Extended finite element-based cohesive zone method for modeling simultaneous hydraulic fracture height growth in layered reservoirs

In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast.The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment.Then,the fracture geometry(e.g.height,aperture,and area)and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model.The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented.The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’tips when propagating in soft layers,which impedes the simultaneous height growth.It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures.After that,the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented,and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing.Finally,it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures.The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed.

Axisymmetric Finite Element Method for Analysis of Plate on Layered Soil

To obtain the fundamental solution of soil has become the key problem for the semi-analytical and semi-numerical (SASN) method in analyzing plate on layered soil. By applying axisymmetric finite element method (FEM),an expression relating the surface settlement and the reaction of the layered soil can be obtained. Such a reaction can be treated as load acting on the applied external load. Having the plate modelled by four-node elements,the governing equation of the plate can be formed and solved. In this case, the fundamental solution can be introduced into the global soil stiffness matrix and five-node or nine-node element soil stiffness matrix.The existing commercial FEM software can be used to solve the fundamental solution of soil, which can bypass the complicated formula derivation and boasts high computational efficiency as well.

FINITE LAYER ANALYSIS FOR SEMI-INFINITE SOILS (Ⅰ)——GENERAL THEORY

In the present paper a finite layer method is studied for the flastodynarnics of transverse isotropic bodies. With this method, semi-infinite soils can be considered as an transverse isotropic half-space, its material functions varying with depth. Dividing the half-space into a scries of layers in the direction of depth, the material junctions in each layer are simulated by exponential functions Consequently, the fundamental equations to be solved can be simplified if the Fourier transform with repsect to coordinates is used. We have obtained the relationship between the 'layer forces' and 'layer displacements'. This finite layer method, in fact, can also be called a semi-analytical method. It possesses those advantages as the usual semi-analytical methods do, and can be used to analyse the problem of the interaction between soils and structures.

FINITE LAYER ANALYSIS FOR SEMI-INFINITE SOILS (Ⅱ)——SPECIAL CASES AND NUMERICAL EXAMPLES

In the present paper reductions of the finite layer mathod once studied in detail by the authors for the elastodvnamics of transverse isotropic bodies are given to several special cases. Two-dimensional problems, axisymmetric problems and static problems are discussed, respectively, and this finite layer method is also generalized to the problems in which materials possess viscous properties. Two numerical examples have been presented for the axisymmetric case. From these two examples it can be concluded that the finite layer method can be used to analyse semi-infinite layered soils and to deal with the problem of the interaction between soils and structures.

Layer-element analysis of multilayered saturated soils subject to axisymmetric vertical time-harmonic excitation

The analytical layer-elements for a single poroelastic soil layer and the underlying half-space are established using an algebraic manipulation and Hankel trans- form. According to the boundary conditions and adjacent continuity conditions of general stresses and displacements, a global matrix equation in the transform domain for multi- layered saturated soil media is assembled and solved. Solutions in the frequency domain can be further obtained with an inverse Hankel transform. Numerical examples are used to examine accuracy of the present method and demonstrate effects of soil parameters and load conditions on dynamic responses of the multilayered poroelastic saturated soils.

Dynamic soil-tunnel interaction in layered half-space for incident plane SH waves

The dynamic soil-tunnel interaction is studied by indirect boundary element method （IBEM）, using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.

Effects of alloy elements on microstructure and crack resistance of Fe-C-Cr weld surfacing layer

Effects of alloy elements on the microstructure and crack resistance of Fe-C-Cr weld surfacing layer were investigated. The results show that microstructures of the layer mainly consist of carbides and austenite matrix. Increasing C and Cr contents impair the crack resistance of the layer due to increased amount of brittle carbides. The addition of Ni, Nb or Mo improves the crack resistance of Fe-C-Cr weld surfacing layer by increasing the amount of austenite and forming fine NbC or M 7C 3 carbides in the layer. But, the excessive Nb (>2.50wt%) or Mo (>1.88wt%) impairs the crack resistance of the layer, which has relation with increased carbides or carbide coarsening and austenite matrix solid solution strengthening. The proper combination of C, Cr, Ni, Nb and Mo can further improve not only the crack resistance of Fe-C-Cr weld surfacing layer but also the erosion resistance as a result of fine NbC and M 7C 3 carbides distributing uniformly in austenite matrix. The optimal layer compositions are 3.05wt%C, 20.58wt%Cr, 1.75wt%Ni, 2.00wt%Nb and 1.88wt%Mo.

Effects of Alloying Elements on Microstructure and Erosion Resistance of Fe-C-Cr Weld Surfacing Layer

Effects of alloying elements on microstructure and erosion resistance of Fe-C-Cr weld surfacing layer have been studied. The experimental results show that increasing C and Cr content favors improving the erosion resistance of the layer, and the excessive C and Cr result in decreasing the erosion resistance at 90 deg. erosion. That Mo, Nb or Ti improves the erosion resistance of Fe-C-Cr weld surfacing layer is mainly attributed to increasing the amount of M7C3 and forming fine NbC or TiC in austenite matrix, but the excessive Mo, Nb or Ti is unfavorable. The addition of Mo, Nb and Ti in proper combination possesses stronger effect on improving the erosion resistance and the erosion resistance (εA) of Fe-C-Cr weld surfacing layer with fine NbC, TiC and M7C3 distributing uniformly in austenite matrix obviously increases to 2.81 at 15 deg. erosion and 2.88 at 90 deg. erosion when the layer composition is 3.05C, 20.58Cr, 1.88Mo, 2.00Nb and 1.05Ti (in wt pct).

Dynamic soil-tunnel interaction in layered half-space for incident P-and SV-waves

The dynamic soil-tunnel interaction is studied by the model of a rigid tunnel embedded in layered half-space, which is simplified as a single soil layer on elastic bedrock to the excitation of P- and SV-waves. The indirect boundary element method is used, combined with the Green＇ s function of distributed loads acting on inclined lines. It is shown that the dynamic characteristics of soil-tunnel interaction in layered half-space are different much from that in homoge- neous half-space, and that the mechanism of soil-tunnel interaction is also different much from that of soil-founda- tion-superstructure interaction. For oblique incidence, the tunnel response for in-plane incident SV-waves is com- pletely different from that for incident SH-waves, while the tunnel response for vertically incident SV-wave is very similar to that of vertically incident SH-wave.

Support pressure for circular tunnels in two layered undrained clay

To estimate the required support pressure for stability of circular tunnels in two layered clay under undrained condition,numerical solutions are developed by performing finite element lower bound limit analysis in conjunction with second-order cone programming.The support system is assumed to offer uniform internal compressive pressure on its periphery.From the literature,it is known that the stability of tunnels depends on the overburden pressure acting over it,which is a function of undrained cohesion and unit weight of soil,and cover of soil.When a tunnel is constructed in layered undrained clay,the stability depends on the undrained shear strength,unit weight,and thickness of one layer relative to the other layer.In the present study,the solutions are presented in a form of dimensionless charts which can be used for design of tunnel support systems for different combinations of ratios of unit weight and undrained shear strength of upper layer to those of lower layer,thickness of both layers,and total soil cover depth.

An efficient source wavefield reconstruction scheme using single boundary layer values for the spectral element method

In the adjoint-state method, the forward-propagated source wavefield and the backward-propagated receiver wavefield must be available simultaneously either for seismic imaging in migration or for gradient calculation in inversion. A feasible way to avoid the excessive storage demand is to reconstruct the source wavefield backward in time by storing the entire history of the wavefield in perfectly matched layers. In this paper, we make full use of the elementwise global property of the Laplace operator of the spectral element method (SEM) and propose an efficient source wavefield reconstruction method at the cost of storing the wavefield history only at single boundary layer nodes. Numerical experiments indicate that the accuracy of the proposed method is identical to that of the conventional method and is independent of the order of the Lagrange polynomials, the element type, and the temporal discretization method. In contrast, the memory-saving ratios of the conventional method versus our method is at least N when using either quadrilateral or hexahedron elements, respectively, where N is the order of the Lagrange polynomials used in the SEM. A higher memorysaving ratio is achieved with triangular elements versus quadrilaterals. The new method is applied to reverse time migration by considering the Marmousi model as a benchmark. Numerical results demonstrate that the method is able to provide the same result as the conventional method but with about 1/25 times lower storage demand. With the proposed wavefield reconstruction method, the storage demand is dramatically reduced;therefore, in-core memory storage is feasible even for large-scale three-dimensional adjoint inversion problems.

Numerical analysis of behavior of active layer in rotary kilns by discrete element method

The behavior of the active layer of material bed within rotary kilns plays a key role in industrial applications.To obtain its influences on industrial process,different regimes of particle motion have been simulated by discrete element method(DEM) in three dimensions under variant rotation speeds,filling degree,based on the background of induration process of iron ore pellets.The influences of the mentioned factors on the maximum thickness of the active layer and the average velocity of particles have been investigated.The average velocity of particles increases with Froude number following the power function over a wide range,and the maximum thickness rises with increasing rotation speed in a way of logarithm.The influence of the filling degree f on the maximum thickness exhibits a good linearity under two classic regimes,but the increasing of the average velocity of the active layer is limited at f=0.4.This basic research highlights the impact of the active layer within rotary kilns,and lays a good foundation for the further investigation in mixing and heat transfer within the particle bed inside rotary kilns.

3D Diffraction of obliquely incident SH waves by twin infinitely long cylindrical cavities in layered poroelastic half-space

Abstract This paper studies three-dimensional diffraction of obliquely incident plane SH waves by twin infinitely long cylindrical cavities in layered poroelastic half-space using indirect boundary element method. The approach is validated by comparison with the literature, and the effects of cavity interval, incident frequency, and boundary drainage condition on the diffraction are studied through numerical examples. It is shown that, the interaction between two cavities is significant and surface displacement peaks become large when two cavities are close, and the surface displacement may be significantly amplified by twin cavities, and the influence range with large amplification can be as wide as 40 times of the cavity radius. Surface displacements in dry poroelastic case and saturated poroelastic cases with drained and undrained boundaries are evidently different under certain circumstances, and the differences may be much larger than those in the free-field response.

3D FEM analysis for layered rock considering anisotropy of shear strength

An empirical expression of cohesion （C） and friction angle （Ф） for layered rock was suggested. This expression was compared with a test result made by the former researchers. The constitutive relationship of a transversely isotropic medium and Mohr-Coulomb criterion in which C and Ф vary with directions were employed, and a relative 3D elasto-plastic FEM code was developed, in which the important thing was to adopt a search-trial method to find the orientation angle （p） of shear failure plane （or weakest shear plane） with respect to the major principal stress as well as the corresponding C and Ф Taking an underground opening as the calculation object, the numerical analyses were carried out by using the FEM code for two cases of transversely isotropic rock and isotropic rock, respectively, and the computation results were compared. The results show that when the rock is a transversely isotropic one, the distributions of displacements, plastic zones and stress contours in the surrounding rock will be non-axisymmetric along the tunnel＇s vertical axis, which is very different from that of isotropic rock. The stability of the tunnel in transversely isotropic rock is relatively low.

Time-Domain Analysis of Underground Station-Layered Soil Interaction Based on High-Order Doubly Asymptotic Transmitting Boundary

Based on the modified scale boundary finite element method and continued fraction solution,a high-order doubly asymptotic transmitting boundary(DATB)is derived and extended to the simulation of vector wave propagation in complex layered soils.The high-order DATB converges rapidly to the exact solution throughout the entire frequency range and its formulation is local in the time domain,possessing high accuracy and good efficiency.Combining with finite element method,a coupled model is constructed for time-domain analysis of underground station-layered soil interaction.The coupled model is divided into the near and far field by the truncated boundary,of which the near field is modelled by FEM while the far field is modelled by the high-order DATB.The coupled model is implemented in an open source finite element software,OpenSees,in which the DATB is employed as a super element.Numerical examples demonstrate that results of the coupled model are stable,accurate and efficient compared with those of the extended mesh model and the viscous-spring boundary model.Besides,it has also shown the fitness for long-time seismic response analysis of underground station-layered soil interaction.Therefore,it is believed that the coupled model could provide a new approach for seismic analysis of underground station-layered soil interaction and could be further developed for engineering.

Time domain method for calculating free field motion of a layered half-space subjected to obliquely incident body waves

In numerical simulation of wave scattering under oblique incident body waves using the finite element method, the free field motion at the incident lateral boundary induced by the background layered half-space complicates the computational area. In order to replace the complex frequency domain method, a time-domain method to calculate the free field motion of a layered half-space subjected to oblique incident body waves is developed in this paper. The new method decouples the equations of motion used in the finite element method and offers an interpolation formula of the free field motion. This formula is based on the fact that the apparent horizontal velocity of the free field motion is constant and can be calculated exactly. Both the theoretical analysis and numerical results demonstrate that the proposed method offers a high degree of accuracy.

Experimental and finite element analysis for fracture of coating layer of galvannealed steel sheet

Mechanical properties of galvannealed (GA) steel sheet used for automotive exposed panel and predicted failure phenomenon of its coating layer were evaluated using finite element method. V-bending test was performed to understand better the fracture of coating layer of GA steel sheet during plastic deformation. Yield strength of the coating layer was calculated by using a relative difference between hardness of coating layer measured from the nano-indentation test and that of substrate. To measure shearing strength at the interface between substrate and coating layer, shearing test with two specimens attached by an adhesive was carried out. Using the mechanical properties measured, a series of finite element analyses coupled with a failure model was performed. Results reveal that the fracture of coating layer occurs in an irregular manner at the region where compressive deformation is dominant. Meanwhile, a series of vertical cracks perpendicular to material surface are observed at the tensile stressed-region. It is found that 0.26-0.28 of local equivalent plastic strain exists at the coating and substrate at the beginning of failure. The fracture of coating layer depends on ductility of the coating layer considerably as well.

High-Pressure Melting Experiments on Basalt-Peridotite Layered Source (KLB-1/N-MORB): Implications for Magma Genesis in Hawaii

In order to understand the melting processes that occur within recycled oceanic crust and mantle in a heterogeneous plume (e.g., that beneath the Hawaiian Islands), a series of high-pressure-high-temperature layered experiments were performed at 2.9 GPa, 5 GPa, and 8 GPa, from 1300°C to 1650°C, using a fertile peridotite KLB-1 and N-MORB. Our experiments at conditions below the dry peridotite solidus produced melt compositions that ranged from basaltic andesite to tholeiite. An Opx reaction band formed between eclogite and peridotite layers, likely via chemical reaction between a silica-rich eclogite-derived partial melt and olivine in the peridotite matrix. At temperatures at or above the dry peridotite solidus, substantial melting occurred in both basalt and peridotite layers, and fully molten basalt melt and melt pockets from the peridotite layer combined. In our layered experiments, major and minor element contents in reacted melts closely matched those of Hawaiian tholeiite and picrite, except for Fe. Partial melts of anhydrous run products had ~55 - 57 wt% SiO2 at low temperature (i.e., were andesitic) and had ~50 - 53 wt% SiO2 at high temperatures, slightly below the dry peridotite solidus (i.e., were tholeiitic, and similar to those that occur during the Hawaii shield-building stage). Based on the Fe- and LREE-enriched signature in Hawaiian tholeiites, we propose that recycled components in the Hawaiian plume are not modern N-MORB, but are Fe-rich tholeiite;a lithology that was common in the Archaean and early Proterozoic. We have demonstrated that the entire compositional spectrum of Hawaiian tholeiites (basalt to picrite) can be formed by basalt-peridotite reactive melting near the dry solidus of peridotite. Based on these results, we propose that the potential temperature of the sub-Hawaiian plume may be much lower than previously estimated.

Three-Dimensional Simulations of RESET Operation in Phase-Change Random Access Memory with Blade-Type Like Phase Change Layer by Finite Element Modeling

An optimized device structure for reducing the RESET current of phase-change random access memory （PCRAM） with blade-type like （BTL） phase change layer is proposed. The electrical thermal analysis of the BTL cell and the blade heater contactor structure by three-dimensional finite element modeling are compared with each other during RESET operation. The simulation results show that the programming region of the phase change layer in the BTL cell is much smaller, and thermal electrical distributions of the BTL cell are more concentrated on the TiN/GST interface. The results indicate that the BTL cell has the superiorities of increasing the heating efficiency, decreasing the power consumption and reducing the RESET current from 0.67mA to 0.32mA. Therefore, the BTL cell will be appropriate for high performance PCRAM device with lower power consumption and lower RESET current.

Comparing Studies on the General Egg Qualities and Mineral Element Contents of Different Layers

[Objective]In order to compare the general egg qualities and mineral element contents of different layers,six commercial breeds in brown shell layer,including Lohmann,Jinghong,Hyline,Xinyang,Hisax,ISA,Suqing green shell layer and Wenchang chicken were used as materials.The general egg quality traits and mineral elements contents of eight breeds at 43 weeks old were mensurated.[Result] There were significant differences in general egg qualities（except yolk weight）of eight breeds.About the mineral element contents,the differences were significant only in P,Mn and Se of some breeds in this experiment.[Conclusion]The results in this study could provide the reference for further researcher,layer producers,nutritionists,consumers and so on.