Dynamic response of UHMWPE plates under combined shock and fragment loading

Ultra-high molecular weight polyethylene(UHMWPE)fiber composite has been extensively used to construct lightweight protective structures against ballistic impacts,yet little is known about its performance when subjected to combined blast and fragment impacts.Built upon a recently developed laboratory-scale experimental technique to generate simulated combined loading through the impact of a fragment-foam composite projectile launched from a light gas gun,the dynamic responses of fullyclamped UHMWPE plates subjected to combined loading were characterized experimentally,with corresponding deformation and failure modes compared with those measured with simulated blast loading alone.Subsequently,to explore the underlying physical mechanisms,three-dimensional(3D)numerical simulations with the method of finite elements(FE)were systematically carried out.Numerical predictions compared favorably well with experimental measurements,thus validating the feasibility of the established FE model.Relative to the case of blast loading alone,combined blast and fragment loading led to larger maximum deflections of clamped UHMWPE plates.The position of the FSP in the foam sabot affected significantly the performance of a UHMWPE target,either enhancing or decreasing its ballistic resistance.When the blast loading and fragment impact arrived simultaneously at the target,its ballistic resistance was superior to that achieved when subjected to fragment impact alone,and benefited from the accelerated movement of the target due to simultaneous blast loading.

Mechanical responses of anchoring structure under triaxial cyclic loading

Dynamic load on anchoring structures(AS)within deep roadways can result in cumulative damage and failure.This study develops an experimental device designed to test AS under triaxial loads.The device enables the investigation of the mechanical response,failure mode,instability assessment criteria,and anchorage effect of AS subjected to combined cyclic dynamic-static triaxial stress paths.The results show that the peak bearing strength is positively correlated with the anchoring matrix strength,anchorage length,and edgewise compressive strength.The bearing capacity decreases significantly when the anchorage direction is severely inclined.The free face failure modes are typically transverse cracking,concave fracturing,V-shaped slipping and detachment,and spallation detachment.Besides,when the anchoring matrix strength and the anchorage length decrease while the edgewise compressive strength,loading rate,and anchorage inclination angle increase,the failure intensity rises.Instability is determined by a negative tangent modulus of the displacement-strength curve or the continued deformation increase against the general downward trend.Under cyclic loads,the driving force that breaks the rock mass along the normal vector and the rigidity of the AS are the two factors that determine roadway stability.Finally,a control measure for surrounding rock stability is proposed to reduce the internal driving force via a pressure relief method and improve the rigidity of the AS by full-length anchorage and grouting modification.

Combined load bearing capacity of rigid piles embedded in a crossanisotropic clay deposit using 3D finite element lower bound

In this study,an iterative-based three-dimensional finite element lower bound in association with the second-order cone programming method is adopted to evaluate the limit load of a single pile embedded in cross-anisotropic soils under general loading condition.The lower bound solutions of the pile embedded in an anisotropic soil deposit can be found by formulating the element equilibrium,equilibrium of shear and normal stresses along discontinuities,boundary conditions,yield function,and optimizing the objective function through the second-order cone programming method in conjunction with an iterative-based update procedure.A general loading condition is considered to profile the expansion of the safe load in the vertical-horizontal-moment(V-H-M)space.The results of this study are compared and validated against three different cases including an isotropic lateral loading,anisotropic end bearing capacity,and a pile embedded in an isotropic soil deposit under general loading condition.A parametric study is conducted to evaluate the impact of different influencing factors.It was found that the effect of anisotropy on the variation of lateral limit load of a single pile is more pronounced than the corresponding vertical and bending moment limit loads,whereas the interface properties have more significant effects on the vertical and bending moment limit loads in comparison to the lateral limit load.

Failure mechanism and coupled static-dynamic loading theory in deep hard rock mining: A review

Rock failure phenomena,such as rockburst,slabbing(or spalling) and zonal disintegration,related to deep underground excavation of hard rocks are frequently reported and pose a great threat to deep mining.Currently,the explanation for these failure phenomena using existing dynamic or static rock mechanics theory is not straightforward.In this study,new theory and testing method for deep underground rock mass under coupled static-dynamic loading are introduced.Two types of coupled loading modes,i.e.'critical static stress + slight disturbance' and 'elastic static stress + impact disturbance',are proposed,and associated test devices are developed.Rockburst phenomena of hard rocks under coupled static-dynamic loading are successfully reproduced in the laboratory,and the rockburst mechanism and related criteria are demonstrated.The results of true triaxial unloading compression tests on granite and red sandstone indicate that the unloading can induce slabbing when the confining pressure exceeds a certain threshold,and the slabbing failure strength is lower than the shear failure strength according to the conventional Mohr-Column criterion.Numerical results indicate that the rock unloading failure response under different in situ stresses and unloading rates can be characterized by an equivalent strain energy density.In addition,we present a new microseismic source location method without premeasuring the sound wave velocity in rock mass,which can efficiently and accurately locate the rock failure in hard rock mines.Also,a new idea for deep hard rock mining using a non-explosive continuous mining method is briefly introduced.

Dynamic tensile behaviour and crack propagation of coal under coupled static-dynamic loading

The fracture behaviour and crack propagation features of coal under coupled static-dynamic loading conditions are important when evaluating the dynamic failure of coal.In this study,coupled static-dynamic loading tests are conducted on Brazilian disc(BD)coal specimens using a modified split Hopkinson pressure bar(SHPB).The effects of the static axial pre-stress and loading rate on the dynamic tensile strength and crack propagation characteristics of BD coal specimens are studied.The average dynamic indirect tensile strength of coal specimens increases first and then decreases with the static axial pre-stress increasing.When no static axial pre-stress is applied,or the static axial pre-stress is 30%of the static tensile strength,the dynamic indirect tensile strength of coal specimens shows an increase trend as the loading rate increases.When the static axial pre-stress is 60%of the static tensile strength,the dynamic indirect tensile strength shows a fluctuant trend as the loading rate increases.According to the crack propagation process of coal specimens recorded by high-speed camera,the impact velocity influences the mode of crack propagation,while the static axial pre-stress influences the direction of crack propagation.The failure of coal specimens is a coupled tensile-shear failure under high impact velocity.When there is no static axial pre-stress,tensile cracks occur in the vertical loading direction.When the static axial pre-stress is applied,the number of cracks perpendicular to the loading direction decreases,and more cracks occur in the parallel loading direction.

Study on Failure Mechanism and Bearing Capacity of Three-Dimensional Rectangular Footing Subjected to Combined Loading

This paper presents two kinematic failure mechanisms of threc-dimensional rectangular footing resting on homogeneous undrained clay foundation under uniaxial vertical loading and uniaxial moment loading. The failure mechanism under vertical loading comprises a plane strain Prandti-type mechanism over the central part of the longer side, and the size of the mechanism gradually reduces at the ends of the longer side and over the shorter side as the corner of rectangular footing is being approached where the direction of soil motion remains normal to each corresponding side respectively. The failure mechanism under moment loading comprises a plane strain scoop sliding mechanism over the central part of the longer side, and the radius of scoop sliding mechanism increases linearly at the ends of the longer side. On the basis of the kinematic failure mechanisms mentioned above, the vertical ultimate bearing capacity and the ultimate bearing capacity against moment or moment ultimate bearing capacity are obtained by use of upper bound limit analysis theory. At the same time, numerical analysis results, Skempton＇ s results and Salgado et al. ＇s results are compared with this upper bound solution. It shows that the presented failure mechanisms and plastic limit analysis predictions are validated. In order to investigate the behaviors of undrained clay foundation beneath the rectangular footing subjected to the combined loadings, numerical analysis is adopted by virtue of the general-purpose FEM software ABAQUS, where the clay is assumed to obey the Mohr-Coulomb yielding criterion. The failure envelope and the ultimate bearing capacity are achieved by the numerical analysis results with the varying aspect ratios from length L to breadth B of the rectangular footing. The failure mechanisms of rectangular footing which are subjected to the combined vertical loading V and horizontal loading H （Vertical loading V and moment loading M, and horizontal loading H and moment loading M respectively are observed in the finite element analysis. ） is explained by use of the upper bound plasticity limit analysis theory. Finally, the reason of eccentricity of failure envelope in H-M loading space is given in this study, which can not be explained by use of the traditional ＇ swipe test＇.

Dynamic response and failure behavior of rock under static-dynamic loading

Dynamic response and failure behavior of rock under static-dynamic loading were studied. The effects of initial static load on the total energy dissipated during the failure process of specimen were analyzed. To simulate the engineering situation that in-situ rock experienced and obtain the dynamic loading with an intermediate strain rate, a low cycle fatigue load with the frequency from 0.5 to 5 Hz was adopted by servo-controlled Instron material testing system. The results show that the obtained strain rate increase with the increase of load frequency. The initial static load has great influence on both the energy and dynamic response of rock. Both the energy and the maximum failure load P_f decreases with the increase of initial static load. P_f under the static-dynamic loading is larger than that under only the static loading but less than that under only the dynamic loading. The load-displacement curves become nonlinear as the pre-added static load reaches the transition point which is about one third of static strength. With the increase of initial static load, Young’s modulus decreases and poisson ratio increases. It shows that rock has a lower strength and a tendency to soften under a higher initial static load. Rock may be broken more easily static-dynamic loading than under only the dynamic loading. The proposed method is useful in the investigation of constitutive relationship and failure behavior of rock under quasi-dynamic loading.

Failure Loci of Suction Caisson Foundations Under CombinedLoading Conditions

Suction caissons are widely used to support offshore fixed platforms in coastal areas. The loadings transferred to suction caissons include the eccentric lateral force induced by waves and self weight of the platform structure. However, under this kind of combined loading conditions, the failure mechanism of caissons with shallow embedment depths is quite different from conventional deep foundations or onshore shallow footings. The behaviour of caissons subjected to combined loadings may be described with the ＂failure locus＂ in force resultant spaces. Here the failure loci of smooth caissons are studied by use of finite dement approach, with the embedment ratio of caissons varying in the range of 0.25 - 1.0 and eccentricity ratio of horizontal loadiugs in 0 - 10. The platform settlement and tilt limits are involved into determination of failure loci, thus the platforms can avoid significant displacements for the combined loadings located inside the failure locus. Three families of loading paths are used to map out the locus. It is found that the shape of failure loci depends on 3 non-dimensional parameters, and the failure locus of a given caisson changes gradually from the elliptical curve to hooked curve with increasing shear strength of soil. The lateral capacity of short caissons may be enhanced by vertical forces, compared with the maximum lateral capacity of long caissons occurring at the vertical force being zero. The critical embedment ratios partitioning elliptical and hooked loci are proposed.

Undrained Bearing Capacity of Spudcan Under Combined Loading

The bearing capacities of spudcan foundation under pure vertical （/1）, horizontal （H）, moment （M） loading and the combined loading are studied based on a series of three-dimensional finite element analysis. The effects of embedment ratio and soil non-homogeneity on the bearing capacity are investigated in detail. The capacities of spudcan under different pure loading are expressed in non-dimensional bearing capacity factors, which are compared with published results. Ultimate limit states under combined loading are presented by failure envelopes, which are expressed in terms of dimensionless and normalized form in three-dimensional load space. The comparison between the presented failure envelopes and available published numerical results reveals that the size and shape of failure envelopes are dependent on the embedment ratio and the non-homogeneity of the soil.

Variable-stiffness composite cylinder design under combined loadings by using the improved Kriging model

The large design freedom of variable-stiffness (VS) composite material presupposes its potential for wide engineering application. Previous research indicates that the design of VS cylindrical structures helps to increase the buckling load as compared to quasi-isotropic (QI) cylindrical structures. This paper focuses on the anti-buckling performance of VS cylindrical structures under combined loads and the efficient optimization design method. Two kinds of conditions, bending moment and internal pressure, and bending moment and torque are considered. Influences of the geometrical defects, ovality, on the cylinder's performances are also investigated. To increase the computational efficiency, an adaptive Kriging meta-model is proposed to approximate the structural response of the cylinders. In this improved Kriging model, a mixed updating rule is used in constructing the meta-model. A genetic algorithm (GA) is implemented in the optimization design. The optimal results show that the buckling load of VS cylinders in all cases is greatly increased as compared with a QI cylinder.

Biaxial mechanical behavior of closed-cell aluminum foam under combined shear-compression loading

Combined shear-compression tests and simulations were performed on a closed-cell aluminum foam over a wide range of loading angles in order to probe their yield behaviors under biaxial loading conditions.Combined shear-compression tests were carried out by using a pair of cylindrical bars with beveled ends.The yield surfaces were experimentally measured and compared with various theoretical yield surface models.The cellular structures of closed-cell aluminum foams were modeled as tetrakaidecahedrons and their biaxial crushing behaviors were simulated by the finite element method.The results show that,yield initiates from the stress-concentrated corners in the specimens under combined shear-compression loading and the stress distribution is no longer uniform at the specimen/bar interfaces.In the range of cell sizes studied,the larger the foam cell size is,the higher the yield stress is.Aluminum foam density is found to be the dominant factor on its mechanical properties compared with the cell size and is much more significant in engineering practice.

Study on Deformation Law of Circular Foundation Under Combined Loading

The foundations of some ocean engineering structures are built to withstand not only the vertical gravity load V, but also the horizontal load H induced by sea waves and current. The horizontal load includes the concentrated force load, the moment load M, and the torque load T termed also as combined loading. It is of academic and engineering significance to study the deformation law of submarine seabed due to combined loading. On the basis of the three-dimensional elastic mechanics solution of circular foundation, numerical methods are used to analyze the deformation law of submarine soil under circular foundation with six degrees of freedom. The finite element analysis results give the elastic deformation law of soil in three dimensional spaces, modify the theoretical elasticity solution, and presents nonlinear soil deformation mechanism under the circular foundation with six degrees of freedom.

Buckling analysis of shear deformable composite conical shells reinforced by CNTs subjected to combined loading on the two-parameter elastic foundation

The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the twoparameter elastic foundation(T-P-EF).It is one of the first attempts to derive the governing equations of the CCSs reinforced with CNTs,based on a generalized first-order shear deformation shell theory(FSDST)which includes shell-foundation interaction.By adopting the extended mixing rule,the effective material properties of CCSs reinforced by CNTs with linear distributions are approximated by introducing some efficiency parameters.Three carbon nanotube distribution in the matrix,i.e.uniform distribution(U)and V and X-types linear distribution are taken into account.The stability equations are solved by using the Galerkin procedure to determine the combined buckling loads(CBLs)of the structure selected here.The numerical illustrations cover CBLs characteristics of CCSs reinforced by CNTs in the presence of the T-P-EF.Finally,a parametric study is carried out to study the influences of the foundation parameters,the volume fraction of carbon nanotubes and the types of reinforcement on the CBLs.

Crack propagation mechanism of compression-shear rock under static-dynamic loading and seepage water pressure

To reveal the water inrush mechanics of underground deep rock mass subjected to dynamic disturbance such as blasting, compression-shear rock crack initiation rule and the evolution of crack tip stress intensity factor are analyzed under static-dynamic loading and seepage water pressure on the basis of theoretical deduction and experimental research. It is shown that the major influence factors of the crack tip stress intensity factor are seepage pressure, dynamic load, static stress and crack angle. The existence of seepage water pressure aggravates propagation of branch cracks. With the seepage pressure increasing, the branch crack experiences unstable extension from stable propagation. The dynamic load in the direction of maximum main stress increases type I crack tip stress intensity factor and its influence on type II crack intensity factor is related with crack angle and material property. Crack initiation angle changes with the dynamic load. The initial crack initiation angle of type I dynamic crack fracture is 70.5°. The compression-shear crack initial strength is related to seepage pressure, confining pressure, and dynamic load. Experimental results verify that the initial crack strength increases with the confining pressure increasing, and decreases with the seepage pressure increasing.

A HALF PLANE CRACK UNDER THREE-DIMENSIONAL COMBINED MODE IMPACT LOADING

The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body, with the crack faces subjected to a traction distribution consisting of two pairs of suddenly-applied shear line loads is consid- ered. The analytic expression for the combined mode stress intensity factors as a function of time is obtained. The method of solution is based on the application of integral transforms and the Wiener-Hopf technique. Some features of the solutions are discussed and graphical numerical results are presented.

General Analytical Shakedown Analysis of a Structure Subjected to Combined Loading with Constant and Cyclic Loads

The shakedown behavior of structures subjected to a combined loading of constant and cyclic loads has been well researched.For some specified problems,shakedown limit loads have been obtained.However,the general effect of combined loading on the structural shakedown has not yet been presented.The general analytic solution of the elastic shakedown limit load is thus derived for a structure subjected to combined loading.Polizzotto's extended static shakedown theorem for combined loading is applied.The stress field in equilibrium with the external constant load required in Polizzotto's extended theorem is constructed by subtracting the reference elastic stress field of the peak cyclic load from the elastic-plastic stress field of the combined constant load and peak cyclic load.The shakedown condition of the stress field is then derived according to the extended theorem.Through the analytical analysis of the shakedown condition,the structural shakedown behavior under combined loading is investigated.A general solution of the shakedown limit load is then derived,and the effects of the combined loading on the shakedown behavior are proposed.The obtained general analytical result is applied to a hollow tension specimen under constant tension and alternating torsion and a plate with a central hole under constant and cyclic tension.The results are consistent with the solutions reported in the literature.

Supporting characteristics analysis of constant resistance bolts under coupled static-dynamic loading

To study the tensile mechanical properties of constant resistance bolts, the RFPA(Rock Failure Process Analysis) statics software is used to perform a uniaxial tensile test on a constant resistance bolt. The numerical test results show that the plastic strain value is 12 times the magnitude of the elastic strain. During plastic deformation, the fluctuation in the stress magnitude is relatively stable, indicating that the bolt has good constant resistance characteristics. The numerical test results are in good agreement with the laboratory test results of M.C. He, and the accuracy and reliability of the numerical test method are verified. Therefore, the RFPA software with coupled static-dynamic loading is further adopted to study the supporting effects of traditional bolts and constant resistance bolts under coupled staticdynamic loading. The numerical comparison of the test results show that the constant resistance bolts can effectively control the deformation amount and rate of the laneway surrounding rock, reduce the total and rate of increase in the accumulated acoustic emissions,decrease the stress on the units in the model and protect the stability of the laneway. This paper verifies that a constant resistance bolt has better impact resistance mechanical properties than those of a traditional bolt and provides an effective way to control rock burst and soft rock that is prone to large deformation damage.

A New Fracture Criterion for a Crack under Combined Mode Loading

A new fracture criterion was proposed. The physical explanation of the criterion is that crack will propagate when the minimum strain energy density in iso hoop stress curve reach a critical strength of the material considered. The resulting curve of critical fracture of mixed mode cracks shows that the present fracture is efficient and more accurate than the previous criteria.

Reliability analysis of marine risers with narrow and long corrosion defects under combined loads

A marine riser,one of the most important components of offshore oil/gas transportation,needs to be designed to eliminate the risks caused by complex ocean environments,platform displacement and internal corrosion,etc.In this study,a new analytical-numerical assessment approach is proposed in order to quantitatively investigate the reliability of internally corroded risers under combined loads including axial tension and internal pressure.First,an analytical solution of the limit state function of intact risers under combined loads is obtained,which is further modified by the non-dimensional corrosion depth （d/ t） for the risers with a narrow and long corrosion defect.The relationship between d/t and limited internal pressure is obtained by finite element analysis and nonlinear regression.Through an advanced first-order reliability method （HL-RF） algorithm,reliability analysis is performed to obtain the failure probability,the reliability index and the sensitivity.These results are further verified by Monte-Carlo importance sampling.The proposed approach of reliability analysis provides an accurate and effective way to estimate the reliability of marine risers with narrow and long corrosion defects under combined loads.

Effects of water intrusion and loading rate on mechanical properties of and crack propagation in coal–rock combinations

Tackling the problems of underground water storage in collieries in arid regions requires knowledge of the effect of water intrusion and loading rate on the mechanical properties of and crack development in coal–rock combinations. Fifty-four coal–rock combinations were prepared and split equally into groups containing different moisture contents(dry, natural moisture and saturated) to conduct acoustic emission testing under uniaxial compression with loading rates ranging from 0.1 mm/min to 0.6 mm/min. The results show that the peak stress and strength-softening modulus, elastic modulus, strain-softening modulus, and post-peak modulus partly decrease with increasing moisture content and loading rate. In contrast, peak strain increases with increasing moisture content and fluctuates with rising loading rate. More significantly, the relationship between stiffness and stress, combined with accumulated counts of acoustic emission, can be used to precisely predict all phases of crack propagation. This is helpful in studying the impact of moisture content and loading rate on crack propagation and accurately calculating mechanical properties. We also determined that the stress thresholds of crack closure, crack initiation, and crack damage do not vary with changes of moisture content and loading rate, constituting 15.22%, 32.20%, and 80.98% of peak stress, respectively. These outcomes assist in developing approaches to water storage in coal mines, determining the necessary width of waterproof coal–rock pillars, and methods of supporting water-enriched roadways, while also advances understanding the mechanical properties of coal–rock combinations and laws of crack propagation.