Random Polygons Research Articles

Freeze-thaw cycling of nano-SiO2-modified recycled aggregate in concretes: Hydro-thermal-mechanical modeling

The freeze-thaw cycling in the cold region causes severe damage to the concrete, which seriously affects the durability of concrete. In this paper, nano-SiO₂ (NS) modified RAC (NS-RAC) specimens were prepared by impregnating RCA with a 3 % NS dispersion for 48 h with following frost resistance assessed experimentally. To further fully understand the performance of NS-RAC under freeze-thaw (F-T) cycles, a comprehensive hydro-thermal-mechanical coupling model was established to simulate the damage behavior of NS-RAC under F-T conditions. A random polygon microstructure model of RAC was developed, and the characteristics of RCA and three types of ITZs were discussed. The damage control equation for RAC during the F-T process was defined based on the coupling effects of percolation, temperature, and stress in a porous medium. The F-T cycle tests show that the compressive strength of NS-RAC samples after 100 F-T cycles is 9.04 MPa higher than that of RAC. Numerical simulation results indicate that, compared to RAC without NS, the maximum pore pressure, crystallization pressure, and maximum principal stress of samples with 3 % NS after the first F-T cycle are reduced by 3.84 %, 4.36 %, and 2.26 %, respectively. During the F-T cycle, with increases in ITZ width, aggregate gradation range, RCA replacement rate, and temperature difference, the internal stress of NS-RAC specimens increased to varying degrees. This study provides insights into the F-T damage of RAC in severe cold regions and promotes the practical engineering application of RAC in such environments.

Mesoscale-based mechanical parameters determination and compressive properties of fully recycled coarse aggregate concrete

The use of recycled coarse aggregate (RCA) to prepare concrete can reduce the depletion of natural resources, such as sand and stone, and solve the issue of environmental pollution resulting from waste concrete materials. To promote the popularization of the RCA application, a study has been carried out on fully recycled coarse aggregate concrete (FRCAC), which is 100 % RCA replacement. The random convex polygon aggregate model was established using a self-compiled program. Then, A five-phase numerical model of FRCAC was proposed through the finite element software further developed, to realize the numerical simulation of uniaxial compression of FRCAC. The discount factor R between the mechanical parameters of the FRCAC mesoscopic components was determined by comparing the 8 groups of compressive strengths from the physical experiments with the 96 groups of compressive strengths from the numerical simulations. Meanwhile, the effects of RCA volume fraction, water-cement ratio (W/C) and mesoscopic composition on the compression performance of FRCAC were analyzed based on experimental and simulation methods. The result shows: 1) Simulation results exhibited good agreement with experimental results when the interface discount factor RITZ and the old mortar discount factor RM fell within the ranges of 0.45–0.55 and 0.8–0.85, respectively. 2) The compressive strength of FRCAC tends to decrease when W/C and the volume fraction of RCA rise, but the trend of declines is not constant. 3) The compressive properties of FRCAC were found to decrease with increased thickness of the old mortar and the interfacial transition zone, highlighting the necessity for pretreatment of RCA before its use. The findings of this research provide valuable insights and methodological references for the application and promotion of FRCAC and its mesoscopic models.

Nonlinear random extrapolation estimates of \(\pi\) under Dirichlet distributions

We construct optimal nonlinear extrapolation estimates of \(\pi\) based on random cyclic polygons generated from symmetric Dirichlet distributions. While the semiperimeter \( S_n \) and the area \( A_n \) of such random inscribed polygons and the semiperimeter (and area) \( S_n' \) of the corresponding random circumscribing polygons are known to converge to \( \pi \) w.p.\(1\) and their distributions are also asymptotically normal as \( n \to \infty \), we study in this paper nonlinear extrapolations of the forms \( \mathcal{W}_n = S_n^{\alpha} A_n^{\beta} S_n'^{\, \gamma} \) and \( \mathcal{W}_n (p) = ( \alpha S_n^p + \beta A_n^p + \gamma S_n'^{\, p} )^{1/p} \) where \( \alpha + \beta + \gamma = 1 \) and \( p \neq 0 \). By deriving probabilistic asymptotic expansions with carefully controlled error estimates, we show that \( \mathcal{W}_n \) and \( \mathcal{W}_n (p) \) also converge to \( \pi \) w.p.\(1\) and are asymptotically normal. Furthermore, to minimize the approximation error associated with \( \mathcal{W}_n \) and \( \mathcal{W}_n (p) \), the parameters must satisfy the optimality condition \( \alpha + 4 \beta - 2 \gamma = 0 \). Our results generalize previous work on nonlinear extrapolations of \( \pi \) which employ inscribed polygons only and the vertices are also assumed to be independently and uniformly distributed on the unit circle.

Variance expansion and Berry-Esseen bound for the number of vertices of a random polygon in a polygon

Variance expansion and Berry-Esseen bound for the number of vertices of a random polygon in a polygon

Study on Chloride Diffusion Behaviors of Recycled Concrete of Random Aggregates

Based on the chloride ions (Cl−) diffusion model and aggregate grading theory, PYTHON and COMSOL are used to construct a mesoscopic model of recycled concrete random polygon aggregate and verify its validity in combination with existing experimental results. The diffusion law of Cl− in recycled concrete and the law of influence of critical factors on the Cl− erosion resistance are studied by calculating and analyzing the Cl− erosion resistance of recycled concrete under different working conditions such as the diffusivity of new and old mortar, the thickness of old mortar and the replacement ratio of recycled aggregate. The results show that the simulation results agree well with the test results, and the method can better reproduce the Cl− diffusion process inside the recycled concrete. There are discontinuous features based on the relationship curves between the Cl− concentration and the depth of the recycled concrete. The Cl− concentration inside the concrete gradually increases with the increase of the diffusion rate of the old and new mortars. The resistance behavior of the recycled concrete to Cl− attack decreases with the increase of the thickness of the old mortar.

A multi-phase numerical simulation method for the changing process of expansion products on concrete under sulfate attack

Concrete constructions used in harsh marine environments are commonly destroyed by sulfate ions. In this paper, by modeling aggregates as random convex polygons, to analyze and forecast the deteriorating condition of concrete under salt attack, a finite element method is suggested. The sulfate attack on concrete is studied using the numerical analytical method to examine changes in sulfate ions and expansion products at the mesoscale. Since concrete is a heterogeneous mixture, the diffusion characteristics of phases, such as the aggregate, interfacial transition zone (ITZ), mortar and pore, were considered. The proposed mesoscale numerical analysis method is validated by experiments. It is demonstrated that: (1) the setting of ITZ thickness and pore has negligible effect on concrete damage in sulfate environment; (2) reducing the water-cement ratio can significantly enhance the erosion resistance of concrete; (3) within a certain range of depth, the surface sulfate concentration is positively correlated with the erosion degree; (4) aluminate determines the peak value of ettringite content in concrete.

The proportion of triangles in a class of anisotropic Poisson line tessellations

AbstractStationary Poisson processes of lines in the plane are studied, whose directional distributions are concentrated on $k\geq 3$ equally spread directions. The random lines of such processes decompose the plane into a collection of random polygons, which form a so-called Poisson line tessellation. The focus of this paper is to determine the proportion of triangles in such tessellations, or equivalently, the probability that the typical cell is a triangle. As a by-product, a new deviation of Miles’s classical result for the isotropic case is obtained by an approximation argument.

Identification of Ballast Fouling Status and Mechanized Cleaning Efficiency Using FDTD Method

Systematic assessment of ballast fouling and mechanized cleaning efficiency through ground penetrating radar (GPR) is vital to ensure track stability and safe train transportation. Nevertheless, conventional methods of ballast fouling inspection and evaluation impede construction progress and escalate the cost of maintenance. This paper proposes a novel method using random irregular polygons and collision detection algorithms to model the ballast layer and simulated using the finite-difference time-domain (FDTD) algorithm. Hilbert transform energy, S-transform, and energy integration curve are employed to identify ballast fouling and cleaning efficiency. The highly fouled ballast exhibits concentrated Hilbert transform energy, increased energy attenuation rate in S-transform with depth in the 1.0-3.0 GHz, along with a stronger energy integration curve. Clean or post-cleaning ballast shows opposite results. Experiments on a passenger trunk line in southern China validated the method’s accuracy after mechanized ballast cleaning. This approach guides GPR-based detection and supports railway maintenance. Future studies will consider heterogeneous properties and the three-dimensional structure of the ballast layer.

Comparison of 2D and 3D meso‐model of concrete under high strain loading rate

AbstractIn this paper, 2D and 3D meso‐models of concrete are developed numerically using different shapes of aggregate. For 2D model, circular and random polygon aggregate shapes are considered while for 3D model, spherical and convex hull aggregate shapes are adopted. Five different spatial distributions are employed in both circular and polygon shapes to get Circle1–Circle5 and Poly1–Poly5 geometrical model. Similarly, for 3D meso‐model, Spherical1–Spherical5 and one Convex hull geometrical models are developed. In all the numerical models, three different phases of concrete are considered, that is aggregate, mortar, and interfacial transition zone. Explicit analysis of the developed models has been performed using LS‐DYNA. All the developed models are verified by comparing the obtained results of stress–strain variations with the existing literature. The behavior of concrete is studied for both the loading conditions, that is quasi‐static and high strain loading rate. Added to this, the effect of spatial distribution of aggregates is also evaluated. Finally, the dynamic impact factors (DIF) are evaluated and compared for all the developed numerical models. Finally, cubic polynomial equations for DIF, for different shape aggregate 3D models, are obtained using regression analysis.

Numerical simulation of mesoscopic cracking of cement-treated base material based on random polygon aggregate model

Numerical simulation of mesoscopic cracking of cement-treated base material based on random polygon aggregate model

Domain switching model embedded on scaled boundary finite element method for nonlinear hysteretic behavior of ferroelectrics

The complex nonlinear hysteretic behavior of polycrystalline ferroelectrics for higher electromechanical loads stems from the underlying microscopic domain switching. A micromechanical model embedded onto an advanced numerical framework, the scaled boundary finite element method, as applied to Voronoi-based discretization of two-dimensional ferroelectric plane is presented in this work. Each ferroelectric grain is represented by a naturally evolving random Voronoi polygon with all possible domain variants during the numerical implementation. The butterfly strain responses and the hysteresis polarization responses of ferroelectrics under various electromechanical loading conditions are simulated and compared with the experimental observations, in addition to complex polarization rotations tests.

Certified grasping

This paper studies the robustness of grasping in the frictionless plane from a geometric perspective. By treating grasping as a process that shapes the free-space object over time, we define three types of certificates to guarantee success of a grasp: (a) invariance under an initial set, (b) convergence toward a goal grasp, and (c) observability over the final object pose. We develop convex-combinatorial models for each of these certificates, which can be expressed as simple semi-algebraic relations under mild-modeling assumptions, such as point-fingers and frictionless contact. By leveraging these models to synthesize certificates, we optimize certifiable grasps of planar objects composed as a union of convex polygons, using manipulators described as point-fingers. We validate this approach in simulations by grasping random polygons, and with real sensorless grasps of several objects.

Numerical Simulation and Field Test Research on Vibration Reduction of PDC Cutting of Pebbled Sandstone under Composite Impact Load

Downhole vibrations caused by rock breaking when drilling through pebbled sandstone formations negatively affect the rate of penetration (ROP) and the safety of downhole tools. Therefore, it is of great significance to study the cutting characteristics of pebbled sandstone and find a method of reducing the drilling vibrations of pebbled sandstone formations. Based on the DEM (discrete element method), a simulation model of pebbled sandstone considering the random filling of high-strength gravels was established by using the random polygon distribution method. The influence of gravel content on the strength parameters and the breaking state of the pebbled sandstone samples was analyzed. Additionally, a DEM model of PDC cutting rocks loaded by a spring–mass system was established, and the Stribeck effect of contact friction between the PDC cutter and the rock was analyzed. The periodic vibration and the stick–slip phenomenon of the cutting system during the drilling process were presented by this model. The model was employed to simulate and explore the influence of composite impact load on stick–slip vibration during PDC cutting of pebbled sandstone. The simulation results showed that the composite impact load had a more obvious effect on mitigating the vibration of PDC cutting of pebbled sandstone under the condition of a higher horizontal impact amplitude coefficient (qh = 40%). Based on the simulation results, a composite impactor with a large impact angle α = 70° was selected to conduct the field tests in the pebbled sandstone formation of Well T1. The results showed that, compared to conventional drilling, the average WOB (weight on bit) of the section drilled with the composite impactor decreased by 57.13%, the standard deviation of the WOB decreased by 57.29%, and the average ROP increased by 98.31%. The employing of composite impactors in pebbled sandstone formations can significantly reduce drilling vibration, improve ROP, and protect bits and downhole instruments.

On random disc-polygons in a disc-polygon

We prove asymptotic formulas for the expectation of the vertex number and missed area of uniform random disc-polygons in convex disc-polygons. Our statements are the r-convex analogues of the classical results of Rényi and Sulanke [10] about random polygons in convex polygons.

Flexible and Accurate Prior Model Construction Based on Deep Learning for 2-D Magnetotelluric Data Inversion

The conventional magnetotelluric (MT) data inversion methods, such as the nonlinear conjugate gradient method, quasi-Newton method, and Gauss–Newton method and so on, can converge robustly, but their results are easily affected by the initial model and regularization term. Although supervised learning can break through the resolution limitation by directly learning the nonlinear relationship between the model and the data, it cannot guarantee the data fitting without considering physical constraints. Here, we propose a novel prior model generation method using deep learning for conventional inversion to jointly take advantages of the two techniques. We first combine Gaussian random rough surface scheme and random polygon generation algorithm to construct practical 2-D geoelectric models, in which the prior information on the geoelectric structure can be flexibly integrated. Then, a fast 2-D MT forward modeling method is applied to calculate the forward responses and establish the training set. Finally, we use the training set to complete the parameter optimization of U-shaped network (U-NET) and run the conventional inversion with prior model generated by the trained U-NET. Numerical experiments with synthetic data show that the proposed method can effectively integrate the advantages of conventional inversion and supervised learning, and remarkably improve the resolution in the inversion if proper training sets are used. The inversions of the USArray data also prove that our method can retain high-resolution structures predicted by the U-NET in the final inversion results with a data fitting as good as the traditional Gauss–Newton method.

Convergence of random polygon sequences

Convergence of random polygon sequences

Experimental and computational modeling of chloride transport behavior in fully recycled coarse aggregate concrete

Exploitation of recycled coarse aggregate (RCA) aimed to produce fully recycled coarse aggregate concrete (FRCAC) has attracted more attention due to the growing requirements for sustainable development and carbon neutralization. In this paper, a novel computational model is developed to study the chloride migration behavior in FRCAC at the mesoscopic level. RCAs are generated by a random convex polygon algorithm to approximate the realistic arrangement, shape and polyphase components of aggregates. FRCAC with different RCA volume fractions (0 %, 20 %, 35 % and 50 %) was made by the optimized triple mixing method (OTM), and its chloride transport behavior was investigated by drying-wetting cycles test exposed to sodium chloride solution (50 g/l) for 250 days. The experimental results demonstrate that the transport depth and concentration of chloride increase with the augment of the RCA volume fraction. The availability and universality of the present computational model were validated by comparing with the experimental data. The numerical results show that RCA has both adsorption and barrier effects on the chloride transport, which makes the chloride isoline bend and the flow direction change. Finally, it is demonstrated that chloride diffusivity in 2D case increases compared with 1D case. The findings of presented study can better enhance the understanding of the chloride transport mechanism in FRCAC at mesoscopic.

Effect of microstructural characteristics of lightweight aggregate concrete on fracture parameters of three-point bending notched beams

The meso-scale model of three-point bending notched beams based on the cohesive force model is developed to study the effect of the meso-scale structural characteristics of lightweight aggregate concrete on the fracture parameters. The python program based on random polygon aggregate generation and placement algorithm is developed, which uses batch insertion of zero-thickness cohesive elements to generate the meso-scale model. The meso-scale models are verified with the relevant experiment. The analytical method for determining the parameters of the double-K fracture model of non-standard three-point bending notched beams is presented. The effects on the macroscopic fracture parameters of the specimens are evaluated by the meso-scale structural characteristics, such as porosity, strength of lightweight aggregate, volume fraction of lightweight aggregate, and shape of lightweight aggregate. The results prove that the meso-scale model is consistent with the experiment, which verifies the reliability of the meso-scale model. The peak load of the specimen decreases by 12.1 % when the porosity increases from 0 % to 6 %. The peak load increases by 14.94 % when the strength of lightweight aggregate increases from 40 % to 120 %. The peak load increases by 32.31 % when the volume fraction of lightweight aggregate increases from 30 % to 60 %. The initial fracture toughness and unstable fracture toughness of different meso-scale structural characteristics first increase and then decrease. The ratio of initial fracture toughness to unstable fracture toughness with different meso-scale structural characteristics to the peak load remains relatively stable. In addition, the relative error between the peak load of the mesoscopic model based on circular aggregate and the experiment is the smallest, which is 2.36 %.

Enumeration of the Additive Degree–Kirchhoff Index in the Random Polygonal Chains

The additive degree–Kirchhoff index is an important topological index. This paper we devote to establishing the explicit analytical expression for the simple formulae of the expected value of the additive degree–Kirchhoff index in a random polygon. Based on the result above, the additive degree–Kirchhoff indexes of all polygonal chains with extremal values and average values are obtained.

Reconstruction of 3D Shapes of Granite Minerals and Generation of Random Numerical Specimens

Abstract The existing methods of generating random mineral grains in numerical rock specimens mostly adopt random polygons (in 2D) or random polyhedrons (in 3D) to represent mineral grains. Although this simplification is effective and reasonable, the complex three-dimensional (3D) shape of mineral grains can be reconstructed by computed tomography (CT) scan and image processing techniques, and then, random grains with real shape can be generated in a numerical specimen. In this paper, we proposed an improved grain-based model to construct random mineral grains with real 3D shape in numerical specimens. The granite specimens with granular minerals are scanned by CT. After the CT slices are denoised and corrected, the minerals, including biotite, quartz, and feldspar, are segmented from the CT slices to reconstruct the 3D mineral shapes; these shapes are stored in grain library. By importing the grain library in PFC (Particle Follow Code, a simulation software), heterogeneous specimens with random mineral grains are constructed, and uniaxial compression tests are carried out on them. Results show that the ranges of Young’s modulus, Poisson’s ratio, and uniaxial compressive strength of these numerical specimens are similar to those of real specimens measured in the laboratory. Therefore, the proposed method is feasible and reasonable. This work can provide a reference for the study of constructing heterogeneous numerical rock specimens in rock mechanics.