Shear Displacement Amplitude Research Articles

Frictional behavior of sandstone fractures under forward-backward pre-peak cyclic loading

The objective of this study is to determine the effect of cyclic loading under pre-peak condition on shearing behavior of fractures in Phra Wihan sandstone, primarily to improve an understanding of the stability conditions of slope embankments along roadways and railways in the north of Thailand where seismic activities have often occurred. The fractures were artificially made in the laboratory by tension inducing method and cyclically sheared under forward to fully backward loading paths with constant normal stresses between 1 and 4 MPa. Two cyclic loading conditions were used on separate sets of specimens: constant stress amplitude and constant displacement amplitude. Fifty shear cycles were applied. The results indicated that the pre-peak cyclic loading under both loading conditions slightly reduce shear strengths and stiffness of the sandstone fractures due to the degradation of the second order fracture asperities. Fracture roughness notably reduced particularly under large shear stress and displacement amplitudes due to the deposition and packing of rock power. The subsequent monotonic loading performed after cyclic loading showed further reduction of fracture roughness due to the degradations of the first order asperities.

Behaviour of the interface between stored wheat and a steel silo under static and cyclic loading conditions

The interface behaviour between the steel surfaces of a silo and the grains wheat stored within plays a decisive role in the design of the structure of the silo. A series of strain-controlled direct shear tests, including monotonic loading, cyclic loading and post-cyclic loading were used to study the behaviour of the wheat-steel interface behaviour. The influence of cycle numbers, shear displacement amplitude, normal stress and initial void ratio on the behaviour of the interface behaviour are examined in detail. It was observed that the cyclic loading results in an increasing peak strength, internal friction angle and apparent cohesion, whereas decreasing interface contraction deformation occurs. The results show that the values of peak stress increase with increasing displacement amplitude and cycles, and they change slightly after 10 cycles. The interface exhibits overall contraction, while the contraction is suppressed by an alternating small dilation during cyclic loading. The ultimate peak shear strength increases with increasing normal stress and decreasing initial void ratio. During the tests, the interfaces displayed larger contraction at higher normal stresses and initial void ratios. These findings provide useful information for the analysis of the wheat-steel interface behaviour during both static and cyclic loading conditions.

Cyclic Frictional Responses of Planar Joints Under Cyclic Normal Load Conditions: Laboratory Tests and Numerical Simulations

An accurate quantification of the frictional behaviour of joints under cyclic normal load conditions during the cyclic shear process is important to characterize the joint and fault interactions during earthquakes and rock bursts. We conducted experimental studies and numerical simulations to investigate the cyclic frictional responses of planar joints subjected to cyclic changes of normal loads. Experiments were conducted on artificial rock-like planar joints using a large shear box device (GS-1000), with different vertical and horizontal impact frequencies, vertical impact load amplitudes, horizontal shear displacement amplitudes, and normal load levels. The average normal displacement of the upper block increased with decreasing normal load and decreased with increasing normal load during each cycle. The normal displacement decreased gradually with increasing number of shear cycles due to damage to the micro-asperities at the contact surface. Shear force and the apparent coefficient of friction (k = FShear/FNormal) changed cyclically with a change in shear direction, where k followed a square wave curve with the same peak value at the stable shear stage. The cyclic normal load amplitudes, horizontal shear displacement amplitudes, cyclic normal load frequencies, cyclic horizontal shear frequencies, and static normal force levels had little influence on the peak values of k. Numerical simulations proved that the spatial movement pattern of the loading plate and upper block of the specimen rotated clockwise or anti-clockwise at different shear displacements. Due to the rotation of the upper block, shear and normal stresses distributed at the contact surface were inhomogeneous, which generated a stress gradient along the interface. Consequently, the samples were damaged at the two edges due to the high local stresses. Finally, a mathematical equation is proposed, which can be used for predicting the shear strength of planar joints under cyclic changes of shear velocity and normal load.

An Experimental Study for the Cyclic Interface Properties of the EPS–sand Mixtures Reinforced with Geogrid

Design and analysis of geosynthetic-reinforced soil structures subjected to repeated loading (e.g. compaction, traffic and earthquake loads) require a proper understanding of the cyclic soil–geosynthetic interface behaviour. This research is undertaken to study the interface properties between sand-expanded polystyrene (EPS) mixtures and geogrid reinforcement under cyclic loading. A series of cyclic tests is performed and the influences of normal stresses, cyclic shear amplitudes and number of cycles are studied. The experiments are conducted using a large-scale direct shear test device allowing to perform displacement-controlled cyclic tests. Accordingly, the influence of the aforementioned parameters on interface shear stiffness and damping ratio is discussed. The results of the experiments showed that adding 0.9% EPS beads to the sand bed leads to the decrease in interface shear stiffness by 30% to 63%, depending on the shear displacement amplitude. In contrast, for the same EPS content ratio, the interface damping increases roughly twice, irrespective of the applied shear displacement amplitude. The value of hardening factor was also found to increase with cycle number under different normal stress levels.

Experimental investigations and constitutive modeling of cyclic interface shearing between HDPE geomembrane and sandy gravel

This paper presents the results of experimental investigations and constitutive modeling of cyclic interface shearing between HDPE geomembrane and cohesionless sandy gravel. A series of cyclic interface shear tests was performed using a large-scale cyclic shear apparatus with servo controlled system. Particular attention was paid to the influences of the amount of shear-displacement amplitude, number of cycles, shear rate and the normal pressure on the mechanical response. The experimental results show that the path of the shear stress against the cyclic shear displacement is strongly non-linear and forms a closed hysteresis loop, which is pressure dependent, but almost independent of the shear rate. For small shear-displacement amplitudes, the obtained damping ratio is significantly greater than zero, which is different to the behavior usually observed for cyclic soil to soil shearing. In order to describe the pressure dependency of the hysteresis loop using a single set of constitutive parameters, new approximation functions are put forward and embedded into the concept of the Masing rule. Further, a new empirical function is proposed for the damping ratios to capture the experimental data for both small and large cyclic shear-displacement amplitudes. The included model parameters are easy to calibrate and the new functions may also be useful in developing enhanced constitutive models for the simulation of the cyclic interface shear behavior between other geosynthetics and soils.

Shear Behavior of Wheat‐Concrete Interface during Monotonic and Cyclic Loading

The interface behavior between wheat and concrete plays a decisive role in the design of silo structures. In this paper, a series of strain‐controlled monotonic direct shear (MDS) tests, cyclic direct shear (CDS) tests, and postcyclic direct shear (PCDS) tests were conducted to investigate the wheat‐concrete interface behavior under monotonic and cyclic loading. The influence of cycle numbers, shear displacement amplitude, normal stress, and preloading consolidation was discussed in detail. In particular, the preloading consolidation simulates the partly discharging state of wheat. The values of peak stress increase with increasing displacement amplitude and cycles, and they change slightly after 10 cycles. The interface exhibits an overall contraction deformation during the MDS tests without preloading, but the contraction is suppressed by an alternating dilation during the DCS tests, and an overall small dilation occurs at small normal stress during PCDS tests. It is observed that the cyclic loading and preloading normal stresses result in an increasing peak strength, internal friction angle, and apparent cohesion, whereas a decrease in interface contraction deformation.

Frictional responses of concrete-to-concrete bedding planes under complex loading conditions

Concrete-to-concrete bedding planes (CCBP) are observed from time to time due to the multistep hardening process of the concrete materials. In this paper, a series of direct/cyclic shear tests are performed on CCBP under static and dynamic normal load conditions to study the frictional behavior effect by the shear velocities, normal impact frequencies, horizontal shear frequencies, normal impact force amplitudes, horizontal shear displacement amplitudes and normal load levels. According to the experimental results, apparent friction coefficient k (k = FShear/FNormal) shows different patterns under static and dynamic load conditions at the stable shear stage. k is nearly constant in direct shear tests under constant normal load conditions (DCNL), while it is cyclically changing with nearly constant peak value and valley value for the direct shear tests under dynamic normal load conditions (DDNL), where k increases with decreasing normal force and decreases with increasing normal force. Shear velocity has little influence on peak values of k for the DCNL tests, but increasing shear velocity leads to increasing valley values of k for DDNL tests. It is also found that, the valley values of k ascend with decreasing impact normal force amplitude in DDNL tests. The changing pattern of k for the cyclic shear tests under constant and dynamic normal load conditions (CCNL and CDNL tests) are similar, but the peak value of k is smaller in CDNL tests than that in CCNL tests. Normal load levels, shear displacement amplitudes, vertical impact frequencies, horizontal shear frequencies and normal impact force amplitudes have little influence on the changing pattern of k for the cyclic shear tests. The tests of this study provide useful data in understanding the frictional behavior of the CCBP under distinct loadings, and these findings are very important for analyzing the stability of the jointed geotechnical structures under complicated in situ stress conditions.

Monotonic and cyclic shear behaviour of geomembrane-sand interface

Geomembranes have been widely applied in hydraulic systems and mineral and environmental engineering. For geomembrane-lined soil structures, such as dikes, dams, and landfills, the geomembrane-soil interface could be a potentially unstable plane under static and dynamic loading. In this study, a large-scale shear apparatus was employed to investigate the monotonic and cyclic shear behaviour of a geomembrane-sand interface under varying normal stress and shear-displacement amplitude. A nonlinear mathematical piecewise model was developed to simulate pre-peak stress-dependent stiffness and post-peak displacement-softening behaviour for the monotonic shear response of the geomembrane-sand interface. Furthermore, the study provided a modeling approach based on the Masing rule to represent the nonlinearity and hysteresis of the cyclic shear behaviour of the interface. The predictions made by the two proposed models were both in good agreement with the experimental monotonic and cyclic shear-test data.

Behaviour of a plane joint under horizontal cyclic shear loading

This paper describes lab test results of artificial rock-like material samples having a plane joint. Cyclic shear tests were performed under different normal loads and different shear displacement amplitudes. For this purpose, multi-stage normal loading tests (30 kN, 60 kN, 90 kN, 180 kN, 360 kN and 480 kN) with cyclic excitation at frequency of 1.0 Hz and different shear displacement amplitudes (0.5 mm, 1.0 mm, 2.0 mm, 4.0 mm, 5.0 mm, and 8.0 mm) were conducted using the big shear box device GS-1000. Experimental results show, that shear forces increase with the increase of normal forces and quasi-static friction coefficient is larger than dynamic one. With the increase of normal loads, approaching the peak value of shear forces needs larger shear displacements. During each cycle the normal displacements increase and decrease (rotational behavior in every cycle). Peak angle of inclination increases with the increase of normal load. A phase shift between maximum shear displacement and maximum shear force is observed. The corresponding time shift decreases with increasing normal load and increases with increasing shear displacement amplitudes.

The Degenerate Mechanism of Sand-Concrete Interface under Cyclic Loading

The sliding interaction between the sand and the surface of the structure is involved in many aspects of geotechnical engineering and is particularly important for the derivation of the shaft capacity of piles. A constant normal stiffness direct shear apparatus is designed and applied herein to research the soil-structure interface weakening mechanism under cyclic loading. The test results show that the sand-concrete shear stress and normal stress change in the Hysteresis loop and Butterfly trends with shear displacement respectively in a complete shear cycle. The difference of adjacent Hysteresis loop or Butterfly is evident in the initial stage of cyclic shear, but tends to gentle after 15 cycles. The evident decays of both the shear stress and the maximum normal stress take place during cyclic shearing, which is approximately logarithmically with the shear cycles. The shear strength of the interface is approximately linear with the normal stress under different cycles. The percentage of particle breakage is between 5.5% and 6% of the original sand after 20 shearing cycles. The percentage of particle breakage and the degeneration rate of shear stress and normal stress increase with the increase of the initial normal stress and the amplitude of shear displacement.

Color Doppler shear wave imaging and its application to breast imaging

Imaging of continuous shear wave (CSW) induced by a small mechanical vibrator attached on tissue surface is low-cost and easy-to-use elastography. A problem of CSW is shear wave's reflection and refraction at tissue boundary, which degrade the accuracy of shear wave velocity estimation. We propose a novel shear wave elastography of CSW (Color Doppler Shear Wave Imaging: CD-SWI). Shear wave’s propagation in soft tissue is reconstructed directly without adding any function to conventional color flow imaging instrument. Two conditions for shear wave frequency and displacement amplitude are required to obtain maps. However, they are not severe restrictions because frequency is chosen among several frequencies suited for elastography and the required displacement amplitude is a few tens of microns. Both Fourier analysis along time axis and a directional filter on wave-number vector space improve image quality. Accuracy and image quality of CD-SWI are evaluated by comparing with ARFI method. CD-SWI is applied to breast in vivo and shear wave propagation in breast (f = 297 Hz) is observed. Inherent shear wave propagation in soft tissue reconstructed by CD-SWI, such as diffraction and refraction around tissue with different stiffness as well as shear wave velocity, may give novel information in tissue characterization by shear wave.

Numerical Modeling of Earthquake-Induced Landslide Using an Improved Discontinuous Deformation Analysis Considering Dynamic Friction Degradation of Joints

Discontinuous deformation analysis (DDA) as an efficient technique has been extensively applied in the dynamic simulation of discontinuous rock mass. In the original DDA (ODDA), the Mohr–Coulomb failure criterion is employed as the judgment principle of failure between contact blocks, and the friction coefficient is assumed to be constant in the whole calculation process. However, it has been confirmed by a host of shear tests that the dynamic friction of rock joints degrades. Therefore, the friction coefficient should be gradually reduced during the numerical simulation of an earthquake-induced rockslide. In this paper, based on the experimental results of cyclic shear tests on limestone joints, exponential regression formulas are fitted for dynamic friction degradation, which is a function of the relative velocity, the amplitude of cyclic shear displacement and the number of its cycles between blocks with an edge-to-edge contact. Then, an improved DDA (IDDA) is developed by implementing the fitting regression formulas and a modified removing technique of joint cohesion, in which the cohesion is removed once the ‘sliding’ or ‘open’ state between blocks appears for the first time, into the ODDA. The IDDA is first validated by comparing with the theoretical solutions of the kinematic behaviors of a sliding block on an inclined plane under dynamic loading. Then, the program is applied to model the Donghekou landslide triggered by the 2008 Wenchuan earthquake in China. The simulation results demonstrate that the dynamic friction degradation of joints has great influences on the runout and velocity of sliding mass. Moreover, the friction coefficient possesses higher impact than the cohesion of joints on the kinematic behaviors of the sliding mass.

Experimental investigations of a rolling-based seismic isolation system

This paper presents the results of an extensive series of experimental tests to identify the mechanical characteristics of a recently-proposed seismic isolation device known as the Roll- In-Cage (RNC) isolator. Several 1/10 reduced-scale experimental prototypes are examined considering different configurations, characteristics and construction materials. Cyclic horizontal displacement tests, varying the test parameters of shear displacement amplitude, axial load, and loading frequency are performed. The RNC isolator’s force-displacement relationship, shear stiffness and damping properties are investigated in terms of different test parameters. In addition, vertical cyclic displacement is applied to examine the RNC isolator’s capability to withstand vertical axial tension. Furthermore, tests at the ultimate-level consisting of an increasing monotonic shear loading beyond the bearing’s design displacement are also carried out to investigate its behavior after activating its self-stopping or buffer mechanism. Some experimentally obtained results are verified using numerical simulation models. A comparative analysis of the results is then performed to allow for highlighting the main features of the RNC isolator.

Novel hexapod-based unidirectional testing and FEM analysis of the RNC isolator

An innovative Stewart platform (hexapod)-based testing rig is designed, constructed, and used herein to experimentally characterize a seismic isolation device named roll-in-cage (RNC) isolator. The testing rig is a result of integrating a mechanical extension, or upgrade, to the hexapod. This allows for performing up to 15 standard mechanical tests using cylinder, block, prism, beam, plate, or bar specimens, besides reduced-scale prototypes of seismic isolation bearings. Several one-tenth reduced-scale prototypes of the RNC isolator are experimentally examined in this paper using this testing rig. Cyclic horizontal displacement tests are performed considering different test parameters including shear displacement amplitude, axial load, and loading frequency. The RNC isolator's force–displacement relationships, shear stiffness, and damping properties are investigated. Vertical cyclic displacements are also applied to examine the RNC isolator's capability to withstand vertical axial tension. Furthermore, tests at the ultimate level consisting of an increasing-amplitude shear loading, beyond the bearing's design displacement limit, are also carried out to investigate the bearing's behavior after activating its inherent self-stopping, or buffer, mechanism. The obtained experimental outputs are then related to analytical and thorough FEM simulation outputs. This relation is intended to validate those previously developed mathematical and numerical models of the RNC isolator based on the real experimental measurements in this paper. A comparative study of the results is then performed, and the main observations are highlighted. Copyright © 2015 John Wiley & Sons, Ltd.

Low cycle fatigue performance of ball grid array structure Cu/Sn–3.0Ag–0.5Cu/Cu solder joints

Low cycle fatigue performance of ball grid array (BGA) structure Cu/Sn–3.0Ag–0.5Cu/Cu joints with different standoff heights (h, varying from 100 to 500μm) and two pad diameters (d, d=320 and 480μm) under displacement-controlled cyclic loading was studied by experimental method and finite element (FE) simulation. A prediction method based on the plastic strain energy density and continuum damage mechanics (CDM) framework was proposed to evaluate the initiation and propagation of fatigue crack in solder joints. The results show that fatigue failure of solder joints is a process of damage accumulation and the plastic strain energy density performs a power function correlation with the cycle numbers of crack initiation and propagation. Crack propagation rate is affected by the stress triaxiality, which is dependent on the loading mode and increases dramatically with decreasing h under tensile loading, while the change of standoff height has very limited influence on the stress triaxiality under shear loading mode. Moreover, crack growth correlation constants identified in Cu/Sn–3.0Ag–0.5Cu/Cu joints with a specific geometry (h=100μm and d=480μm) can be well used to predict the fatigue life of BGA joints with other geometries. Furthermore, the results have also shown that the fatigue life of solder joints increases with decreasing the geometric ratio of h/d under the same nominal shear strain amplitude, while it drops with decreasing h/d under the same shear displacement amplitude in cyclic loading. When the geometric ratio (i.e., h/d ratio) is unchanged, the miniaturization of BGA joints brings about a decrease in fatigue life of the joints.

Shear-Displacement-Amplitude Dependent Pore-Pressure Generation in Undrained Cyclic Loading Ring Shear Tests: An Energy Approach

By conducting a series of shear-torque-controlled (STC) and shear-displacement-controlled (SDC) ring shear tests under undrained conditions, the effects of cyclic loading frequency, shear displacement rate, and overconsolidation ratio (OCR) on the pore-pressure generation were examined and analyzed by means of an energy approach. Cyclic STC tests demonstrated that as the frequency of loading increased, the shear energy ( Wtotal ) as well as the total shear displacement ( ltotal ) until liquefaction substantially decreased, while the number of cycles to liquefaction (N) increased with frequency. Nevertheless, SDC tests showed that Wtotal , ltotal , N did not vary with frequency. This dependency of Wtotal on the loading frequency in STC tests was inferred to be due to the different resultant shear displacement amplitude after shear failure but before liquefaction during cyclic shearing. The results of STC tests on samples with different OCRs showed that all these three parameters of Wtotal , ltotal , N incr...

An Analytical Model for Time-Dependent Shearing Deformation in Area-Array Interconnects

An analytical model is developed for predicting the time-dependent shearing displacement in area-array solder interconnects due to global CTE mismatch under thermal cycling. As a first step toward incorporating the creep deformation of the solder, the material is modeled as viscoelastic and temperature-independent. This permits one to invoke the correspondence principle of viscoelasticity to map the authors’ previously derived, closed-form solution for an elastic nonprismatic (concave, convex, or cylindrical) Timoshenko beam under shear loading into the associated viscoelastic solution. This leads to general analytical results for the frequency-dependent shear displacement amplitude in the critical joint. The results are expressed conveniently in terms of a “full-creep correction factor” and a “frequency correction factor,” which explicitly show the effects of the following parameters on the joint deformation: joint shape; array population; array, component, and substrate dimensions; viscoelastic material properties of the interconnect material; elastic properties of the component and substrate materials; and loading frequency. To demonstrate the technique for a particular viscoelastic constitutive law, the solder is assumed to behave elastically under hydrostatic loads and as a viscoelastic Kelvin solid under deviatoric conditions. For this special case the creep portion of the deformation is shown to be dependent upon only two dimensionless parameters: a dimensionless loading frequency and a material- and shape-dependent joint parameter. The results of the study may be useful in identifying design and process modifications that may improve the thermal fatigue life of area arrays. [S1043-7398(00)00404-7]

Excitation of shear waves in a piezoceramic medium withpartially electrodized tunnel openings strengthened by a rigidstringer

An antiplane mixed boundary electroelasticity of a stationary wave process in an unbounded piezoceramic medium containing tunnel heterogeneities of opening or thin rigid inclusion (stringer) type is considered. The excitation of an electric field occurs at the expense of differences of electric potentials applied to the system of electrodes located on a free from stresses opening surface. Using the correct integral representations of the solutions, the boundary problem is reduced to the system of singular integrodifferential equations of the second type with resolvent kernels. The results of the parametric investigations characterizing the behavior of the components of an electroelastic field in the medium area and on the opening surface are given. A system of singular integrodifferential equations is obtained for investigation of a conjugated electroelastic field in a piezomedium with a tunnel along the material axis opening a rigid curvilinear inclusion, excited by a system of active electrodes, located on the opening surface. The solvable system of equations of the boundary problem is reduced to two differential equations of Helmhöltz and Laplace with respect to the amplitude of shear displacement and some auxiliary functions. The obtained system is solved numerically by a special scheme of the method of quadrature.

Damping Force Characteristics of High-Damping Rubber Damper in Small Shear Strain Regions.

In this study we discuss the applicability of a high-damping rubber damper, which is composed of micro-networks and viscous material, as the damping device in microvibration-isolation devices or tables. For those purposes, damping force characteristcs of the high-damping rubber damper were measured using a new measuring device. We could estimate damping force characteristics to a shear displacement amplitude of 2.5×10-6m, and this high-damping rubber damper was found to have energy-absorption capacity in the regions of very small shear displacement amplitude. Also, the damping force characteristics of a viscous shear damper using silicone oil, which is the most popular damper for vibration-isolation devices, were measured. On comparing the damping force characteristics, our high damping rubber damper was found to have a larger energy absorption ability than the viscous shear damper. Furthermore, the rubber dampers were installed to the vibration isolation table which can mainly isolate microvibrations in horizontal direction. Through microvibrationisolation tests it was confirmed that this high damping rubber could be applied to microvibrationisolation devices.

Hysteretic characteristics of unstiffened plate shear panels

A series of quasi-static cyclic loading tests on unstiffened plate shear panels is described. All the panels tested exhibited adequate ductility and stable S-shaped hysteresis loops, with the energy absorbed per cycle increasing with the maximum amplitude of shear displacement. A theoretical model for predicting the hysteretic characteristics is presented, which incorporates the influences of shear buckling of the web plate and plastic yielding of the web plate and surrounding frame. Theoretical predictions are compared and show satisfactory agreement with the experimental results. The simplicity of the theoretical model is such that it can be readily incorporated in nonlinear dynamic analyses of steel plate shear walls.