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It has been found that the physical and mechanical properties of rockfill materials deteriorate when subjected to wetting–drying cycles. Previous studies have mainly focused on the variations of mechanical properties of rockfill materials with wetting–drying cycles. However, the effects of wetting–drying cycles on the breakage characteristics of rock grains still remain unclear. In this study, we perform extensive single grain crushing tests on slate rock grains that have suffered from different wetting–drying cycles. We then investigate the effects of cyclic wetting–drying on the crushing strength, fracture energy, and fragment size distribution of slate rock grains. The results show that both the crushing strength and fracture energy per volume decrease exponentially with increasing wetting–drying cycles, indicating that the deterioration of the mechanical properties of slate grains gradually slows down. The size of fragments follows a fractal distribution, and the fractal dimension shows a linear relationship with the number of wetting–drying cycles, suggesting more small fragments for highly deteriorated rock grains. SEM scanning indicates that the micropores and cracks expand due to wetting–drying cycles. An X-ray diffraction analysis shows that the mineral composition content of slate grains changes after wetting–drying cycles.

The flow of small particles in porous media is of interest in many branches of science. In geotechnical engineering, this phenomenon usually occurs in graded granular materials and is termed as internal erosion. In this work, graded granular materials are simplified as binary mixtures under vertical compression, and water flows perpendicular to the vertical direction. We use the coupled Lattice Boltzmann method (LBM) and discrete element method (DEM) to investigate the initiation of internal erosion under different stress levels and hydraulic gradients. Suffusion was observed as the fine particles are transported by the seepage flow. The change of void ratio due to water flow and vertical compression demonstrates three patterns: erosion, stability, and compaction. Particles with low engagement in force transmission are more prone to erosion, while the hydraulic gradient is an external disturbance factor. The ballistic, caging, and diffusive regimes are observed in the initial process of internal erosion.

Isogeometric analysis (IGA) has been widely applied in the finite element method and boundary element method (BEM), in which the geometry discretization error can be avoided. This paper proposes a NURBS-enhanced meshless improved interpolating boundary element-free method for 2D potential problems. In the proposed method, non-uniform rational B-spline (NURBS) basis functions are applied to reproduce the geometry like in IGA, and the boundary integral cells, called isogeometric cells, are defined by the knot vector of NURBS in parameter space. Thus, the geometry can remain the same at all stages because refining a NURBS curve will not change its shape. An improved interpolating moving least-square (IIMLS) method is applied to approximate the field in parameter space, and the boundary nodes can be defined using Greville abscissae definition. Compared with IGA in BEM, the shape functions obtained by IIMLS in the proposed method have the delta function property, and the boundary conditions can be applied directly. In addition, most methods for the treatment of the singular integrals in BEM can be applied easily in the proposed method. Fast multipole method is further coupled with the proposed method for large-scale computation.

Background There is a paucity of literature about prognostic evaluation for patients with breast cancer (BC) and bone metastasis at presentation. To date, little is known about how to accurately predict the prognosis of BC patients with bone metastasis at presentation. Thus, an accurate prediction tool of prognosis in this population is urgently needed. Our goal is to construct novel and prognostic nomograms for BC patients with bone metastasis at presentation. Methods We searched Surveillance, Epidemiology, and End Results (SEER) database for BC patients with bone metastasis at presentation between 2010 and 2016. Multivariate analysis was performed to obtain significantly independent variables. Then, novel prognostic nomograms were constructed based on those independent predictors. Results Tumor grade, histological type, primary tumor size, tumor subtype, surgery, chemotherapy and number of metastatic organs except bone were recognized as significantly independent variables of both overall survival (OS) and cancer-specific survival (CSS). Then those significant variables were integrated to construct nomograms for 3- and 5-year survival. Calibration plots for the 3- and 5-year survival in training and validation sets showed that the prediction curve was close to a 45 degree slash. The C-indices of OS in training and validation cohorts were 0.705 and 0.678, respectively. Similar results were observed for CSS in training and validation cohorts. Conclusions Our proposed nomograms can effectively and accurately predict the prognosis of BC patients with bone metastasis at presentation, which provide a basis for individual treatments for metastatic lesions.

A numerical method based on the boundary integral equation is proposed for the point location problem. For a bounded domain, the integral value is close to 1.0 if a point is inside the domain, and is close to 0.0 when the point is outside the domain. For convenience of integration, the boundary of the domain can be discretized into boundary integral cells. The idea of isogeometric analysis can be easily coupled with the proposed method, i.e., using the parametric functions in geometric modeling to create the integral cells, which results in a mesh-free procedure for which the geometry can be exactly produced at all stages. Thus, the method can be applied to arbitrary shapes and easily embedded in computer-aided design (CAD) packages. The method is time-consuming if implemented directly; a fast multipole method is coupled with the proposed method to accelerate the integral procedure. Some examples of 2D and 3D cases are tested to show the accuracy and efficiency of the proposed method.

Non-uniform rational B-spline (NURBS) in Isogeometric analysis (IGA) is coupled with the boundary element method (BEM) for 2D potential problems in this paper. The geometry and field are usually approximated by the same basis functions in IGA, such as the B-spline or the NURBS basis functions. In the proposed method, these two kinds of approximation are performed independently, i.e. the geometry is reproduced by the NURBS basis functions while the field is approximated by the traditional Lagrangian basis functions which are used in the conventional BEM. The proposed method has the advantage that the geometry can be reproduced exactly at all stages in IGA methods. Actually, one can use the computer aided design (CAD) software or NURBS library to perform the operations related to the geometry. The field approximation is performed in parameter space and separated from the geometry. Thus, it can be implemented easily as the conventional BEM since most algorithms for BEM can be applied directly, such as the methods for treatment of the singular integrals, and the boundary conditions can be imposed directly. Numerical examples have demonstrated the accuracy of the proposed method.

Purpose Domain integrals, known as volume potentials in 3D elasticity problems, exist in many boundary-type methods, such as the boundary element method (BEM) for inhomogeneous partial differential equations. The purpose of this paper is to develop an accurate and reliable technique to effectively evaluate the volume potentials in 3D elasticity problems. Design/methodology/approach An adaptive background cell-based domain integration method is proposed for treatment of volume potentials in 3D elasticity problems. The background cells are constructed from the information of the boundary elements based on an oct-tree structure, and the domain integrals are evaluated over the cells rather than volume elements. The cells that contain the boundary elements can be subdivided into smaller sub-cells adaptively according to the sizes and levels of the boundary elements. The fast multipole method (FMM) is further applied in the proposed method to reduce the time complexity of large-scale computation. Findings The method is a boundary-only discretization method, and it can be applied in the BEM easily. Much computational time is saved by coupling with the FMM. Numerical examples demonstrate the accuracy and efficiency of the proposed method.. Originality/value Boundary elements are used to create adaptive background cells, and domain integrals are evaluated over the cells rather than volume elements. Large-scale computation is made possible by coupling with the FMM.

Different fracture patterns can be observed because of different material properties, even the geometry and loading are the same. However, most of the known phase-field fracture models have only considered the tensile failure and may not be directly applicable to the shear fracture. In this paper, a phase-field model for mixed-mode fracture is proposed based on a unified tensile fracture criterion. The proposed model is developed from the unified phase-field theory and the original unified phase-field model can be recovered as a particular case. General softening laws for cohesive zone models can also be considered. The unified tensile fracture criterion is embedded in the proposed mixed-mode phase-field model and different fracture patterns can be obtained in the simulation according to the material properties, including failures based on both maximum normal stress and maximum shear stress criteria. The crack propagation direction can be easily determined by the unified tensile fracture criterion. Compared with the classical phase-field model, two additional material parameters are needed, i.e., the failure tension strength and the ratio of the critical shear failure stress to the critical normal fracture stress. Numerical examples have shown that the proposed model has the ability to model mixed-mode fractures, and can also be applied to rock-like brittle materials under compression.

A line integration method is presented in this paper for evaluation of domain integrals in 3D problems. The method is a boundary-only discretization method and the domain integrals can be computed by sum of integrals on one-dimensional straight lines. Divergence theorem is used to transform the domain integrals into boundary integrals with one-dimensional integrals. The boundary integrals can be evaluated by boundary elements with integral points. Each integral point can be used to construct an integral line, and the domain integrals can be finally computed by line integrals on integral lines. Only the boundary discretization is needed and background cells are used to cut the integral lines into sub-lines to obtain the desired accuracy. The method is proved and applied in boundary element method for 3D potential and elasticity problems. Numerical examples have demonstrated the accuracy of the proposed method.

An adaptive cell-based domain integration method (CDIM) is proposed for the treatment of domain integrals in 3D boundary element method (BEM). The domain integrals are computed in background cells rather than volume elements. The cells are created from the boundary elements based on an adaptive oct-tree structure and no other discretization is needed. Cells containing the boundary elements are subdivided into smaller sub-cells adaptively according to the sizes and levels of the boundary elements; and the sub-cells outside the domain are deleted to obtain the desired accuracy. The method is applied in the 3D potential and elasticity problems in this paper.

A line integration method (LIM) is proposed to calculate the domain integrals for 3D problems. In the proposed method, the domain integrals are transformed into boundary integrals and only line integrals on straight lines are needed to be computed. A background cell structure is applied to further simplify the line integrals and improve the accuracy. The method creates elements only on the boundary, and the integral lines are created from the boundary elements. The procedure is quite suitable for the boundary element method, and we have applied it to 3D situations. Directly applying the method is time-consuming since the complexity of the computational time is O(NM), where N and M are the numbers of nodes and lines, respectively. To overcome this problem, the fast multipole method is used with the LIM for large-scale computation. The numerical results show that the proposed method is efficient and accurate.

A background cell-based domain integration method is proposed in this paper for evaluating domain integrals in 3D problems. The cells are created by an adaptive oct-tree structure based on the information of boundary elements, and no other discretization is needed. Cells that contain boundary elements can be subdivided into smaller sub-cells adaptively to obtain the desired accuracy according to the sizes and levels of the boundary elements. Applying the method directly in the boundary element method is time-consuming since the time complexity is O ( NM ), where N and M are the numbers of nodes and cells, respectively. The fast multipole method is coupled with the cell-based domain integration method to further accelerate the computational efficiency, and the main formulations are introduced in this paper. Numerical examples have demonstrated the accuracy and efficiency of the proposed method.

A novel microporous metal-organic framework (MOF) based on Zn(II) ion as node with the chemical formula of {[Zn(H2O)(HL)]·(DMF)2(H2O)2}n (1, H3L ​= ​2-(4-carboxyphenyl)-1H-benzo[d]imidazole-5-carboxylic acid, DMF ​= ​N,N-dimethylformamide), which has rich water-coordinated metal centers and high density of free N-donor groups has been successfully prepared via H3L ligand and Zn(NO3)2·6H2O reaction within H2O, EtOH along with DMF mixed solvent. The presence of open metal sites along with the basic N-donor sites in the resulting activated 1a induces a moderate high sorption capacity of CO2. In addition, because of basic N-donor groups along with Lewis acidic Zn2+ ions, 1a has become an efficient heterogeneous catalyst, which can chemically fix CO2 in the carbonate of cyclic annular at mild room temperature. Furthermore, the influence of compound on the activation of PI3K/AKT signaling pathway was studied by Western blot. The ELISA was carried out the evaluate the IL-18 and IL-6 content in synovial cells after compound treatment.

This paper presents simulations of true triaxial tests on crushable granular materials. Considering both the shear and tensile fracture modes of the particle, the Mohr–Coulomb model with tension cut-off is employed as the fracture criterion of single particle. When the particle stresses satisfy the fracture criterion, three new balls are generated to replace the broken particle. The new balls overlap enough within the bounding parent sphere to obey the mass conservation law. A polydisperse assembly consisting of 7935 spheres was isotropically compressed until the desired confining pressure was reached. Then the sample with no bias in initial fabric was subjected to axial compression at a constant minor principal stress under different intermediate principal stress ratios, b. The simulated stress–strain–dilation responses were in agreement with the experimental observations. The macro–micro responses including stress–strain characteristics, fabric tensors, anisotropies, the orientation tensor and force chain characteristics were discussed in details. It is shown that volumetric responses is affected by b. The anisotropies vary with b, but a unique macro–micro linkage exists between the anisotropies and stress ratio, q / p, irrespective of the value of b. A linear relationship is found between the obliquity of $${\sigma _{1} }/{\sigma _{3} }$$ and the strength indicator ( $$\beta =\ln ({\tau _{1} }/{\tau _{3} }))$$ using the orientation tensor method.

Thermal analysis is one of the main components in the design and construction of mass concrete structures. A procedure for a heat-fluid coupling model (HFCM) is presented to simulate the thermal field of mass concrete with a pipe cooling system, which can accurately reflect the temperature gradient near the pipe and the temperature rise along the pipe. Additionally, to make it suitable for the simulation of forced-convection during pipe cooling, a modified particle swarm optimization (MPSO) method, based on particle migration is adopted for parameter identification of the Dittus–Boelter equation used by the heat-fluid coupling model, according to field tests. To verify the accuracy and computation efficiency of the method, a simplified 3D model is simulated and compared to other numerical models. Subsequently, the model is applied to the analysis of a monolith of the Dagangshan high arch concrete dam in the construction period. The actual climatic conditions, cooling pipe system, cooling schedule and thermal properties of the materials are considered in the analysis. The simulation results indicate that the proposed method can effectively simulate the cooling pipe state, water temperature rise along the flow, and directional changes of the flow in the thermal field of mass concrete. Moreover, the temperatures determined by the numerical simulation are in good agreement with the monitoring values. Findings in this research show that the proposed HFCM is feasible and has attractive advantages in the simulation of the thermal field in practical complex mass concrete engineering projects with cooling pipe systems.

The aim of this study was to develop a practical way of modeling the time-dependent behavior of rockfill materials and to provide useful information that is difficult to obtain from physical tests. Because the micro-mechanism governing the time-dependent rockfill behavior is delayed particle breakage, an updated rock aging model is implemented in an existing code. Particle breakage is represented by the failure of zero-thickness cohesive interface elements that are pre-inserted into the finite element discretization associated with each particle. With only three additional parameters together with temporal integration, we can account for the aging of rock blocks under various stress states and climatic conditions. A series of two-dimensional simulated creep tests were performed on a dense assembly of polygonal particles. By varying rock aging parameters, we can reproduce the typical creep behaviors. The effects of weathering and cyclic loading are investigated by performing five comparative creep tests. The influences of the stress level on the creep deformation are in agreement with experimental observations. A multi-stage creep test is also conducted to verify that the creep behavior has stress history dependence.

This paper aims to compare three collocation point methods associated with the odd order stochastic response surface method (SRSM) in a systematical and quantitative way. The SRSM with the Hermite polynomial chaos is briefly introduced first. Then, three collocation point methods, namely the point method, the root method and the without origin method underlying the odd order SRSMs are highlighted. Three examples are presented to demonstrate the accuracy and efficiency of the three methods. The results indicate that the condition that the Hermite polynomial information matrix evaluated at the collocation points has a full rank should be satisfied to yield reliability results with a sufficient accuracy. The point method and the without origin method are much more efficient than the root method, especially for the reliability problems involving a large number of random variables or requiring complex finite element analysis. The without origin method can also produce sufficiently accurate reliability results in comparison with the point and root methods. Therefore, the origin often used as a collocation point is not absolutely necessary. The odd order SRSMs with the point method and the without origin method are recommended for the reliability analysis due to their computational accuracy and efficiency. The order of SRSM has a significant influence on the results associated with the three collocation point methods. For normal random variables, the SRSM with an order equaling or exceeding the order of a performance function can produce reliability results with a sufficient accuracy. The order of SRSM should significantly exceed the order of the performance function involving strongly non-normal random variables.

This research tends to develop robust numerical methods for solving the highly nonlinear partial differential equation describing unsaturated soil flow. Based on the research of a modified transformation method with under-relaxation, the numerical performance of this promising method with automatic temporal adaptive scheme is investigated. Example shows that such a combination approach can be a robust numerical method for practical unsaturated flow simulations, as it provides the most efficient solution at minimal computational cost; its performance is rather robust with moderate changes of several parameters introduced; and it is conceptually and computationally simple which can be easily incorporated into existing software codes based on the backward Euler scheme.

Accurate prediction of the propagating wetting front arising from rainfall infiltration into an unsaturated soil slope is of considerable importance to stability analysis of the slope. However, difficulties exist in numerical simulations of unsaturated flow analyses because of the highly nonlinear soil hydraulic properties. This paper emphasizes the slow convergence of calculated pressure heads with the refinement of mesh sizes and time steps, and discusses possible solutions.

It is costly to measure the soil water characteristic curve. A first-order estimate from statistical generalization of experimental data belonging to soils with similar textural and structural properties is useful. A simple approach is to fit the data with a nonlinear function and model the curve-fitting parameters as a random vector. This approach is demonstrated using sandy clay loam data in UNSODA. It was found that the classical lognormal distribution is unable to reproduce the skewness and kurtosis of the curve-fitting parameters accurately. A simple four-term Hermite expansion was found to be more suitable. The Hermite coefficients are determined by minimizing lack-of-fit errors in the 25 th , 50 th , and 75 th quantiles.