which may dominantly affect system performances in smaller scale applications. This paper presents an effective approach to characterize a random field for probability analysis and design. The Proper Orthogonal Decomposition (POD) method is employed to extract the important signatures of the random field over product samples. A normalized posteriori error is defined to automatically decide the minimal number of the important signatures while preserving a prescribed accuracy in approximating the random field. The random projected values of the spatial variability over the samples onto each important signature are modeled as a random parameter. The signatures and corresponding random parameters are thus used for modeling the random field. A Chi-Squae goodness-of-fit test is used for determining statistical models of random parameters. This proposed approach can facilitate to characterize the random field for probability analysis and design. By modeling the random field with the most significant random signatures, the Eigenvector Dimension Reduction (EDR) method can be employed for probability analysis because of its relatively high efficiency and accuracy. Two examples (one beam and Micro-Electro-Mechanical Systems (MEMS) bistable mechanism) are used to illustrate the effectiveness of the proposed approach while considering only a geometric random field. Compared to Monte Carlo Simulation (MCS), the proposed random field approach is appeared to be very accurate and efficient. Moreover, the results show that the random field variation cannot be neglected for probability analysis and design practices.


Author(s):  
Chao Shi ◽  
Yu Wang

Consolidation analysis is a key task for reclamation design. Although consolidation is a long-term process, acceleration of consolidation is often preferred for speeding up the reclamations. Before proposing measures to accelerate consolidation and reclamation process, it is imperative to have an accurate prediction of consolidation settlement for fine-grained materials, which is greatly affected by spatial distribution of subsurface zones with different soil types (i.e., stratigraphic heterogeneities and uncertainty) and spatial variability of soil properties. In current practice, calculation of consolidation settlement often uses simplified stratigraphic boundaries and deterministic consolidation parameters without considering stratigraphic uncertainty or soil property spatial variability. The oversimplified practice might result in unconservative estimations of consolidation settlement and pose threats to safety and serviceability of constructed facilities on reclaimed lands. In this study, a stochastic framework is proposed for consolidation settlement assessment with explicit modeling of stratigraphic uncertainty and spatial variability of soil properties by machine learning and random field simulation from limited site investigation data. The proposed method effectively generates multiple realizations of geological cross-section and random field samples of geotechnical properties from limited measurements and offers valuable insights into spatial distribution of the estimated total primary consolidation settlement curves and angular distortion.


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