Damage response of conventionally reinforced two-way spanning concrete slab under eccentric impacting drop weight loading

Reinforced concrete(RC)structures are generally designed to carry quasi-static gravity loads through almost indispensable components namely slab,however,it may be subjected to high intense loads induced from the impact of projectiles generated by the tornado,falling construction equipment,and also from accidental explosions during their construction and service lifespan.Impacts due to rock/boulder falls do occur on the structures located especially in hilly areas.Such loadings are not predictable but may cause severe damage to the slab/structure.It stimulates structural engineers and researchers to investigate and understand the dynamic response of RC structures under such impulsive loading.This research work first investigates the performance of 1000×1000×75 mm^(3)conventionally reinforced two-way spanning normal strength concrete slab with only tension reinforcement(0.88%)under the concentric impact load(1035 N)using the finite element method based computer code,ABAQUS/Explicit-v.6.15.The impact load is delivered to the centroid of the slab using a solid-steel cylindroconical impactor(drop weight)with a flat nose of diameter 40 mm,having a total mass of 105 kg released from a fixed height of 2500 mm.Two popular concrete constitutive models in ABAQUS namely;Holmquist-Johnson-Cook(HJC)and Concrete Damage Plasticity(CDP),with strain rate effects as per fib MODEL CODE 2010,are used to model the concrete material behavior to impact loading and to simulate the damage to the slab.The slab response using these two models is analyzed and compared with the impact test results.The strain rate effect on the reinforcing steel bars has been incorporated in the analysis using the Malvar and Crawford(1998)approach.A classical elastoplastic kinematic idealization is considered to model the steel impactor and support system.Results reveal that the HJC model gives a little overestimation of peak displacement,maximum acceleration,and damage of the slab while the predictions given by the CDP model are in reasonable agreement with the experimental test results/observations available in the open literature.Following the validation of the numerical model,analyses have been extended to further investigate the damage response of the slab under eccentric impact loadings.In addition to the concentric location(P1)of the impacting device,five locations on a quarter of the slab i.e.,two along the diagonal(P2&P3),the other two along the mid-span(P4&P5),and the last one(P6)between P3 and P5,covering the entire slab,are considered.Computational results have been discussed and compared,and the evaluation of the most damaging location(s)of the impact is investigated.It has been found that the most critical location of the impact is not the centroid of the slab but the eccentric one with the eccentricity of 1/6th of the span from the centroid along the mid-span section.

Nonlinear analytical solution for one-dimensional consolidation of soft soil under cyclic loading

This paper presents an analytical solution for one-dimensional consolidation of soft soil under some common types of cyclic loading such as trapezoidal cyclic loading, based on the assumptions proposed by Davis and Raymond （1965） that the decrease in permeability is proportional to the decrease in compressibility during the consolidation process of the soil and that the distribution of initial effective stress is constant with depth the solution obtained, some diagrams are prepared and the It is verified by the existing analytical solutions in special cases. Using telex ant consolidation behavior is investigated.

Study on one-dimensional consolidation of soil under cyclic loading and with varied compressibility

This paper presents a semi-analytical method to solve one dimensional consolidation problem by taking consideration of varied compressibility of soil under cyclic loading. In the method, soil stratum is divided equally into n layers while load and consolidation time are also divided into small parts and time intervals accordingly. The problem of one-dimensional consolidation of soil stratum under cyclic loading can then be dealt with at each time interval as one-dimensional linear consolidation of multi-layered soils under constant loading. The compression or rebounding of each soil layer can be judged by the effective stress of the layer. When the effective stress is larger than that in the last time interval, the soil layer is compressed, and when it is smaller, the soil layer rebounds. Thus, appropriate compressibility can be chosen and the consolidation of the layered system can be analyzed by the available analytical linear consolidation theory. Based on the semi-analytical method, a computer program was developed and the behavior of one-dimensional consolidation of soil with varied compressibility under cyclic loading was investigated, and compared with the available consolidation theory which takes no consideration of varied compressibility of soil under cyclic loading. The results showed that by taking the variable compressibility into account, the rate of consolidation of soil was greater than the one predicted by conventional consolidation theory.

ONE-DIMENSIONAL CONSOLIDATION OF LAYERED AND VISCO-ELASTIC SOILS UNDER ARBITRARY LOADING

Based on the layered visco-elastic soil model, according to the Terzaghi's one dimensional consolidation theory, by the method of Laplace transform and matrix transfer technique, the problems about the consolidation of layered and saturated visco-elastic soils under arbitrary loading were solved. Through deductions, the general solution, in the terms of layer thickness, the modulus and the coefficients of permeability and Laplacian transform's parameters was obtained. The strain and deformation of the layered and saturated visco-elastic soils under arbitrary loading can be calculated by Laplace inversion. According to the results of several numerical examples, the consolidation of visco-elastic soils logs behind that of elastic soils. The development of effective stress and the displacement is vibrant process under cyclic loading. Finally, an engineering case is studied and the results prove that the methods are very effective.

Behavior of eccentrically loaded concrete-filled GFRP tubular short columns

The glass fiber reinforced polymer (GFRP) tube is an effective material that can increase the bearing capacity and ductility of concrete.To study the mechanical behavior of this composite structure,twenty-one concrete-filled GFRP tubular short columns were tested under an eccentric load.The principle influencing factors,such as the eccentricity ratio,concrete strength and ratio of longitudinal reinforcement were also studied.In addition,the course of deformation,failure mode,and failure mechanism were analyzed by observing the phenomena and summarizing the data.The test results indicated that the strength and deformation characteristics of core concrete increase as a result of the addition of the GFRP tube.However,the gain in strength due to the addition of the GFRP tube decreases as the ratio of e /d increases.An increase in the longitudinal steel ratio can improve the bearing capacity of the composite short column effectively.Furthermore,the study showed that the constraint effect of the GFRP tube on high-strength concrete is not as effective as that on common concrete.The reason is that the lateral deformation of the high-strength concrete is less than that of the common concrete when the concrete column was tested under the same axial compression ratio.

The Effect of Core Eccentricity on the Structural Behavior of Concrete Tall Buildings

The main purpose of this paper is to investigate the effect of core eccentricity on the structural behavior of concrete tall buildings.Concrete buildings of 55 floors with plan dimensions 48.0×48.0 m2 were investigated.Three cases of main core locations are studied:centric(A),eccentric by one sixth(B)and one third(C)of building width.The three-dimensional finite element method has been used in conducting structural analysis through ETABS software.Gravity and lateral(wind and seismic)loadings are applied to all building cases.It has been concluded that the core location is the prime parameter governing the structural behavior of tall buildings.Although the first two cases(A,B)have acceptable and similar structural behaviors conforming to code limits,in the third case(C),the building behavior came beyond code limits.The author introduced remedial action by adding two secondary cores in the opposite direction of the main core(C-R)to restore the building behavior to the code limits.The results of this action were satisfactory.

Analytical solution to one-dimensional consolidation in unsaturated soils under sinusoidal cyclic loading

An analytical solution was presented to the unsaturated soil with a finite thickness under confinement in the lateral direction and sinusoidal cyclic loading in the vertical direction based on Fredlund's one-dimensional consolidation equation for unsaturated soil. The transfer relationship between the state vectors at the top surface and any depth was gained by applying the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy's law and Fick's law. The excess pore-air and pore-water pressures and settlement in the Laplace-transformed domain were obtained by using the Laplace transform with the initial and boundary conditions. The analytical solutions of the excess pore-air and pore-water pressures at any depth and settlement were obtained in the time domain by performing the inverse Laplace transforms. A typical example illustrates the consolidation characteristics of unsaturated soil under sinusoidal loading from analytical results. Finally, comparisons between the analytical solutions and results of the numerical method indicate that the analytical solution is correct.

One-dimensional consolidation of double-layered soil with non-Darcian flow described by exponent and threshold gradient

Based on non-Darcian flow law described by exponent and threshold gradient within a double-layered soil, the classic theory of one-dimensional consolidation of double-layered soil was modified to consider the change of vertical total stress with depth and time together. Because of the complexity of governing equations, the numerical solutions were obtained in detail by finite difference method. Then, the numerical solutions were compared with the analytical solutions in condition that non-Darcian flow law was degenerated to Dary's law, and the comparison results show that numerical solutions are reliable. Finally, consolidation behavior of double-layered soil with different parameters was analyzed, and the results show that the consolidation rate of double-layered soil decreases with increasing the value of exponent and threshold of non-Darcian flow, and the exponent and threshold gradient of the first soil layer greatly influence the consolidation rate of double-layered soil. The larger the ratio of the equivalent water head of external load to the total thickness of double-layered soil, the larger the rate of the consolidation, and the similitude relationship in classical consolidation theory of double-layered soil is not satisfied. The other consolidation behavior of double-layered soil with non-Darcian flow is the same as that with Darcy's law.

Study on Seepage Characteristics of Composite Bucket Foundation Under Eccentric Load

Under the effect of eccentric loads,when the suction pressure of the composite bucket foundation is leveled,the seepage failure is very easy to occur.The seepage failure occurrence causes the foundation to settle unevenly and impairs the bearing performance.This study uses ABAQUS finite element software to establish a composite bucket foundation model for finite element analysis.The model simulates the seepage of the foundation penetrating process under eccentric load to reveal the induced seepage characteristics of the bucket foundation.The most vulnerable position of seepage failure under the eccentric loading is elucidated.Critical suction formulas for different offset eccentric moment strategies are derived and compared with existing literature formulas.Then the derived formula is supplemented and corrected according to the pressure difference between adjacent cabins.Conclusions can be drawn:(1)Under eccentric loads,the critical suction decreases about 7%−10%.(2)The pressure difference between adjacent cabins impacts significantly on the seepage field,and the critical suction,at most,can be reduced by 17.56%.(3)the offset strategies have little effect on the seepage field.Efficient and appropriate strategies can be selected to meet the requirement of leveling in engineering project.

Influence of location of large-scale asperity on shear strength of concrete-rock interface under eccentric load

The location and geometry of large-scale asperity present at the foundation of concrete gravity dams and buttress dams affect the shear resistance of the concrete-rock interface.However,the parameters describing the frictional resistance of the interface usually do not account for these asperities.This could result in an underestimate of the peak shear stre ngth,which leads to significantly conservative design for new dams or unnecessary stability enhancing measures for existing ones.The aim of this work was to investigate the effect of the location of first-order asperity on the peak shear strength of a concrete-rock interface under eccentric load and the model discrepancy associated with the commonly used rigid body methods for calculating the factor of safety(FS)against sliding.For this,a series of direct and eccentric shear tests under constant normal load(CNL)was carried out on concrete-rock samples.The peak shear strengths measured in the tests were compared in terms of asperity location and with the predicted values from analytical rigid body methods.The results showed that the large-scale asperity under eccentric load significantly affected the peak shear strength.Furthermore,unlike the conventional assumption of sliding or shear failure of an asperity in direct shear,under the effect of eccentric shear load,a tensile failure in the rock or in the concrete could occur,resulting in a lower shear strength compared with that of direct shear tests.These results could have important implications for assessment of the FS against sliding failure in the concrete-rock interface.

General semi-analytical solutions to one-dimensional consolidation for unsaturated soils

This paper presents general semi-analytical solutions to Fredlund and Hasan＇s one-dimensional （1D） consolidation equations for unsaturated soils subject to different initial conditions, homogeneous boundaries and time-dependent loadings. Two variables are introduced to transform the two-coupled governing equations of pore-water and poreair pressures into an equivalent set of partial differential equations （PDEs）, which are solved with the Laplace transform method. The pore-water and pore-air pressures and settlement are obtained in the Laplace transform domMn. The Crump＇s method is used to perform inverse Laplace transform to obtain the solutions in the time domain. The present solutions are more general in practical applications and show good agreement with the previous solutions in the literature.

Behavior of ring footing resting on reinforced sand subjected to eccentric-inclined loading

Ring footings are suitable for the structures like tall transmission towers, chimneys, silos and oil storages.These types of structures are susceptible to horizontal loads(wind load) in addition to their dead weight.In the literature, very little or no effort has been made to study the effect of ring footing resting on reinforced sand when subjected to eccentric, inclined and/or eccentric-inclined loadings. This paper aims to study the behavior of ring footing resting on loose sand and/or compacted randomly distributed fiberreinforced sand(RDFS) when subjected to eccentric(0 B, 0.05 B and 0.1 B, where B is the outer diameter of ring footing), inclined(0°,5°,10°, 15°,-5°,-10° and-15°)and eccentric-inclined loadings by using a finite element(FE) software PLAXIS 3 D. The behavior of ring footing is studied by using a dimensionless factor called reduction factor(RF). The numerical model used in the PLAXIS 3 D has been validated by conducting model plate load tests. Moreover, an empirical expression using regression analysis has been presented which will be helpful in plotting a load-settlement curve for the ring footing.

Load eccentricity effects on behavior of circular footings reinforced with geogrid sheets

In this paper, an experimental study for an eccentrically loaded circular footing, resting on a geogridreinforced sand bed, is performed. To achieve this aim, the steel model footing of 120 mm in diameterand sand in relative density of 60% are used. Also, the effects of depth of first and second geogrid layersand number of reinforcement layers （1e4） on the settlement-load response and tilt of footing undervarious load eccentricities （0 cm, 0.75 cm, 1.5 cm, 2.25 cm and 3 cm） are investigated. Test results indicatethat ultimate bearing capacity increases in comparison with unreinforced condition. It is observed thatwhen the reinforcements are placed in the optimum embedment depth （u/D ？0.42 and h/D ？0.42）, thebearing capacity ratio （BCR） increases with increasing load eccentricity to the core boundary of footing,and that with further increase of load eccentricity, the BCR decreases. Besides, the tilt of footing increaseslinearly with increasing settlement. Finally, by reinforcing the sand bed, the tilt of footing decreases at 2layers of reinforcement and then increases by increasing the number of reinforcement layers.

Numerical and experimental analyses for bearing capacity of rigid strip footing subjected to eccentric load

A footing may get an eccentric load caused by earthquake or wind, thus the bearing capacity of footing subjected to eccentric load become a fundamental geotechnical problem. The conventional limit equilibrium method used for this problem usually evaluates the material properties only by its final strength. But the classical finite element method(FEM) does not necessarily provide a clear collapse mechanism associated with the yield condition of elements. To overcome these defects, a numerical procedure is proposed to create an explicit collapse mode combining a modified smeared shear band approach with a modified initial stress method. To understand the practical performance of sand foundation and verify the performance of the proposed procedure applied to the practical problems, the computing results were compared with the laboratory model tests results and some conventional solutions. Furthermore, because the proposed numerical procedure employs a simple elasto-plastic model which requires a small number of soil parameters, it may be applied directly to practical design works.

Analysis of one-dimensional consolidation of soft soils with non-Darcian flow caused by non-Newtonian liquid

Based on non-Darcian flow caused by non-Newtonian liquid, the theory of one-dimensional (1D) consolidation was modified to consider variation in the total vertical stress with depth and time. The finite difference method (FDM) was adopted to obtain numerical solutions for excess pore water pressure and average degree of consolidation. When non-Darcian flow is degenerated into Darcian flow, a comparison between numerical solutions and analytical solutions was made to verify reliability of finite difference solutions. Finally, taking into account the ramp time-dependent loading, consolidation behaviors with non-Darcian flow under various parameters were analyzed. Thus, a comprehensive analysis of 1D consolidation combined with non-Darcian flow caused by non-Newtonian liquid was conducted in this paper.

Determination of the load bearing capacity of pre-stressed expandable props for ground support in underground mines

This paper aims to determine the load bearing capacity of pre-stressed expandable props with different geometries and load eccentricities for flexible support in underground mining or excavation.It is deduced that the expandable device could have much higher strength(>89 MPa)by laboratory tests,and the load bearing capacity of the expandable prop may depend on the stability of the supporting steel pipe structure.A good agreement was found between the laboratory test and numerical results in terms of the load bearing capacity and the final macro-bending failure pattern for expandable props with heights of 1.5 and 2.7 m,and the theoretical calculation for the strength of traditional steel structures is not directly suitable for the expandable props.Moreover,additional numerical simulations were performed for the expandable props with different normalized slenderness ratiosλ_(n)and loading eccentric distances e.The variation of stability coefficient of the expandable prop is in line with the Perry-Robertson equation and its correlation coefficients are fitted as a of 0.979 and b of 0.314.For estimating the load bearing capacity of the expandable props,the strength equation for traditional steel structures is improved by introducing a bending magnification factor and by modifying the normalized slenderness ratio to a converted slenderness ratio.Based on the underground field monitoring for the strength of expandable props with different heights,the empirical eccentric distances were back calculated,and a safety factor is introduced to obtain the designed strength of the expandable prop.In addition,a four-step design procedure is proposed for the expandable prop.

Penetration Resistance of Composite Bucket Foundation with Eccentric Load for Offshore Wind Turbines

The penetration of the composite bucket foundation(CBF)is crucial in its construction process.In actual projects,the foundation is inevitably subjected to eccentric load caused by towers and turbines,as well as wind,wave,and flow,during the one-step installation.Moreover,the eccentric load is bound to affect the penetration method and penetration resistance of the foundation.To examine the above-mentioned issues,the penetration resistance of CBF with eccentric load was calculated and analyzed based on model tests,and the seepage field of the CBF under eccentric load was analyzed using ABAQUS.The influence of different magnitudes of eccentric load and various offset strategies on penetration resistance was analyzed,and the theoretical and measured values were compared.The result indicated that the negative pressure of the offset room was found to be smaller than that of other rooms when the CBF penetrated the soil under eccentric load.The penetration resistance of CBF under eccentric load was larger than that without eccentricity,and the larger the eccentric load is,the greater the penetration resistance.The influence of different eccentric load offset strategies on penetration resistance was found to be negligible.The calculated penetration resistance under eccentric load was in good agreement with the measured value.

Ultimate Bearing Capacity of Hollow Spherical Joints Welded with Circular Pipes under Eccentric Loads

The hollow spherical joints welded with circular pipes applied to the National Swimming Center of China are subjected to large bending moments, but the influence of bending moments is not considered in the design equations in Technical Specification for Latticed Shells. Based on the von Mises yield criterion, multilinear isotropic hardening rule and associated flow rule, the elasto-plastic finite element model is put forward to analyze the behavior of the joints, and a calculation method for the joints under bending moments or eccentric loads is proposed. It is shown by the analytical results of joint that the stiffening rib can improve the ultimate bearing capacity by 10% for joints under axial tensile load, by 40% for joints under axial compressive load, and by 50% for joints under bending moment. The unified calculation equations for joints with or without stiffening rib are put forward, which can be applied to calculating the ultimate bearing capacity of the hollow spherical joints with circular pipes under eccentric loads.

Near Surface Mounted Application for the Strengthening of Rectangular Reinforced Concrete Slender Columns under Eccentric Load

The behavior of slender columns under the effect of eccentric loading has always taken the attention of researchers. When investigating the strengthening of reinforced concrete columns, mainly short and circular columns are the targeted elements. This is why the data about slender columns with rectangular sections is limited and infrequent specially when loaded eccentrically. This paper aims to increase the available experimental data in this specific area. The experimental program consisted of twenty seven specimens. The specimens were divided into three groups; one control group and two groups strengthened using two strengthening schemes. Scheme 1 implied the use of near surface mounted （NSM） longitudinal steel bars, while in scheme 2, NSM longitudinal steel bars partially wrapped with one ply of carbon fibers reinforced polymers （CFRP） sheets was used. The test specimen had an overall length of 2000 mm and a 100 x 200 mm rectangular cross section. In addition to the strengthening schemes, the test parameters included three ratios for the internal longitudinal steel bars ＂μ＂ 1%, 1.57% and 2.26%. The parameters were extended to cover three stirrups＇ volumetric ratio ＂ρv＂ 0.73%, 0.49% and 0.37%. The specimens were tested under the effect of eccentric loading with eccentricity-to-section height e/h equals 0.25. The research revealed that the strength gain in specimens strengthened with scheme 2 was higher than with scheme 1. Analytical modeling of the stress strain relation of the strengthened RC columns considering the effect of strengthening scheme, internal reinforcement ratio μ, and stirrups＇ volumetric ratio ＂ρv＂ was proposed. Verification was made using available experimental data. The proposed model showed a reasonable agreement with the experimental results.

不同损伤模型下偏心不耦合装药爆破特性

在实际爆破工程中,药包因自身重量与炮孔处于偏心不耦合的相对位置。此装药结构下,爆破荷载对其炮孔近区的岩体作用分布不均匀,会造成炮孔近区爆炸能量及损伤演化分布的差异。利用数值模拟软件,分别采用HJC模型和RHT模型建立岩石单孔爆破结构,探究了不同本构模型下偏心不耦合装药岩体的爆炸损伤特性。结果表明,基于本文的模拟环境,同心不耦合装药条件下,炮孔周围损伤程度基本相同,但RHT模型下的损伤范围比HJC模型大近一倍;随着偏心系数的增大,HJC模型损伤范围偏向于炮孔耦合侧,RHT模型炮孔耦合侧与非耦合侧爆破损伤范围分布不均;RHT模型能更准确地呈现实际爆破工程中岩体裂纹的扩展形态。