Strength and failure characteristics of marble spheres subjected to paired point loads

Failure of irregular rock samples may provide implications in the rapid estimation of rock strength,which is imperative in rock engineering practice.In this work,analytical,experimental and numerical investigations were carried out to study the mechanical properties and failure characteristics of rock spheres under paired point loads.Analytical solutions indicted that with the increase in sample size(contact angle)and decrease in Poisson’s ratio,the uneven tensile stress in theta direction decreased.Then laboratory experiments were carried out to investigate the load characteristics and failure mode of spherical marble samples with different sizes subjected to a pair of diametral point loads.The discrete element method(DEM)was adopted to study the failure process of rock spheres.The effect of the sphere diameter on the point load contact angle was examined in terms of peak load,crushed zone distribution and energy dissipation.Experimental and numerical results showed that the samples primarily fail in tension,with crushed zones formed at both loading points.With increase in the sample size,the contact angle,crushed area and total work increase.As the specimen diameter increases from 30 mm to 50 mm,the peak load on the specimen increases from 3.6 kN to 8.8 kN,and the percentage of crushed zone(ratio of crushing zone to sample radius,d/r)increased from 0.191 to 0.262.The results of the study have implications for understanding the failure of irregular rock specimens under point loading conditions and their size effects.

Complete solutions for elastic fields induced by point load vector in functionally graded material model with transverse isotropy

The paper develops and examines the complete solutions for the elastic field induced by the point load vector in a general functionally graded material(FGM)model with transverse isotropy.The FGMs are approximated with n-layered materials.Each of the n-layered materials is homogeneous and transversely isotropic.The complete solutions of the displacement and stress fields are explicitly expressed in the forms of fifteen classical Hankel transform integrals with ten kernel functions.The ten kernel functions are explicitly expressed in the forms of backward transfer matrices and have clear mathematical properties.The singular terms of the complete solutions are analytically isolated and expressed in exact closed forms in terms of elementary harmonic functions.Numerical results show that the computation of the complete solutions can be achieved with high accuracy and efficiency.

Mechanical behavior of red sandstone under cyclic point loading

The mechanical properties of red sandstone subjected to cyclic point loading were investigated. Tests were conducted using MTS servohydraulic landmark test system, under cyclic loadings with constant amplitudes and increasing multi-level amplitudes. The frequencies range from 0.1 to 5 Hz and lower limit load ratios range from 0 to 0.60. Laboratory investigations were performed to find the effect of the frequency and the lower limit load ratio on the fatigue life and hysteresis properties of sandstone. The results show that the fatigue life of sandstone decreases first and then increases with the increase of frequency and lower limit load ratio. Under the same cycle number, the spacing between hysteresis loops increases with rising frequency and decreasing lower limit load ratio. The existence of “training” and “memory” effects in red sandstone under cyclic point loading was proved.

The use of point load test for Dubai weak calcareous sandstones

Intact rock is typically described according to its uniaxial compressive strength （UCS）. The UCS is needed in the design of geotechnical engineering problems including stability of rock slopes and design of shallow and deep foundations resting on and/or in rocks. Accordingly, a correct measure-ment/evaluation of the UCS is essential to a safe and economic design. Typically, the UCS is measured using the unconfined compression tests performed on cylindrical intact specimens with a minimum length to width ratio of 2. In several cases, especially for weak and very weak rocks, it is not possible to extract intact specimens with the needed minimum dimensions. Thus, alternative tests （e.g. point load test, Schmidt hammer） are used to measure rock strength. The UCS is computed based on the results of these tests through empirical correlations. The literature includes a plethora of these correlations that vary widely in estimating rock strength. Thus, it is paramount to validate these correlations to check their suitability for estimating rock strength for a specific location and geology. A review of the available correlations used to estimate the UCS from the point load test results is performed and summarized herein. Results of UCS, point load strength index and Young＇s modulus are gathered for calcareous sandstone specimens extracted from the Dubai area. A correlation for estimating the UCS from the point load strength index is proposed. Furthermore, the Young＇s modulus is correlated to the UCS.

Effect of loading point position on fracture mode of rock

Anti symmetric four point bending specimen with different loading point positions was used to study effect of loading point position on fracture mode of rock in order to explore a feasible method for achieving Mode Ⅱ fracture and determining Mode Ⅱ fracture toughness of rock, K ⅡC . Numerical and experimental results show that the distance between the inner and outer loading points, L 1+ L 2, has a great influence on stresses at notch tip and fracture mode. When L 1+ L 2>0.5 L or 0.1 L < L 1+ L 2<0.5 L , maximum principal stress σ 1 exceeds the tensile strength σ t. The ratio of τ max / σ 1 is relatively low or high and thus Mode Ⅰ or mixed mode fracture occurs. When L 1+ L 2< 0.1 L , σ 1 is smaller than σ t and the ratio of τ max / σ 1 is much higher, which facilitates the occurrence of Mode Ⅱ fracture.

Nanoindentation Models of Monolayer Graphene and Graphyne under Point Load Pattern Studied by Molecular Dynamics

Molecular dynamics simulations are performed to study the nanoindentation models of monolayer suspended graphene and graphyne. Fullerenes are selected as indenters. Our results show that Young＇s modulus of monolayer-thick graphyne is almost half of that of graphene, which is estimated to be 0.50 TPa. The mechanical properties of graphene and graphyne are different in the presence of strain. A pre-tension has an important effect on the mechanical properties of a membrane. Both the pre-tension and Young＇s modulus plots demonstrate index behavior. The toughness of graphyne is stronger than that of graphene due to Young＇s modulus magnitude. Young＇s moduli of graphene and graphyne are almost independent of the size ratio of indenter to membrane.

Numerical Simulation on Effect of Indenter Radius During Point Load Test

To investigate the effect of the radius of the spherical heads of the indenter on the results of a point load test,this study uses a discrete element model based on the flat joint contact for numerical simulation.Results show that the discrete element model based on the flat joint model can accurately describe the damage process and size effects of rocks under point loads.Damage of rock samples under the loading of different radii of the indenter can be characterized as vertical splitting damage,and the larger the radius of the indenter is,the larger the damage area.Values of the point load strength of rock samples increase with increasing the radius of the indenter and obey a power function relationship.The results of this study provide a theoretical basis for the selection of the spherical heads of indenters in point load tests and tool design for mechanical rock breaking.

A comparative assessment of rock mass deformation modulus

Deformation modulus of a rock mass(E_m) is one of the most important design parameters in construction of rock engineering projects such as underground excavations.However,difficulties are frequently encountered during in-situ tests which are also time-consuming and expensive for determining this parameter.Although E_m is often estimated indirectly from proposed equations by different researchers,many of these equations cannot be used in case of problematic rock conditions(thinly bedded,highly jointed rock masses,etc.) as high quality core samples are required.This study aims to explore more practical and useful equation for E_m estimation using Rock Quality Designation(RQD) and point load index values.Comparisons were made between available empirical equations and the proposed E_m equation in terms of the estimation capacity.Multiple comparison tests(ANOVA) showed that E_m can be reliably estimated using proposed equation especially at the preliminary stages of projects.

Investigation into engineering parameters of marls from Seydoon dam in Iran

The quality of designed structures embedded in rocks is strongly related to rock strength parameters of intact rock.Measuring different parameters from tests could be very expensive in designing phase of projects.Estimating some parameters from other ones can reduce costs and time of project procedure.In this paper,the relationships between static and dynamic parameters of marls are studied by using the single and multiple linear regressions.For this purpose,several marl core samples from Seydoon region,Khoozestan Province in Iran are collected and tested.Some equations with sufficient correlation have been obtained to predict the engineering parameters of marls,especially the uniaxial compressive strength(UCS).

Addressing Economic Dispatch Problem with Multiple Fuels Using Oscillatory Particle Swarm Optimization

Economic dispatch has a significant effect on optimal economical operation in the power systems in industrial revolution 4.0 in terms of considerable savings in revenue.Various non-linearity are added to make the fossil fuel-based power systems more practical.In order to achieve an accurate economical schedule,valve point loading effect,ramp rate constraints,and prohibited operating zones are being considered for realistic scenarios.In this paper,an improved,and modified version of conventional particle swarm optimization(PSO),called Oscillatory PSO(OPSO),is devised to provide a cheaper schedule with optimum cost.The conventional PSO is improved by deriving a mechanism enabling the particle towards the trajectories of oscillatory motion to acquire the entire search space.A set of differential equations is implemented to expose the condition for trajectory motion in oscillation.Using adaptive inertia weights,this OPSO method provides an optimized cost of generation as compared to the conventional particle swarm optimization and other new meta-heuristic approaches.

A Guide to the Influence of Ground Reaction on Ship Stability

Grounded ship faces up exceptionally different stability forces unlike in her normal operating condition. This critical situation must be corrected as soon as can minimize hull stress, the risk of pollution and stability failure. Re-floating the ship need full understanding of the impact of ground reaction （R） on the ship buoyancy and stability. Re-floating the ship has different phases and there are several immediate actions that should be taken by ship＇s crew; one of these phases is re-calculation of ship stability conditions. In this paper, a guide to understanding the effect of the ground reaction （R）, determines the amount of ground pressure and its location. With consideration of the seabed form whether symmetric of asymmetric. Calculating the magnitude of the ground reaction （R） using different applicable methods, explaining the effect of using weight to re-float the ship by her own means, focusing on GM calculation after grounding.

Alternative Method for Concrete Structures Compressive Strength Estimation with Small-Scale Destruction

To estimate a compressive strength from existing concrete structures by core drilling are usually gathered with a diameter specimen of 100 mm or three times of maximum coarse aggregate size and examined by uniaxial compressive strength （UCS）. It is relatively difficult to gather a large sized core, and a pit place will be limited by main members. To get an alternative solution with smaller specimen, point load test （PLT） has been sele,：ted which is a simple test and widely accepted in rock materials research, but relatively new in concrete. The reliability of PLT is evaluated by extracting a lot of core drilled specimen from ready mixed concrete blocks with maximum coarse aggregate size, G of 20 mm in representative of architectural structures and 40 mm in representative of civil structures on the range of concrete grade from 16 to 50. Compressive strengths were classified into general categories, conversion factors were determined, and scattering characteristics were also investigated. The relationship between point load index （Is） and compressive strength of concrete core specimen （fcc） can be written as linear approximation as fcc = k.Is- C.

A Heuristic Method for Vehicle Scheduling Problems

This paper presents a sequential optimum algorithm for vehicle schedulingproblem, which includes obtaining initial theoretical solution, adjustingsolution, forming initial routes and adjustins routes. This method can beapplied to general transportation problems with multiple depots and multiplevehicle types on complex network. In comparison with manual scheduling ofChengdu Transportation Company II, the result shows that this method isreasonable, feasible and applicable.

Solution to economic dispatch loading effect by using catfish problem with valve-point PSO algorithm

This paper proposes application of a catfish particle swarm optimization （PSO） algorithm to economic dispatch （ED） problems. The ED problems considered in this paper include valve-point loading effect, power balance constraints, and generator limits. The conventional PSO and catfish PSO algorithms are applied to three different test systems and the solutions obtained are compared with each other and with those reported in literature. The comparison of solutions shows that catfish PSO outperforms the conventional PSO and other methods in terms of solution quality though there is a slight increase in computational time.

Prediction of uniaxial compressive strength of rock based on lithology using stacking models

Uniaxial compressive strength(UCS)of rock is an essential parameter in geotechnical engineering.Point load strength(PLS),P-wave velocity,and Schmidt hammer rebound number(SH)are more easily obtained than UCS and are extensively applied for the indirect estimation of UCS.This study collected 1080 datasets consisting of SH,P-wave velocity,PLS,and UCS.All datasets were integrated into three categories(sedimentary,igneous,and metamorphic rocks)according to lithology.Stacking models combined with tree-based models and linear regression were developed based on the datasets of three rock types.Model evaluation showed that the stacking model combined with random forest and linear regression was the optimal model for three rock types.UCS of metamorphic rocks was less predictable than that of sedimentary and igneous rocks.Nonetheless,the proposed stacking models can improve the predictive performance for UCS of metamorphic rocks.The developed predictive models can be applied to quickly predict UCS at engineering sites,which benefits the rapid and intelligent classification of rock masses.Moreover,the importance of SH,P-wave velocity,and PLS were analyzed for the estimation of UCS.SH was a reliable indicator for UCS evaluation across various rock types.P-wave velocity was a valid parameter for evaluating the UCS of igneous rocks,but it was not reliable for assessing the UCS of metamorphic rocks.

Application of the invasive weed optimization algorithm to economic dispatch problems

In this paper the invasive weed optimization algorithm has been applied to a variety of economic dispatch （ED） problems. The ED problem is concerned with minimizing the fuel cost by optimally loading the electrical generators which are committed to supply a given demand. Some involve prohibited operating zones, transmission losses and valve point loading. In general, they are non-linear non-convex optimization problems which cannot be directly solved by conventional methods. In this work the invasive weed algorithm, a meta-heuristic method inspired by the proliferation of weeds, has been applied to four numerical examples and has resulted in promising solutions compared to published results.