Elastic Stiffness Coefficients Research Articles

Evaluation of carotid artery elasticity and its influencing factors in non-obese PCOS patients using a technique for quantitative vascular elasticity measurement.

To evaluate the intima-media thickness (IMT) and elasticity of the carotid artery in non-obese polycystic ovary syndrome (PCOS) patients using a quantitative technique for vascular elasticity measurement and to explore the influencing factors. Sixty non-obese patients without metabolic and cardiovascular diseases who were diagnosed with PCOS in the Women and Children's Hospital of Chongqing Medical University from January to December 2022 were prospectively selected (case group), and 60 healthy volunteers matched for body mass index were included as the control group. Body weight, height, heart rate, blood pressure, and waist-to-hip ratio were recorded. Fasting blood samples were drawn from the elbow vein to measure hormone levels including total testosterone (TT), sex hormone-binding globulin (SHBG), fasting plasma glucose (FPG), fasting insulin (FINS), lipids, and homocysteine (Hcy). The insulin resistance index (HOMA-IR) and free androgen index (FAI) were calculated. Ultrasound elastography was used to measure the IMT and elastic function parameters of the right carotid artery, including vessel diameter, wall displacement, stiffness coefficient, and pulse wave velocity. Differences in various parameters between the two groups were analyzed, and correlations between the carotid stiffness coefficient and other serological indicators were assessed using Spearman correlation analysis. No significant differences in age, body mass index, heart rate, systolic blood pressure, and diastolic blood pressure were observed between the two groups (all P>0.05), while the waist-to-hip ratio (WHR) was higher in the case group than in the control group (P<0.05).The hormone level serological indicators TT and FAI were higher in the case group than in the control group, and SHBG was lower in the case group than in the control group (all P<0.05). The metabolism-related serum indicators LDL-C, HDL-C, FPG, triglycerides, and total cholesterol levels were not statistically different between the two groups (all P>0.05), and serum FINS, HOMA-IR, and Hcy levels were significantly higher in the case group than in the control group (all P<0.05).No significant difference in carotid artery diameter was observed between the case group and control group (P>0.05). The carotid artery displacement in the case group was significantly smaller than that in the control group (P<0.05), and carotid IMT, hardness coefficient, and pulse wave propagation velocity were greater in the case group than in the control group (all P<0.05). The carotid elastic stiffness coefficient was positively correlated with WHR, TT, SHBG, FAI, FINS, HOMA-IR and Hcy to varying extents and negatively correlated with SHBG. In non-obese PCOS patients with no metabolic or cardiovascular disease, the carotid stiffness coefficient was increased and correlated with indicators of hyperandrogenism, insulin resistance, and hyperhomocysteinemia.

Omni-directional wavenumber dictionary modified imaging method for orthotropic composites damage detection using ultrasonic guided waves

The sparse reconstruction imaging method is promising for detecting damage in isotropic and quasi-isotropic materials. However, its effectiveness relies on an accurate dictionary. When applied to orthotropic materials without accounting for wavenumber directionality, the accuracy of the dictionary degrades, leading to inaccurate damage localization. To address this limitation, this paper presents an omnidirectional wavenumber dictionary modified imaging method for orthotropic composites damage detection. The omni-directional wavenumber dispersion curve of ultrasonic guided waves is calculated numerically by converting of elastic stiffness coefficient of orthotropic composites at various propagation angles. A modified propagation model, informed by the omni-directional wavenumber dispersion curve, enhances the precision of the acoustic field dictionary. Utilizing a coherent matched field processor, the method compares the scattered signal's envelope with the acoustic field dictionary's envelope to generate an ambiguity function, which in turn forms a damage image. Simulation and experimental results confirm the method's superiority in resolving damage localization inaccuracies and artifacts typically associated with orthotropic composites. The proposed method exhibits enhanced signal-to-noise ratio and lower positioning error, facilitating precise multi-damage detection in orthotropic composites compared to existing methods.

Electronic, optical and elastic properties of AgCuS

DFT calculation is used to investigate the structural, electronic, optical, and elastic properties of AgCuSe and AgCuS. The calculations are performed using the ATK with generalized gradient approximation (GGA) in combination with Hubbard U correction parameters for both structures. The calculated band gap energies and partial density of state reveal that AgCuS has semiconductor properties unlike this AgCuSe has a metallic nature. The optical properties, real and imaginary parts of dielectric function are obtained for the energy range of 0 to 5 eV. Elastic stiffness coefficients (Cij), bulk modulus (B), shear modulus (G), and Young modulus (E) have been calculated.

Computational exploration of janus ZrMCO2 (M=Ti, hf) MXenes for optoelectronic and photocatalytic applications

MXenes exhibit unique structural flexibility, excellent carrier mobility and abundant active sites, making them valuable catalysts in photocatalysis. The electronic properties and photocatalytic activity of Janus ZrMCO2 (M = Ti, Hf) MXenes are investigated by hybrid HSE06 functional. Photocatalytic activities of hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) are further explored. Structural stability is proved by negative cohesive energy and elastic stiffness coefficients. ZrTiCO2 and ZrHfCO2 are all direct semiconductors. Ti/Hf doping makes conduction band minimum (CBM) have a redshift and induces the reduction of band gaps of Janus systems. The three systems are potential photocatalysts due to their appropriate bandgaps and significant absorption in visible region. The irradiation-generated holes and electrons can easily drive the HER or OER on ZrHfCO2 MXene due to the small overpotential. ZrHfCO2 and Zr2CO2 are highly efficient for photocatalytic hydrogen production with STH efficient of 30.3%. Hf doping improves the photocatalytic reduction of CO2, while The Ti/Hf doping doesn't improve the N2 reduction.

Research on a Calculation Method for the Horizontal Displacement of the Retaining Structure of Deep Foundation Pits

The precise calculation and effective control of the horizontal displacement of deep foundation pit retaining structures are critical for foundation pit support design and construction. Based on stress–strain linear elastomer theory and considering the deformation coordination between an enclosure wall and its internal support member, a formula for the redundant restraint force acting on the retaining wall was derived through the unit load method and the principle of elastic superposition. Moreover, a method for calculating the horizontal displacement of the retaining structure of a deep foundation pit was formulated, which is convenient for engineering applications. The method can also be used to calculate the horizontal displacement of cantilevered and anchored retaining structures when the loading conditions of the deep foundation pit and the relevant parameters of the enclosure structure are known. A case study was conducted on a standard section with an excavation width H of 19.3 m and an excavation depth h of 17.8 m. The structural parameters of the enclosure wall, along with the elastic support stiffness coefficient and soil layer parameters of the pit, were inputted into a MATLAB calculation code. Then, four internal support constraint forces Fi and the calculated values for the horizontal displacement of the enclosure wall were obtained after running the code. The calculated curve closely matched the curve of values measured in the field. The horizontal displacements of the top of the wall of several cement–soil gravity enclosure structures mentioned in the literature were also calculated. The results of these calculations were then compared with the measured data and corresponding data from the literature. The examples provided clear evidence demonstrating that the proposed method is highly reliable for calculating the horizontal displacement of deep foundation pit enclosure structures.

Using resonant ultrasound spectroscopy to characterize thermally conditioned high explosive materials

The ability to nondestructively quantify changes in mechanical properties of granular high explosive materials due to thermal conditioning is of importance for a myriad of civil and defense applications and could lead to better understanding of environmental aging-related effects for explosive material performance and safety. In this study, we report the first demonstration of using resonant ultrasound spectroscopy (RUS) to quantify the bulk elastic properties of granular high explosive materials at different bulk pressing densities and degree of thermal conditioning. Monitoring elastic property changes in granular explosive pressings has not yet been demonstrated using RUS, which is an appealing nondestructive characterization tool since it requires only dry point contact with the explosive material and can be applied to explosives with small form factors. Here, explosive material was studied in the form of binderized plastic bonded explosive pressings and unbinderized neat pressings, both of which are used commercially. Elastic stiffness coefficients calculated from the RUS measurements on the binderized and neat pressings show a significant increase for the post-conditioned samples compared to the pre-conditioned samples. This trend of increasing elastic properties with thermal conditioning was consistent for different density pressings and different thermal exposure conditions. [This work was performed by LLNL under Contract No. DE-AC52-07NA27344 and document release number LLNL-ABS-858868.]

Elastic anomalies across the P21mn→Pnnm structural phase transition in δ-(Al,Fe)OOH

Abstract Hydrogen may be recycled into the Earth's lower mantle by subduction and stabilized in solid solutions between phase H (MgSiO4H2), δ-AlOOH, ε-FeOOH, and SiO2 post-stishovite. In high-pressure oxyhydroxide phases, hydrogen is incorporated following the typical (OHO) sequence, adopting the asymmetric configuration O-H···O that evolves into a symmetric disordered state upon compression. Moreover these iron-/aluminum-bearing oxyhydroxides [δ-(Al,Fe)OOH] present a structural phase transition from P21nm to Pnnm as pressure increases. Here, the single-crystal elasticity of the P21nm phase of δ-(Al0.97,Fe0.03)OOH has been experimentally measured across the P21nm→Pnnm transition up to 7.94(2) GPa by simultaneous single-crystal X-ray diffraction (XRD) and Brillouin spectroscopy at high pressures. The transition appears to be continuous, and it can be described with a second, fourth and six order terms Landau potential. Our results reveal an enhanced unit-cell volume compressibility, which is linked to an increase of the b- and a-axes linear compressibility in the P21nm phase of δ-(Al0.97,Fe0.03)OOH prior to the transition. In addition, we observed the presence of elastic softening in the P21nm phase that mostly impacts the elastic stiffness coefficients c12, c22 and c23. The observed elastic anomalies cause a significant change in the pressure dependence of the adiabatic bulk modulus (KS). These results provide a better understanding of the relation between elasticity, P21mn→Pnnm structural phase transition and hydrogen dynamics in δ-(Al0.97,Fe0.03)OOH, which may be applied to other O-H···O-bearing materials.

Demonstrating resonant ultrasound spectroscopy as a viable technique to characterize thermally conditioned high explosive materials

We present results of resonant ultrasound spectroscopy (RUS) measurements applied to granular high explosive materials at different bulk pressing densities and degree of thermal conditioning. The material chosen in this study is a ubiquitously used explosive material known as pentaerythritol tetranitrate (PETN), which is used commercially in civil and defense applications both as a binderized plastic bonded explosive material and an unbinderized neat material. However, changes in granular PETN bulk elastic properties due to thermal conditioning, which could have implications for better understanding environmental aging-related effects, have not been well studied even though it is believed that elasticity may play an important role in explosive material initiation mechanisms. Furthermore, monitoring elastic property changes in granular explosive pressings has not yet been demonstrated using RUS, which is an appealing non-destructive characterization tool that requires only dry point contact with the explosive material. To this end, we report the first study using RUS to quantify the elastic properties of binderized and neat PETN pressings as well as to quantify changes in elastic properties as a function of both thermal conditioning and bulk pressing density. Elastic stiffness coefficients, sometimes more commonly referred to as elastic constants, calculated from the RUS measurements on the different PETN-based materials show a significant increase for the post-conditioned samples compared to the pre-conditioned samples. This trend of increasing elastic properties with thermal conditioning was consistent for different density pressings, different thermal exposure conditions, and even different neat PETN pressings of differing average crystal sizes and/or specific surface areas.

Analysis of an interfacial crack between two nonhomogeneous piezoelectric materials using a new domain-independent interaction integral

Considering the difficulties introduced by piezoelectric material non-homogeneity and discontinuities to interfacial crack analysis, a domain-independent interaction integral (DII-integral) is proposed to derive the stress intensity factors (SIFs) and electric displacement intensity factor (EDIF) of an interfacial crack between nonhomogeneous piezoelectrics. For continuously varying material properties, traditional interaction integral (I-integral) needs to compute the derivatives of material parameters with respect to the x1 direction of the local coordinate system, while the proposed DII-integral is demonstrated to be unrelated to any derivatives of material parameters. Furthermore, a significant improvement is achieved that the new formulation of I-integral remains valid even when the integration domains include intricate and multiple interfaces, as long as the material interfaces are perfectly bonded. Firstly, the intensity factors (IFs) calculated by the combination of the DII-integral and the extended finite element method are compared with the analytical solutions, and it is found that the relative errors of the IFs are all less than 1.79 % with various crack lengths, which verifies the accuracy of the proposed method. For the piezoelectric bi-material model with continuously nonhomogeneous properties, the calculated IFs match each other well (relative deviation < 1.3 %) for different sizes of integration domains. In addition, for the perfectly bonded interface with discontinuous electromechanical properties, the IFs are almost identical (relative deviation < 0.85 %) whether or not the integration domain contains the material interface, which further numerically verifies the good domain-independence of the established DII-integral. For an interfacial crack near extra interfaces, the differences in elastic stiffness and piezoelectric coefficient between interface sides have an obvious influence on mode-I SIF, but mode-II SIF and EDIF are affected mainly by piezoelectric coefficient and dielectric permittivity.

Ab-initio Investigation of Elastic Properties of Monoclinic ZnAs2 Crystal

Elastic properties of monoclinic ZnAs2 crystal are studied under the PBEsol scheme using the CRYSTAL Program. Independent elastic stiffness coefficients have been computed. Various elastic properties, such as shear modulus, bulk modulus, Young’s modulus and Poisson’s ratio have been analyzed. The directional dependence of the computed Young’s modulus and linear compressibility is studied using ELATE software. Our investigation reveals the finite elastic anisotropy of the monoclinic ZnAs2 crystal.

Probabilistic investigations on the elastic stiffness coefficients for suction caisson considering spatially varying soils

The importance of accurate estimation of elastic stiffness coefficients of suction caisson has been already highlighted in previous works. Nonetheless, studies related to the spatial non-uniformity of the clayey seabed are somewhat limited, and current theoretical solutions are usually established using deterministic soil properties, overlooking the inherent uncertainty of the soil. This study focuses on the elastic performance of suction caisson in spatially random soils using three-dimensional (3D) small strain random finite element analyses within a Monte-Carlo framework. The non-uniformity of soil is mapped by modeling the shear modulus as a random field. The influences of soil profiles, embedment ratios and random field parameters on the elastic stiffness coefficients are comprehensively quantified. Results demonstrate that the spatially varying shear modulus notably alters the failure mechanism, which in turn significantly affects the elastic stiffness coefficients, ignoring soil variation will provide non-conservative predictions. To deal with the uncertainty of soil shear modulus, a series of expressions are developed by adding reliability-related parameters to the existing theoretical solutions, which can be adopted to calculate quantiles of stiffness coefficients corresponding to several given probabilities. The findings of this research may potentially facilitate the elastic performance assessment of suction caisson.

Study of Elastic and Structural Properties of BaFe2As2 Ultrathin Film Using Picosecond Ultrasonics.

We obtain the through-thickness elastic stiffness coefficient (C33) in nominal 9 nm and 60 nm BaFe2As2 (Ba-122) thin films by using picosecond ultrasonics. Particularly, we reveal the increase in elastic stiffness as film thickness decreases from bulk value down to 9 nm, which we attribute to the increase in intrinsic strain near the film-substrate interface. Our density functional theory (DFT) calculations reproduce the observed acoustic oscillation frequencies well. In addition, temperature dependence of longitudinal acoustic (LA) phonon mode frequency for 9 nm Ba-122 thin film is reported. The frequency change is attributed to the change in Ba-122 orthorhombicity (a-b)/(a+b). This conclusion can be corroborated by our previous ultrafast ellipticity measurements in 9 nm Ba-122 thin film, which exhibit strong temperature dependence and indicate the structural phase transition temperature Ts.

Pine wood extraction by fermentation to improve its acoustical efficiency

Wood is a main material in the construction of musical instruments and speaker boxes, especially in developed countries. This study investigated the changes in acoustic properties of pine wood during the processes of fermentation, water washing, and organic washing solvent. The results indicated that both methods of water washing and ethanol-acetone mixture washing of the samples improved the values of density, modulus of elasticity, elastic stiffness, acoustic coefficient, vibration damping, and acoustic conversion efficiency. The effect of ethanol-acetone mixture washing was greater than water washing the samples. Additionally, results revealed that pretreatment before ethanol-acetone mixture washing had the most effect on vibration damping and acoustic conversion efficiency values. In general, the values obtained from ethanol-acetone mixture washing resulted in more improvement in acoustic properties compared to water washing, but the results showed that the pretreatment before water washing had a greater effect on the values of density, modulus of elasticity, elastic stiffness, and acoustic coefficient.

Thermoelastic properties of non-metamict zircon

Abstract The thermoelastic properties and thermal expansion of natural single-crystal zircon without detectable radiation damage were determined in the temperature range between 100 and 1650 K on five samples from Cambodia, Sri Lanka, and Tanzania. Up to about 1500 K, the results are in excellent agreement and fully reversible. The average adiabatic elastic stiffness coefficients at room temperature in GPa are c11 = 426.8(6), c12 = 68.1(4), c13 = 152.0(4), c33 = 490.8(9), c44 = 113.1(2), and c66 = 49.0(1). Polycrystalline averaging for the aggregate bulk and shear modulus (Voigt-Reuss-Hill average) yields K = 229.3(4) GPa and G = 109.3(1) GPa. From 293 to 1573 K, the elastic stiffnesses soften almost linearly with the temperature coefficients in MPa/K: dc11/dT = –45.36(7), dc12/dT = –2.03(7), dc13/dT = –9.59(7), dc33/dT = –42.85(12), dc44/dT = –9.60(3), and dc66/dT = –2.19(1). Below room temperature, the behavior of the cij is nonlinear, with decreasing absolute values of the temperature coefficients. Above about 1500 K, a temperature- and time-dependent irreversible elastic stiffening accompanied by an increasing ultrasound dissipation was observed in all samples. These anomalies are interpreted to be the consequence of increased dislocation densities.

Graph neural network for predicting the effective properties of polycrystalline materials: A comprehensive analysis

We develop a polycrystal graph neural network (PGNN) model for predicting the effective properties of polycrystalline materials, using the Li7La3Zr2O12 ceramic as an example. A large-scale dataset with >5000 different three-dimensional polycrystalline microstructures of finite-width grain boundary is generated by Voronoi tessellation and processing of the electron backscatter diffraction images. The effective ion conductivities and elastic stiffness coefficients of these microstructures are calculated by high-throughput physics-based simulations. The optimized PGNN model achieves a low error of <1.4% in predicting all three diagonal components of the effective Li-ion conductivity matrix, outperforming a linear regression model and two baseline convolutional neural network models. Sequential forward selection method is used to quantify the relative importance of selecting individual grain (boundary) features to improving the property prediction accuracy, through which both the critical and unwanted node (edge) feature can be determined. The extrapolation performance of the trained PGNN model is also investigated. The transfer learning performance is evaluated by using the PGNN model pretrained for predicting conductivities to predict the elastic properties of the same set of microstructures.:

A rock physics model in vertical transverse isotropy media and its application to Eagle Ford shale

AbstractShales are rocks with a complex structure. Shales contain high clay content, which constitutes a load‐bearing skeleton. In this study, we present a novel rock physics model to obtain elastic stiffness coefficients of both clays and shales. The robustness of the model is then verified by a field dataset from Eagle Ford shale. We utilize the extended Maxwell homogenization scheme as a rock physics model for transversely isotropic media, which honours the aspect ratio of each inhomogeneity embedded in an effective inclusion domain. Estimated anisotropy parameters ε, γ and δ, on average, are 0.19, 0.29 and 0.04, respectively, based on our modelling results in Eagle Ford shale. Anisotropic modelling results exhibit a good correlation with dipole sonic logs. Both dipole sonic log analysis and rock physics results demonstrate that clay content is the main driver of anisotropy in the field, and there is a direct relationship between clay volume and anisotropy parameters of ε and γ. The method shown here can be readily applied to other unconventional reservoirs.

Development of modulation, pairing mechanism, and slip system with optimum vanadium substitution at Bi-sites in Bi-2212 ceramic structure

Present study focuses extensively on the change in electrical, superconducting and microhardness parameters with partial substitution of trivalent V+3 impurities replacing Bi+3 ions in Bi-2212 ceramic compound with the aid of dc electrical resistivity and microhardness test measurements. Experimental findings, calculation results, and phenomenological discussions provide that the optimum vanadium substitution level is found to be x = 0.01 in the Bi2.0-xVxSr2.0Ca1.1Cu2.0Oy (Bi-2212) ceramic system for the highest conductivity, crystallinity quality, superconducting, and mechanical performance features depending on the decreased microscopic structural problems. All the findings are wholly verified by scanning electron microscopy (SEM) and X-Ray diffraction (XRD) analyses. The dc electrical measurements indicate that the optimum vanadium ions support the pairing mechanism for the formation of new polaronic states in the clusters of microdomains, and hence expand superconducting energy gap due to the enhancement of amplitude part of pair wave function in the spin-density wave systems. The excess vanadium content degrades all the basic thermodynamics and quantum mechanical quantities mentioned due to the stress-induced phase transformation. Numerically, the Bi-2212 advanced ceramic matrix prepared by the optimum vanadium impurity is noticed to present the smallest residual resistivity value of 0.08 mΩ cm, room temperature resistivity value of 8.84 mΩ cm, and broadening degree of 0.36 K. Similarly, the ceramic material is found to possess the highest residual resistivity ratio of 3.05, carrier concentration number of 0.153041, critical transition offset and onset value of 84.66 K and 85.02 K, respectively. Besides, the microhardness findings reveal that the same compound with the least sensitivity to the applied test loads exhibits the largest Hv value of 4.799 GPa, Young's moduli of 393.303 GPa, yield strength of (0.969 GPa), and elastic stiffness coefficient of 15.5574 (GPa)7/4 under the applied test load of 0.245 N. The XRD investigations show that the presence of optimum vanadium impurity supports the formation of a high superconducting phase, c-axis length, and average crystallite size. All the findings are morphologically confirmed by the SEM images. It is found that the crystallographically best crystallinity quality and view of surface morphology is observed for the optimum vanadium substitution level. All in all, new higher properties for the conductivity, crystallinity quality, surface morphology, superconducting, and microhardness parameters based on the optimum vanadium replacement encourage the Bi-2212 crystal system to use in much more application places.

Effect of hard magnetic ferrite (Ba0.5Sr0.5Fe12O19) nanoparticles on the mechanical properties of the (Bi, Pb)-2223 phase

To manifest the effect of hard magnetic Ba0.5Sr0.5Fe12O19 nanoparticles on the mechanical performance of the (Bi,Pb)-2223 superconducting phase, nano-(Ba0.5Sr0.5Fe12O19)x/Bi1.8Pb0.4Sr2Ca2Cu3.2O10+δ, with x = 0.00, 0.01, 0.02, 0.03, 0.04, 0.05, 0.10, and 0.20 wt%, were synthesized using a conventional solid-state reaction method. The X-ray diffraction (XRD) data revealed that adding nano-(Ba0.5Sr0.5Fe12O19) to the host (Bi,Pb)-2223 phase preserved the orthorhombic structure. The porosity (P%) calculations revealed a decrease until x = 0.04 wt%, which suggests that the addition of nano-(Ba0.5Sr0.5Fe12O19)x reduces the number of voids and improves inter-grain connections, as confirmed by SEM micrographs. The superconducting transition temperature (Tc) increased to 112 K with the inclusion of nano-(Ba0.5Sr0.5Fe12O19) up to x = 0.04 wt%. Vickers microhardness (HV) measurements were conducted at various applied loads (0.245–9.800 N) and a duration time of 45 s. The HV number increased with the addition of x up to x = 0.04 wt% but then decreased with further addition. Various models were employed for analysis and modelling of Vickers hardness (HV) versus test load (F), including Meyer’s law, Hays–Kendall (H–K) model, the elastic/plastic deformation (EPD) model, the proportional sample resistance (PSR) model, the modified proportional sample resistance (MPSR), and indentation-induced cracking (IIC) model. It was found that the PSR model was the most appropriate theoretical model for describing the microhardness of nano-(Ba0.5Sr0.5Fe12O19)x/(Bi,Pb)-2223 composites. Moreover, the elastic modulus (E), yield strength (Y), fracture toughness (K), brittleness index (B), and elastic stiffness coefficient (C11) were estimated as a function of the inclusion of nano-(Ba0.5Sr0.5Fe12O19)x. Furthermore, the indentation creep test (time-dependent Vickers microhardness) revealed that the dislocation creep mechanism exists in composite samples with low concentrations (x < 0.05 wt%), whereas the dislocation climbs creep mechanism was observed for x ≥ 0.05 wt%.

Interpreting the effects of shale rock properties on seismic anisotropy by statistical and machine learning methods

The elastic anisotropy of unconventional shale reservoirs plays a crucial role in their economic hydrocarbon production. The strong anisotropy of organic-rich shale rocks, characterized by clay platelets, elongated pores, and organic material, presents challenges for traditional reservoir characterization methods, which are designed for isotropic or weakly anisotropic conventional sandstone reservoirs. To effectively describe the geomechanical behaviors of organic-rich shales and estimate changes in stress caused by hydraulic fracturing, it is necessary to develop practical methods for predicting anisotropy parameters from conventional rock property logs. This study proposes a statistical approach for predicting independent elastic stiffness coefficients for vertically transverse isotropic (VTI) shale from three shale rock properties: clay volume fraction, kerogen volume fraction, and total porosity. The results of this study show that the stiffness coefficients, C11 and C33, are related to P-wave anisotropy and porosity has a greater impact on P-wave anisotropy than clay and kerogen volume fractions. In contrast, changes in clay volume have a more sensitive effect on C44 and C66, providing S-wave anisotropy information that can help detect lithology changes. Furthermore, kerogen variation has a greater influence on both C12 and C13 than the effects of porosity and clay variations. From these relationships, we develop exponential nonlinear regression (ENLR) models for predicting independent elastic stiffness coefficients from three shale rock properties. These models are validated with the Midland Basin log data, and we improve the accuracy of the C13 estimation model using the deep feedforward neural network (DFNN) method. The results show that the statistical approach can help understand the effect of shale rock components on seismic anisotropy variations and better predict the variations in lithology, fluid, and organic contents in shales from anisotropic seismic data. Furthermore, the methodology can provide robust estimates of the stress changes from hydraulic fracturing, supporting the efficient and economically viable production of shale hydrocarbons.

Efficient Machine Learning Model for Predicting the Stiffness of Circular Footings on Clay Overlying Sand

Assessing the stiffness of circular foundations is the key to evaluating their deformation; thus, it is important for foundation design. The current determination methods for the stiffness coefficient are either time-consuming or inaccurate. In this paper, a novel stiffness prediction model has been proposed, using the decision tree (DT) algorithm optimized by particle size optimization (PSO). The condition of the embedded foundation, the embedded depth (ZD/2R), the thickness of the clay layer beneath the foundation base (T/2R), and the ratio of shear stiffness between clay and sand (Gsand/Gclay) were used as input variables, while the elastic stiffness coefficients (Kc, Kh, Km, and Kv) were used as output variables. The optimum DT model has undergone comprehensive validation, and independent model verification using extra simulations. The results illustrate that PSO could promote further increases in the capability of DT modeling in predicting stiffness coefficients. The optimum DT model achieved a good level of performance on stiffness coefficient modeling. (The R for the training set was greater than 0.98 for all of the stiffness coefficients.) The variable importance analysis showed that the T/2R was the most significant variable for all stiffness coefficients, followed by Gsand/Gclay. The optimum DT model achieved good predictive performance upon independent verification, with the R being 0.97, 0.99, 0.99, and 0.95 for Kv, Kh, Km, and Kc, respectively. The proposed reliable and efficient DT-PSO model for stiffness coefficients in layered soil could further promote the safe and efficient utilization of circular foundations.