Analytical prediction of aggregates' effects on the ITZ volume fraction and Young's modulus of concrete

In order to evaluate analytically the ITZ volume fraction (f_ITZ) in concrete, a three phase model is proposed for the random concrete microstructure using the Voronoï tessellation. Within this model, the ITZ local thickness is a statistical variable depending on the local paste thickness available between each couple of neighbouring aggregates. The f_ITZ is found to not exceed 7% for typical concretes. Then, the concrete Young's modulus is predicted analytically using a four‐phase generalized self consistent model but in which the proposed f_ITZ is considered. It is found that the concrete Young's modulus increases when increasing aggregates volume fraction, aggregates maximum size and the proportion of coarse aggregates and when decreasing the ITZ thickness and Young's modulus. Finally, the validity of the proposed model is discussed based on a comparison between its predictions and three sets of experimental results related to normal and high strength concretes taken from literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Probabilistic analysis of strip footings resting on a spatially random soil using subset simulation approach

The failure probability of geotechnical structures with spatially varying soil properties is generally computed using Monte Carlo simulation (MCS) methodology. This approach is well known to be very time-consuming when dealing with small failure probabilities. One alternative to MCS is the subset simulation approach. This approach was mainly used in the literature in cases where the uncertain parameters are modelled by random variables. In this article, it is employed in the case where the uncertain parameters are modelled by random fields. This is illustrated through the probabilistic analysis at the serviceability limit state (SLS) of a strip footing resting on a soil with a spatially varying Young's modulus. The probabilistic numerical results have shown that the probability of exceeding a tolerable vertical displacement (P _e) calculated by subset simulation is very close to that computed by MCS methodology but with a significant reduction in the number of realisations. A parametric study to investigate the effect of the soil variability (coefficient of variation and the horizontal and vertical autocorrelation lengths of the Young's modulus) on P _e was presented and discussed. Finally, a reliability-based design of strip footings was presented. It allows one to obtain the probabilistic footing breadth for a given soil variability.     

Inverse analysis for geomaterial parameter identification using Pareto multiobjective optimization

An inverse analysis method that combines the back propagation neural network (BPNN) and vector evaluated genetic algorithm (VEGA) was proposed to identify mechanical geomaterial parameters for a more accurate prediction of deformation. The BPNN is used to replace the time‐consuming numerical calculations, thus enhancing the efficiency of the inverse analysis. The VEGA is used to find the Pareto‐optimal solutions to multiobjective functions. Unlike traditional back‐analysis methods which are based on only 1 type of field measurement and a single objective function, this proposed method can consider multiple field observations simultaneously. The proposed method was applied to the Shapingba foundation pit excavation located in Chongqing city, China. Two types of measurements are considered in the method simultaneously: the displacements in the x‐direction (north orientation) and those in the y‐direction (east orientation). Five deformation modulus parameters for artificial backfill soil, silty clay, siltstone, sandstone, and mudstone were selected as the inversion parameters. Compared with the weighted sum approach, the proposed method was demonstrated as an efficient multi‐objective optimization tool for back calculating undetermined parameters. After performing a forward‐calculation using the optimized parameters obtained by the inverse analysis, the predicted results were well consistent with the practical deformation in magnitude and trend.     

Room-temperature equation of state of Li<Subscript>2</Subscript>VOSiO<Subscript>4</Subscript> up to 8.5 GPa

High-pressure single-crystal X-ray diffraction measurements of lattice parameters of the compound Li₂VOSiO₄, which crystallises with a natisite-type structure, has been carried out to a pressure of 8.54(5) GPa at room temperature. Unit-cell volume data were fitted with a second-order Birch-Murnaghan EoS (BM-EoS), simultaneously refining V ₀ and K ₀ using the data weighted by the uncertainties in V. The bulk modulus is K ₀ = 99(1) GPa, with K′ fixed to 4. Refinements of third order equations-of-state yielded values of K′ that did not differ significantly from 4. The compressibility of the unit-cell is strongly anisotropic with the c axis (K ₀(c) = 49.7 ± 0.5 GPa) approximately four times more compressible than the a axis (K ₀(a) = 195 ± 3 GPa).     

Elasticity of CaSnO3 perovskite

The elastic properties of CaSnO₃ perovskite have been measured by both ultrasonic interferometry and single-crystal X-ray diffraction at high pressures. The single-crystal diffraction data collected using a diamond-anvil cell show that CaSnO₃ perovskite does not undergo any phase transitions at pressures below 8.5?GPa at room temperature. Ultrasonic measurements in the multianvil press to a maximum pressure of ～8?GPa at room temperature yielded S- and P-wave velocity data as a function of pressure. For a third-order Birch-Murnaghan EoS the adiabatic elastic moduli and their pressure derivatives determined from these velocity data are K _S0=167.2±3.1?GPa, K ^′ _S0=4.89±0.17, G ₀=89.3±1.0?GPa, G ^′ ₀=0.90±0.02. The quoted uncertainties include contributions from uncertainties in both the room pressure length and density of the specimen, as well as uncertainties in the pressure calibration of the multianvil press. Because the sample is a polycrystalline specimen, this value of K _S0 represents an upper limit to the Reuss bound (conditions of uniform stress) on the elastic modulus of CaSnO₃ perovskite. If the value of αγT is assumed to be 0.01, the value of K _S0 corresponds to K _T0=165.5±3.1?GPa. The 10 P-V data obtained by single-crystal diffraction were fit with a third-order Birch–Murnaghan equation-of-state to obtain the parameters V ₀=246.059±0.013 ų, K _T0=162.6±1.0?GPa, K ^′ _T0=5.6±0.3. Because single-crystal measurements under hydrostatic conditions are made under conditions of uniform stress, they yield bulk moduli equivalent to the Reuss bound on a polycrystalline specimen. The results from the X-ray and ultrasonic experiments are therefore consistent. The bulk modulus of CaSnO₃ perovskite lies above the linear trend of K ₀ with inverse molar volume, previously determined for Ca perovskites. This prevents an estimation of the bulk modulus of CaSiO₃ perovskite by extrapolation. However, our value of G ₀ for CaSnO₃ perovskite combined with values for CaTiO₃ and CaGeO₃ forms a linear trend of G ₀ with octahedral tilt angle. This allows a lower bound of 150?GPa to be placed on the shear modulus of CaSiO₃ by extrapolation.     

Consolidation in spatially random unsaturated soils based on coupled flow‐deformation simulation

This paper integrates random field simulation of soil spatial variability with numerical modeling of coupled flow and deformation to investigate consolidation in spatially random unsaturated soil. The spatial variability of soil properties is simulated using the covariance matrix decomposition method. The random soil properties are imported into an interactive multiphysics software COMSOL to solve the governing partial differential equations. The effects of the spatial variability of Young's modulus and saturated permeability together with unsaturated hydraulic parameters on the dissipation of excess pore water pressure and settlement are investigated using an example of consolidation in a saturated‐unsaturated soil column because of loading. It is found that the surface settlement and the pore water pressure profile during the process of consolidation are significantly affected by the spatially varying Young's modulus. The mean value of the settlement of the spatially random soil is more than 100% greater than that of the deterministic case, and the surface settlement is subject to large uncertainty, which implies that consolidation settlement is difficult to predict accurately based on the conventional deterministic approach. The uncertainty of the settlement increases with the scale of fluctuation because of the averaging effect of spatial variability. The effects of spatial variability of saturated permeability k_sat and air entry parameters are much less significant than that of elastic modulus. The spatial variability of air entry value parameters affects the uncertainties of settlement and excess pore pressure mostly in the unsaturated zone. Copyright © 2016 John Wiley & Sons, Ltd.     

Analysis of Critical Excavation Depth for a Jointed Rock Slope Using a Face-to-Face Discrete Element Method

Summary The critical excavation depth of a jointed rock slope is an important problem in rock engineering. This paper studies the critical excavation depth for two idealized jointed rock slopes by employing a face-to-face discrete element method (DEM). The DEM is based on the discontinuity analysis which can consider anisotropic and discontinuous deformations due to joints and their orientations. It uses four lump-points at each surface of rock blocks to describe their interactions. The relationship between the critical excavation depth D _s and the natural slope angle α, the joint inclination angle θ as well as the strength parameters of the joints c _r ,φ _r is analyzed, and the critical excavation depth obtained with this DEM and the limit equilibrium method (LEM) is compared. Furthermore, effects of joints on the failure modes are compared between DEM simulations and experimental observations. It is found that the DEM predicts a lower critical excavation depth than the LEM if the joint structures in the rock mass are not ignored.     

The behaviour of an elastic non-homogeneous half-space. Part I-line and point loads

In the first part of this paper solutions are developed for the response of a non-homogeneous half-space subjected to either a surface point load or a surface line load. The non-homogeneity considered is a variation in Young's modulus (E) with depth (z) which takes the form E=m_EZ^α where m_E is a constant and α is referred to as the non-homogeneity parameter. The variation of these solutions as the non-homogeneity parameter α varies between the limits of zero (homogeneous soil) to unity (Gibson soil) gives some fresh insight into both these limiting cases.     

Probabilistic analysis of the inverse analysis of an excavation problem

This study presents the probabilistic analysis of the inverse analysis of an excavation problem. Two techniques are used during two successive stages. First, a genetic algorithm inverse analysis is conducted to identify soil parameters from in situ measurements (i.e. first stage of the construction project). For a given tolerable error between the measurement and the response of the numerical model the genetic algorithm is able to generate a statistical set of soil parameters, which may then serve as input data to a stochastic finite element method. The second analysis allows predicting a confidence interval for the final behaviour of the geotechnical structure (i.e. second stage of the project). The tools employed in this study have already been presented in previous papers, but the originality herein consists of coupling them. To illustrate this method, a synthetic excavation problem with a very simple geometry is used.     

The compressibility of a natural apatite

In-situ synchrotron X-ray diffraction (XRD) experiments of a natural apatite with the formula of Ca₅(PO₄)₃F_0.94Cl_0.06 were carried out using a diamond anvil cell and angle-dispersive technique at Photon Factory (PF), Japan. Pressure–volume data were collected up to 7.12 GPa at 300 K. The pressures were determined from the ruby fluorescence spectra shift. The unit-cell parameters and volume decreased systematically with increasing pressure, and a reliable isothermal bulk modulus and its pressure derivative were obtained in this study. The third-order Birch–Murnaghan equation of state yielded the isothermal bulk modulus of K_T=91.5(38) GPa, its pressure derivative K_T= 4.0(11), and the zero-pressure volume V₀=524.2(3) ų.     

Application of extended Kalman filter to back analysis of the natural stress state accounting for measuring uncertainties

In this work, we present a numerical procedure for determining the nature stress state in the rock mass around a tunnel. A finite element method is applied for analyzing the direct problems of tunneling during the back analysis of parameter estimation, in which a no‐tension elastic–plastic model is used to simulate the elastic–tensile and elastic–plastic‐tensile failure states which often occur in the cases of underground excavation in heavily jointed rock masses. By considering the natural stress state as random parameters of the tunneling system, the Kalman filter method is employed for feedback analysis to modify the parameter values in a statistical context, which uses the prior information in the process of estimation and employs a set of displacements obtained from field measurements. To verify the effectiveness of the proposed method of inverse analysis, the developed numerical procedure is applied to a synthetic example of deep tunnels in yielding rock masses. The relative importance of the a priori and updating information is investigated, as is the importance of their uncertainty. The results show great potential of the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Compressibility of calcium ferrite-type MgAl2O4

 In situ X-ray diffraction experiments of calcium ferrite-type MgAl₂O₄ have been carried out using a diamond anvil cell combined with synchrotron radiation and an imaging plate X-ray detector under hydrostatic pressures up to 9 GPa. The observed unit-cell volumes at various pressures were fitted to the Birch-Murnaghan equation of state, yielding a bulk modulus of K _{T 0}= 241(3) GPa when K′ _{T 0}=4 is assumed. This relatively large bulk modulus of calcium ferrite-type MgAl₂O₄ is consistent with that expected from the systematic relation between bulk modulus and molar volume for the most compounds possessing fcc oxygen packing. Received March 5, 1996/Revised, accepted October 15, 1996     

The effect of composition and cation ordering on the compressibility of columbites up to 7 GPa

The unit-cell parameters of two columbite samples along the (Fe,Mn)Nb₂O₆ solid solution were measured by means of high-pressure single-crystal X-ray diffraction up to pressures of 7 GPa. The compressional behaviour of these minerals was studied as a function of composition and degree of order. The P–V data of all the samples were fitted with a third-order Birch–Murnaghan equation of state. For the two samples with different compositions but identical degree of order the substitution of Mn for Fe causes a decrease of the bulk modulus K _T0, from 153(1) to 146(1) GPa, without any effect on the pressure first derivative K′. For the two samples with the same composition, cation ordering causes an increase of the bulk modulus from 149(1) to 153(1) GPa and of the pressure first derivative from 4.1(2) to 4.8(3). The compressional behaviour is anisotropic with a linear axial compressibility scheme β _b > β _c ≥ β _a for all samples, regardless of composition and degree of order. Such anisotropy increases sligthly with increasing Mn content.     

An approach to large-scale field stress determination

The construction of stable structures in rock masses requires knowledge of the in situ stresses at the scale of excavations. However, the measurements obtained by the conventional overcoring technique are related to a small scale (centimetres). To extrapolate them to the scales of interest to rock mechanics (from meters to kilometres) requires a large number of individual stress measurements, followed by statistical analysis to avoid a considerable scatter of the measured values. In this paper, a method is proposed based on (a) large-scale surface stress and modulus measurements using the cylindrical jack method complemented by a special measuring scheme and then (b) back analysis for a given excavation shape. The method allows the simultaneous reconstruction of the stress components at the scale of excavation. A numerical simulation for a cylindrical excavation in an isotropic rock mass demonstrates the high accuracy and robustness of the method. The presence of a fractured zone surrounding the excavation can hamper the stress reconstruction, hence special measures should be taken to conduct the measurements in competent rock.     

Development of a framework of automated water quality parameter optimization and its application

This paper presents a methodology and framework for the development of an automated least-squares optimization tool for calibrating water quality parameters in QUAL2E. The method has been applied to estimate the optimal water quality parameters in simulation of stream water quality for the Anyang stream in Korea. The Monte Carlo analysis is used to assess the relative importance of model parameters for water quality constituents. It is found that μ_max and ρ are the most influential parameters for Chlorophyll-a modeling and K ₁ and K ₃ are critical parameters for variation of DO and BOD in the Anyang stream. A computer program for automated parameter calibration has been developed using a nonlinear GRG optimization algorithm. The application framework provides an intuitive and easy-to-use interface and allows visual evaluation of results. According to the simulation results, the automated approach is computationally efficient for evaluation of model parameters and converges on a best fit more rapidly and reliably than a trial and error method. The methodology proposed herein can be extended to other models to obtain the best possible parameter values.     

A case study on the behaviour of a deep excavation in sand

A complete case record of an excavation in sand is explored in this study. Numerical analyses were conducted to evaluate the influences of soil elasticity, creep and soil–wall interface. Back-analyses indicate small strain parameters should be used if an elastic–perfect plastic model is selected. In addition, excavation-induced seepage has only a limited effect on vertical displacements. Delayed installation of 3rd level struts and base slab construction caused significant time-dependent (creep) movements during the excavation. Back-analyses show that the dynamic viscosity (D_v) used in the visco-elastic model for creep simulation is in the range of 1.5 × 10¹⁵–2.0 × 10¹⁵ Pa, but there are still inconsistencies in movements both near to and far from the excavation. Interpreting from observation data, the creep rate of wall movement caused in the non-supported stage of the excavation varies between 0.14 and 0.38 mm/day. Finally, parametric studies of interface elements indicate that the most sensitive parameters are the normal (K_n) and shear stiffness (K_s) of the interface. Back-analyses using an elastic–perfect plastic model indicate that using 3 × 10⁶ Pa for K_n and K_s produces more acceptable results.     

Compressed History Matching: Exploiting Transform-Domain Sparsity for Regularization of Nonlinear Dynamic Data Integration Problems

In this paper, we present a new approach for estimating spatially-distributed reservoir properties from scattered nonlinear dynamic well measurements by promoting sparsity in an appropriate transform domain where the unknown properties are believed to have a sparse approximation. The method is inspired by recent advances in sparse signal reconstruction that is formalized under the celebrated compressed sensing paradigm. Here, we use a truncated low-frequency discrete cosine transform (DCT) is redundant to approximate the spatial parameters with a sparse set of coefficients that are identified and estimated using available observations while imposing sparsity on the solution. The intrinsic continuity in geological features lends itself to sparse representations using selected low frequency DCT basis elements. By recasting the inversion in the DCT domain, the problem is transformed into identification of significant basis elements and estimation of the values of their corresponding coefficients. To find these significant DCT coefficients, a relatively large number of DCT basis vectors (without any preferred orientation) are initially included in the approximation. Available measurements are combined with a sparsity-promoting penalty on the DCT coefficients to identify coefficients with significant contribution and eliminate the insignificant ones. Specifically, minimization of a least-squares objective function augmented by an l ₁-norm of DCT coefficients is used to implement this scheme. The sparsity regularization approach using the l ₁-norm minimization leads to a better-posed inverse problem that improves the non-uniqueness of the history matching solutions and promotes solutions that are, according to the prior belief, sparse in the transform domain. The approach is related to basis pursuit (BP) and least absolute selection and shrinkage operator (LASSO) methods, and it extends the application of compressed sensing to inverse modeling with nonlinear dynamic observations. While the method appears to be generally applicable for solving dynamic inverse problems involving spatially-distributed parameters with sparse representation in any linear complementary basis, in this paper its suitability is demonstrated using low frequency DCT basis and synthetic waterflooding experiments.     

Single-crystal x-ray diffraction of brucite to 14 GPa

Single-crystal brucite, Mg(OH)₂, was studied to 14 GPa in a quasi-hydrostatic pressure medium using a diamond anvil cell and energy-dispersive synchrotron x-ray diffraction. The parameters of a third-order Birch-Murnaghan equation of state fit to the data are: K _OT=42(2) GPa, and (?K _OT/?P)_T= 5.7(5). The bulk modulus is significantly lower than that obtained in recent shock compression and powder x-ray diffraction experiments under non-hydrostatic conditions. No evidence was found for a transition involving the Mg -O sub-structure over the pressure range of these experiments. This implies that the structural change previously identified at high pressure by Raman spectroscopy probably involves rearrangement of hydrogen atoms, leaving the Mg — O substructure largely unaffected.     

The high-pressure and temperature equation of state of a majorite solid solution in the system of Mg4Si4O12-Mg3Al2Si3O12

The high-pressure and temperature equation of state of majorite solid solution, Mj_0.8Py_0.2, was determined up to 23 GPa and 773 K with energy-dispersive synchrotron X-ray diffraction at high pressure and high temperature using the single- and double-stage configurations of the multianvil apparatuses, MAX80 and 90. The X-ray diffraction data of the majorite sample were analyzed using the WPPD (whole-powder-pattern decomposition) method to obtain the lattice parameters. A least-squares fitting using the third-order Birch-Murnaghan equation of state yields the isothermal bulk modulus, K _T0  = 156 GPa, its pressure derivative, K′ = 4.4(±0.3), and temperature derivative (∂K _T /∂T) _P = −1.9(±0.3)× 10⁻² GPa/K, assuming that the thermal expansion coefficient is similar to that of pyrope-almandine solid solution. Received: 5 October 1998 / Revised, accepted: 24 June 1999