Maximum Shear Modulus Research Articles

Improvement of vibration response of a foundation resting on Salt-Encrusted Flat Soil by cement addition: a numerical investigation

ABSTRACT Excessive vibrations can negatively impact machinery performance by causing misalignment, decreased accuracy, increased wear and tear, and reduced overall operational efficiency. By conducting a numerical investigation on improving vibration response through cement addition to salt-encrusted flat soil, the study aims to enhance the performance and reliability of machine foundations, thereby optimizing machinery operation. The properties of untreated sabkha and cement-sabkha were calibrated to use in the Finite Element Method (FEM) model. The variables investigated have the thickness of cemented sabkha ratio, operation frequency, three types of subsoils (Sabkha and cemented sabkha of 5% and 10%), and vertical amplitude loading. The main findings revealed that the maximum shear modulus (Gmax) increases by 47% with a 5% to 10% increase in cement content. In addition, as the vibration’s frequency increases, the amplitude displacement is observed because the reflected waves become smaller for the foundation resting on cemented sabkha. The natural frequency rises as the thickness ratio and cement amount of cemented sabkha increase. The influence of the thickness ratio on displacement amplitude is considerable when the operation frequency is less than 20 hz. The study implies that engineers can optimize the design of machine foundations to achieve better performance and stability.

Effect of layering and pre-loading on the dynamic properties of sand-rubber specimens in resonant column tests

AbstractSeveral studies show that scrap tyre rubber mixed with sand is an effective and sustainable method for mitigating vibrations. The dynamic and cyclic response of this composite soil has already been investigated. However, layered sand-rubber configurations have not been considered yet. This study reports findings of resonant column tests on three types of specimen: (a) sand-only or rubber-only, (b) layered sand-rubber, and (c) sand-rubber mixtures. The analysis allowed for an evaluation of the maximum shear modulus and its degradation with strain over a wide range of confining stress and shear strain. The evolution of the damping ratio with strain was determined analogously. Effects of pre-loading and pre-straining were also considered. The results show that the behaviour of layered specimens is much more similar to that of pure rubber than to sand-rubber mixtures, with very low shear modulus values, smaller degradation of stiffness with strain and pre-loading, and higher damping. For example, at the confining stress of 100 kPa and rubber content of 0/33.3/50/67.7/100% by volume, the small strain shear moduli for sand-rubber mixtures are equal to 98.3/30.4/15.4/7.1/1.3 MPa and 98.3/3.6-4.2/2.4-2.8/2.1/1.3 MPa for sand-rubber layered specimens, depending on the arrangement of layers. A shear beam model is shown to be adequate for calculating the response of the layered specimens comprising layers of large stiffness contrast.

Impact of fiber diameter and surface substituents on the mechanical and flow properties of sonicated cellulose dispersions

This study investigates how sonication amplitude and time affect 2 wt% cationic nanofibrils (CCNF) and microfibrils (CCMF) dispersions, focusing on mechanical properties and flow behavior. Sonication reduces fiber diameter and increases the concentration of substituent groups available for hydrogen bonding. This effect becomes significant when diameters fall below 100 nm, leading to enhanced storage and loss moduli. CCNF achieves a maximum shear modulus of 600 Pa, whereas CCMF fibers do not undergo similar size reductions. CCNF's viscosity and critical stress follow a square root relationship with sonication amplitude, due to minimal fiber size reduction at high sonication levels (smaller than 20 nm), unlike CCMF (diameter reduction up to 50 nm), which exhibits a linear increase due to more pronounced fiber fragmentation. At high sonication levels, CCNF shows an exponential rise in critical stress (up to 800 Pa), suggesting tiny fibers infiltrate the hydrogel network, thereby improving its integrity and resistance to shear stresses. By integrating theoretical models with experimental findings, this work presents a unified view of sonication's essential role in fine-tuning the mechanical and flow properties of cellulose-based materials. This research enhances understanding of cellulose dispersion behavior under sonication and provides a foundation for designing optimized cellulose-based materials.

Dynamic characteristics and microscopic mechanism of graphene oxide modified coastal soft soil under small strain

Graphene oxide (GO) has been shown to improve the static mechanical properties of cement soils. However, the dynamic mechanical properties of GO-modified cement soils are rarely investigated. Therefore, in this study, the effects of different confining pressures, GO contents, and curing ages on the small-strain dynamic shear modulus (G) and damping ratio (D) of GO-modified coastal cement soil (GOCS) are investigated via resonant column tests. The results show that the G of GOCS increases with the confining pressure, GO content, and curing age, whereas D decreases. Moreover, the GOCS indicate the highest stiffness improvement when 0.05 % GO is used as a modifier. The variation patterns of the maximum dynamic shear modulus and maximum damping ratio with the increase in the confining pressure, GO content, and curing age of the GOCS are consistent with the measured results. Microstructural analysis shows that the incorporation of GO can promote the early cement hydration of GOCS and increase its internal calcium-silicate-hydrate gel as well as its crystal types and numbers. The filling and bridging effects of GO not only enhance the stiffness of GOCS, thus increasing its G value, but also effectively reduce the energy consumption of the vibration wave in the sample, thus reducing its D value. The results of this study can provide important references and guidance for the design and construction of coastal soft-soil roadbed projects.

Establishment of Dynamic Properties for Malaysian Peat Soil Using Multichannel Analysis of Surface Waves

A poor understanding of peat behavior has introduced several engineering problems including differential settlements or slides which greatly impact society. Problematic characteristics of peat including a high moisture content and the presence of fresh fibers, cause a significant challenge in obtaining high-quality samples for laboratory-based investigation. Therefore, the application of in-situ geophysical methods is sought to mitigate these problems. The dynamic properties of a peat deposit in West Malaysia are described in this study. The Multichannel Analysis of Surface Waves (MASW) was conducted at six different locations. These peat soils had considerably different characteristics due to the different natures of decomposed materials. The samples obtained from the five locations had organic contents of 66.5 to 97.1%, water contents of 447 to 964%, and fiber content between 22.1 and 75.2%. Based on Von Post classification, the peat type ranged from H3 (fibrous) to H8 (amorphous). Shear wave velocity (Vs) and maximum shear modulus (Gmax) are presented, and their dependence on variables such as moisture content, organic content, fiber content, specific gravity and bulk density are illustrated. The general trend shows an increase in Vs and Gmaxwith decreasing moisture, organic and fiber content of peat soil. The difference in the degree of humification did not result in significant differences in Vs and Gmax obtained. The results showed that the value of Vs and Gmax ranged from 24.0 to 67.1m/s and 0.40 to 7.06 MPa respectively. Correlation between the index and dynamic properties peat shows that the Vs and Gmax increase as the moisture, organic and fiber content decreases. Successful determination of in-situ Vs and Gmax on peat soil minimized the potential of underestimation due to sample disturbance and provide a sustainable, rapid and economic method.

Investigation of the Effect of Relative Density on the Dynamic Modulus and Damping Ratio for Coarse Grained Soil

As the critical dynamic parameters for soil, an extensive examination of the dynamic elastic modulus Ed and damping ratio λ in coarse-grained soil is of significant theoretical and practical importance. Currently, there is a scarcity of experimental equipment and methods for measuring the dynamic elastic modulus and damping ratio of coarse-grained soils. Moreover, studies examining the influence of relative density on these parameters in coarse-grained soils are largely absent. To investigate the behavior of the dynamic elastic modulus and damping ratio in coarse-grained soil under varying relative densities, a number of dynamic triaxial tests were conducted on a specific coarse-grained soil using the DYNTTS type dynamic triaxial test apparatus. The findings reveal that, under various gradations, the Ed of coarse-grained soils exhibits a decreasing trend with increasing dynamic strain, a trend that intensifies with higher relative densities. Additionally, as relative density increases, the degradation rate of the dynamic shear modulus ratio Gd/Gdmax to dynamic shear strain γd curve escalates. The maximum dynamic shear modulus Gdmax rises with increasing relative density Dr, displaying a linear relationship between Gdmax and Dr. Furthermore, both the increasing rate of λ to γd curve and the maximum damping ratio λmax progressively diminish with the escalation of relative density Dr. Notably, the maximum damping ratio has a power function relationship with the relative density.

Maximum shear modulus anisotropy of rooted soils

The maximum shear modulus (G0(ij)) of rooted soils is crucial for assessing the deformation and liquefaction potential of vegetated infrastructures under seismic loading conditions. However, no data or theory is available to account for the anisotropy of G0(ij) of rooted soils. This study presents a new model that can predict G0(ij) anisotropy of rooted soils by incorporating the projection of the stress tensor on two independent tensors that describe soil fabric and root network. Bender element tests were conducted on bare and vegetated specimens under isotropic and anisotropic loading conditions. The presence of roots in the soil increased G0(VH) at all confining pressures (p′), as well as G0(HH) and G0(HV) at low p′. However, the trend was reversed at higher p′ because the roots reduced the effects of confinement on G0(ij) by replacing stronger soil–soil interfaces with weaker soil–root interfaces. Roots made the soil fabric and G0(ij) more anisotropic. The proposed model can effectively predict the observed anisotropy of G0(ij) under isotropic and anisotropic loading conditions. The new model also offers a new method for determining the fabric anisotropy of sand based on the anisotropy of shear modulus.

Hydro-mechanical response of volcanic ash on removal of fines: Shear stiffness to critical state mechanics

Natural volcanic soils containing pumice particles are commonly found in Hokkaido, Japan, and this type of soil is prone to landslides, internal erosion, and liquefaction. Therefore, the purpose of this paper is to summarise the hydro-mechanical response of volcanic ash soil subjected to internal erosion using the modified erosion triaxial apparatus, based on the literature and additional investigations. The results of the study show that the rate of erosion and shear strain during the erosion process are influenced by initial density, stress state, and hydraulic gradient. Notably, anisotropic consolidation is experienced by specimens under seepage flow. Additionally, the removal of fines leads to a slight decrease in the grading state index. Moreover, suffosion increases the maximum shear modulus and Poisson’s ratio of the soil, while increasing seepage time stabilises the peak shear strength of eroded specimens. Furthermore, the critical state line does not change much with internal erosion. To sum up, this study offers valuable insights into the behaviour of volcanic ash soil subjected to internal erosion and provides an integrated interpretation of hydro-mechanical response of volcanic ash on removal of fines.

Shear modulus of sand-rubber mixtures: element testing and constitutive modeling

In this study, a series of resonant column tests was conducted to measure the shear modulus of sand-rubber mixtures at small strain amplitudes (i.e. between 10−4% and 10−2%), considering different rubber percentages and confining stress levels. The results were then combined with data obtained by dynamic hollow cylinder tests to investigate shear modulus degradation of the mixtures over a wider shear strain range. Based on the test results, a new expression was proposed to improve the prediction of maximum shear modulus of sand-rubber mixtures using the modified equivalent void ratio concept. A new constitutive model was also developed for estimation of strain-dependent shear modulus of the mixtures based on the modified hyperbolic framework. The shear modulus of the mixtures was found to be a function of rubber percentage, confining stress, the modified equivalent void ratio and the relative shear stiffness of rubber and sand. The experimental data and the developed models showed that the shear modulus decreased with rubber percentage and increased with confining stress. Moreover, the reference shear strain of the modified hyperbolic model increased with both rubber percentage and confining stress while its curvature coefficient increased more considerably with rubber percentage compared to the confining stress.

Static and dynamic strength properties of highly structured clay-rich diatomite in Shengzhou, China

Diatomite is a widespread geological substance found in coastal and lake areas worldwide. Although diatomites are increasingly used in geotechnical engineering construction, a significant knowledge gap exists regarding their mechanical responses to static and dynamic loadings, particularly in high-speed railway projects. This study investigates the static and dynamic behaviors of diatomites through extensive experiments, considering both natural and remolded states. It focuses on representative diatomite specimens obtained from the Shengzhou region in China, an area intersected by the Hang-Shao-Tai high-speed railway. The results of uniaxial compression and undrained triaxial shear tests show that the structural degradation of diatomite significantly impacts its stress-strain responses, failure patterns, and mechanical parameters under static and dynamic loading conditions. The structural effects of natural diatomite tend to degrade as the confining pressure level increases, resulting in corresponding changes in its mechanical parameters. Undrained triaxial shear tests conducted on natural diatomite reveal that the inclinations of the shear band closely correspond to those predicted by the Mohr-Coulomb solution. Additionally, we present a modified hyperbolic-type model to evaluate the damping ratio of diatomites. Furthermore, a power-law model based on Hardin's formula was used to predict the maximum shear modulus of diatomites under varying stress levels and void ratios. Microstructural and chemical analyses were conducted using scanning electron microscopy and X-ray diffraction to gain insights into the observed structural effects at the microscale.

High Temperature Experiments and Properties of Carbon Polyimide Composites

The interlayer shear tests of AC741/M55JB carbon fiber reinforced composite at room temperature, 400℃, 600℃ and 800℃ were carried out.The longitudinal and transverse shear tests of AC741/CCF800 carbon fiber reinforced composite were carried out at room temperature, 400℃, 600℃ and 800℃ dry conditions, as well as the experiments to calculate material property parameters. The results showed that the main failure mode of the sample in the interlayer shear test was stratified damage, and the fracture of the upper surface material was not obvious.This is due to the different types of tests, the interlayer shear pattern is short and small, and it is not easy to occur the fracture damage of the material without stratification.In addition, with the increase of temperature, the interlaminar shear strength also decreased significantly.In crossbar shear test, the maximum in-plane shear stress, maximum in-plane shear strength and in-plane shear modulus of the material gradually decrease with the increase of temperature, thus changing the bearing property of the material.

Stiffness Anisotropy and Micro-Mechanism of Calcareous Sand with Different Particle Breakage Ratios Subjected to Shearing Based on DEM Simulations

Stress-induced anisotropy in calcareous sand can cause an uneven displacement in island reef engineering. In this study, stiffness, as a quantitative indicator, is explored to reveal the stress-induced anisotropy in calcareous sand. Based on the discrete element method, the stiffness anisotropic characteristics of calcareous sand during shearing, as well as the impact of particle breakage, are investigated by numerical simulations. Both the macro and micro responses, i.e., the maximum shear modulus, contact normal, strong and weak contact normal force, and the direction of particle breakage, are explored for calcareous sand with different particle breakage ratios. The results show that calcareous sand exhibits notable anisotropy during shearing, with the maximum shear modulus in the vertical direction (deviatoric stress direction) being significantly greater than that in the horizontal direction. Moreover, the higher the particle breakage rate, the lower the stiffness and its anisotropy. The micro-mechanism results indicate that the primary particle breakage during the shearing process occurs in the vertical direction. That is, the particle breakage weakens the strong contact force in the vertical direction, leading to a redistribution of the strong contact forces from the vertical direction to other directions. This redistribution mainly manifests in a decrease in the anisotropy of contact normal and contact vector within the sample, as well as a decrease in the proportion of strong contact forces in the overall contacts. This, in turn, reduces the shear strength and stiffness of calcareous sand, particularly in the vertical direction, and results in a decrease in the maximum shear modulus and its anisotropy. The maximum reduction can be up to 50% of the original value. These insights can provide a certain theoretical support for the uneven displacement and long-term stability of calcareous sand for islands and reefs.

Shear modulus and damping ratio of granulated rubber-sand mixtures: Influence of relative particle size

Rubber-sand mixtures (RSM) have gained recognition as a valuable, lightweight, and cost-efficient energy-absorbing material with extensive potential application in engineering construction. However, the small-strain dynamic properties and prevailing mechanisms of RSM have not been thoroughly understood. This study conducted a series of resonant column tests on the small-strain dynamic modulus and damping ratio of RSM, considering the effects of particle size ratio (PSR), rubber content (RC), and confining pressure. The results reveal that the dynamic shear modulus of RSM generally decreases with increasing RC and increases with rising confining pressure. For all RC and confining pressure levels, the maximum dynamic shear modulus of RSM reaches the minimum value as the PSR approaches 1.0. In this case, the dynamic shear modulus of RSM decreases most gently with the strain. The addition of rubber consistently augments the damping ratio, whereas the PSR initially diminishes the damping ratio before eventually enhancing it. Simultaneously, as the PSR is nearing 1.0, the damping ratio achieves its lowest point. Furthermore, new empirical equations were developed to quantitatively analyze the dynamic properties of RSM, in which the predicted values of the dynamic shear modulus and the modulus attenuation coefficient show good agreement with the observed values. This work will facilitate the preparation of artificial RSM-cored geotechnical seismic isolation layers tailored to specific engineering requirements.

Elastic anisotropy, mechanical, lattice dynamics, and electronic properties of MPdZ (M = Hf, Zr, Ti; Z = Sn, Ge, Si). DFT study

Elastic anisotropy, mechanical, lattice dynamics, and electronic properties of MPdZ (M = Hf, Zr, Ti; Z = Sn, Ge, Si) compounds have all been computed from first principles. All compounds are ductile according to Pugh’s ratio, Cauchy’s pressure, and Poisson’s ratio values. Based on the Born stability criteria, each MPdZ compound is mechanically stable. The high machinability index values of TiPdSn and ZrPdSi indicate their high quality of machinability. The hardness of the compounds is between 5.5 and 8.0 GPa, and the highest hardness is found in the HfPdSn (7.966 GPa) compound. The computed Kleinman parameter indicates that the bond stretching for all MPdZ compounds is minimal. The anisotropy indices incorporating graphical presentation indicate all MPdZ compounds are anisotropic. Young’s modulus elastic anisotropy is less compared to the Zener anisotropy index, equivalent Zener anisotropy measure, and anisotropy ratio of the maximum and minimum shear moduli. Prominent anisotropy for sound velocities is observed in HfPdSi, ZrPdSi, and TiPdSi compounds. With the exception of TiPdGe, other compounds in this work are dynamically stable due to the lack of imaginary phonon modes. HfPdSn, ZrPdSn, and TiPdSn have narrow energy band gaps among the compounds that were studied.

An experimental study to investigate the mechanical behaviour of low plasticity fine-grained soil stabilized with different contents of lime and fly ash

ABSTRACT Shear strength, small and large strain stiffness moduli, and cyclic stiffness degradation of fine-grained soil with low plasticity (CL-ML) stabilized with different contents of lime and fly ash were investigated in this work. The results of static triaxial tests showed that adding fly ash to the soil-lime mixture increases significantly the compressive strength of the samples due to an increase in pozzolanic reactions. By varying fly ash up to 15% and lime up to 7%, an optimal composition with 5% lime and 15% fly ash was achieved, in which the shear strength was maximum. The results of the bender element tests also showed that the mixture of 5% lime and 15% fly ash has the highest maximum shear modulus. The results of the cyclic triaxial tests on the samples with the optimal composition; showed cyclic degradation of the stiffness due to the failure of cement bonds.

ResUNet involved generative adversarial network-based topology optimization for design of 2D microstructure with extreme material properties

Topology optimization is one of the most common methods for design of material distribution in mechanical metamaterials, but resulting in expensive computational cost due to iterative simulation of finite element method. In this work, a novel deep learning-based topology optimization method is proposed to design mechanical microstructure efficiently for metamaterials with extreme material properties, such as maximum bulk modulus, maximum shear modulus, or negative Poisson’s ratio. Large numbers of microstructures with various configurations are first simulated by modified solid isotropic material with penalization (SIMP), to construct the microstructure data set. Subsequently, the ResUNet involved generative and adversarial network (ResUNet-GAN) is developed for high-dimensional mapping between optimization parameters and corresponding microstructures to improve the design accuracy of ResUNet. By given optimization parameters, the well-trained ResUNet-GAN is successfully applied to the microstructure design of metamaterials with different optimization objectives under proper configurations. According to the simulation results, the proposed ResUNet-GAN-based topology optimization not only significantly reduces the computational duration for the optimization process, but also improves the structure precise and mechanical performance.

Experimental model updating of slope considering spatially varying soil properties and dynamic loading

AbstractThe widespread threat posed by slope structure failures to human lives and property safety is widely acknowledged. Additionally, natural soil often displays spatial variability due to geological deposition and other factors. Therefore, predicting the seismic response of slopes subjected to ground motions and inversely analyzing the spatial distribution of soils remains an unresolved issue. In the present work, a shaking table experimental test is first designed and carried out, in which a soft‐soil slope dynamic system is established. To capture the seismic response of the soft‐soil slope, specifically the experimental characteristic of acceleration and soil pressure response in both spatial domain and time domain, a series of sensors were pre‐embedded in the slope. Subsequently, a model updating approach is proposed for slope seismic analysis that incorporates spatial variability of soil. In addition, to enhance computational efficiency, the dimensionality reduction of Karhunen–Loève expansion method is introduced to reduce inverse analysis parameters. On the basis of 34 samples collected from experimental data, it is shown that near‐fault pulse‐like ground motions deliver greater concentrated energy, causing more severe damage to slope structures, especially the topsoil layer. Furthermore, using data obtained from a shaking table test subjected to ground motion Recorded Sequence Number 158H1 from the Pacific Earthquake Engineering Research Center NGA‐West2 database as an example, it is also shown that the proposed approach demonstrates high accuracy in predicting the spatial distribution of the maximum shear modulus in soil slope dynamic systems. The present work not only addresses the challenges posed by mainshock–aftershock effects but also highlights the potential of model updating approaches to enhance the understanding of slope behavior under seismic loading conditions.

Experimental study on the effect of different cement content on the improvement of dynamic characteristics of seismic-prone poor soil.

The improvement of sandy soils with poor seismic properties to modify their dynamic characteristics is of great importance in seismic design for engineering sites. In this study, a series of dynamic tests on sandy soils sandy soils with poor seismic conditions were conducted using the GCTS resonant column system to investigate the improvements effects of different cement contents on dynamic characteristic parameters. The research findings are as follows: The cement content has certain influences on the dynamic shear modulus, dynamic shear modulus ratio, the maximum dynamic shear modulus, and the damping ratio of sandy soils with poor seismic properties. Among them, the influence on dynamic shear modulus is limited, while the damping ratio is significantly affected. The addition of cement to seismic-poor sandy soils significantly enhances their dynamic characteristics. The most noticeable improvement is observed when the cement content is 8%. Through curve fitting analysis, a relationship equation is established between the maximum dynamic shear modulus and the cement content, and the relevant parameters are provided. A comparative test between the improved soils and the remolded soils reveals that the addition of cement significantly improves the seismic performance of the poor soils. The recommended values for the range of variation of the dynamic shear modulus ratio and damping ratio are provided, considering the effect of improvement. These research findings provide reference guidelines for seismic design and engineering sites.

Small-strain stiffness of liquefiable sands: A comparison between bender elements and resonant-column tests

Soil stiffness can be estimated by geophysical and dynamic testing methods. In the laboratory, the most common methods to measure the small-strain stiffness are the bender elements (BE) and resonant-column (RC) tests. This paper focuses on the comparison between the results of the small-strain stiffness of sands by BE and RC tests. For this purpose, an experimental program involving three liquefiable sandy soils (i.e., NB, TP-Lisbon and Toyoura sands) was carried out. Such program covered the measurement of the small-strain stiffness of these soils by BE in triaxial and RC apparatuses for different mean effective stress conditions. All tests were carried out on saturated soil specimens, which were remoulded using the air pluviation method for various relative densities. The experimental results were interpreted in terms of shear-wave velocity (Vs) and maximum shear modulus (Gmax) to derive the stress-dependency laws of these parameters. The experimental results revealed differences between Vs obtained from BE and RC tests, evidencing a clear effect of relative density on the shear-wave propagation. However, such a variation may be significantly reduced when a normalisation of Gmax in terms of a void ratio function F(e) is applied. As a result, this study demonstrated and validated the importance of accounting for the soil state conditions, for adequate compatibility of BE and RC tests in the estimate of the small-strain stiffness of liquefiable sands.

Use of machine learning in determining Gmax from bender element tests

The use of bender element is one of the most popular methods of determining shear wave velocity, and hence elastic shear modulus due to its relatively straightforward experimental set-up. While several analysis methods have been proposed, manual interpretation using the first arrival continues to be favoured owing to its simplicity. This paper presents a novel automated program for determining the shear wave velocity and associated maximum shear modulus. The proposed new method involves the use of Convolutional Neural Networks (CNNs) to predict the most probable shear wave velocity using a range of input frequencies as the inputs. Estimates made by the trained CNN are compared to values determined using more traditional interpretation methods (first-arrival, cross-correlation and frequency domain). The program is able to autonomously determining the shear modulus in the three principal orientations (Gvh, Ghv, and Ghh) at a range of stress levels. The shear modulus determined using the range of techniques showed great agreement. Statistical analysis of the determined shear modulus regression of over 0.99 between interpretations made using first arrival and that estimated using the new CNN approach.