Hardin-Drnevich Model Research Articles

Soil utilization of solid waste: Small-strain dynamic properties and microscopic mechanism of phosphogypsum-modified coastal cement soil

Phosphogypsum (PG), a solid waste from the wet process phosphoric acid industry, but the utilization rate is low at present. The effect of phosphogypsum and cement on small strain dynamic characteristics of coastal soft soil was studied by resonance column test, and characterize the micro-mechanisms of the specimens by SEM and EDS test. The results show that the dynamic shear modulu (G) and the damping ratio (D) firstly increase and then decrease with the PG level increasing. PG can motivate the formation of hydrated calcium silicate (C–S–H) gel and react with calcium aluminate to form calcium. The critical value for assessing the dynamic behavior of PCS under small strain is γ = 10−4. The Hardin-Drnevich model eigenmodel can well characterize the dynamics of the PCS. Based on this model, a modified dynamic model is established to describe the dynamic characteristics of PCS. The microscopic results showed that the addition of phosphogypsum promoted the production of hydration products and made the particles more closely arranged. The content of this study provides a new reference for the application of solid waste phosphogypsum in cement soil.

Research on Multiple-Factor Dynamic Constitutive Model of Poured Asphalt Concrete.

This study conducted dynamic triaxial tests on a typical poured asphalt concrete material of core walls in Xinjiang, exploring the dynamic characteristics of poured asphalt concrete under various confining pressures, principal stress ratios, and vibration frequencies. On this basis, the dynamic constitutive relationship of poured asphalt concrete was investigated using the Hardin-Drnevich model. The results indicate that under different confining pressures, principal stress ratios, and vibration frequencies, the variation patterns of the backbone lines of dynamic stress-strain of poured asphalt concrete are basically identical, consistent with a hyperbolic curve. The confining pressure and principal stress ratio significantly affect the backbone line of dynamic stress-strain. By comparison, frequency has a minimal effect. The changing trends of dynamic elasticity modulus and damping ratio of poured asphalt concrete under various factors are almost the same. When the material has high dynamic stress and strain, the hysteresis loop is large. When the curve of the damping ratio becomes flat, the asymptotic constant can be used as the maximum damping ratio. The relationship between the reciprocal of the dynamic elasticity modulus and the dynamic strain of poured asphalt concrete exhibits a linear distribution. Under different ratios of confining pressure to principal stress, there are large discrepancies between the calculated values from the formula and the experimental fitting values of the maximum dynamic elasticity modulus, and the maximum relative errors reach 16.65% and 18.15%, respectively. Therefore, the expression for the maximum dynamic elasticity modulus was modified, and the calculated values using the modified formula were compared with the experimental fitting values. The relative errors are significantly reduced, and the maximum relative errors are 3.02% and 2.04%, respectively, in good agreement with the fitting values of the experimental data. The findings of this article render a theoretical basis and reference for the promotion and application of poured asphalt concrete.

Enhancement effect of calcium carbide residue and rice husk ash on soft soil: Small-strain property and micro mechanism

The resource utilization of calcium carbide residue (CCR) and rice husk ash (RHA) is helpful to save resources and alleviate environmental pollution. In this research, CCR and RHA were used to modify soft clay, and the resonant column test was conducted to explore its small-strain dynamic characteristics. The micro-mechanism of CCR-RHA modified soft clay (CRSC) was investigated by using scanning electron microscopy, X-ray diffraction and mercury intrusion tests. The findings demonstrated that the dynamic shear modulus of the CRSC increased with the increase of RHA content and confining pressure, but decreased with the increase of shear strain. In contrast, the damping ratio presents the opposite change law. The Hardin-Drnevich (H-D) model was used to fit the dynamic shear modulus/maximum dynamic shear modulus (G/Gmax)-shear strain γ and the damping ratio D-shear strain γ. As confining pressure increased, Gmax increased but Dmax dropped in CRSC specimens with the same RHA content. The changes of the fitted G/Gmax-γ curve could be divided into progressively decrease stage and rapid decrease stage, while the changes of the fitted D-γ curve could be separated into linear stage and slow stage, with the same turning point γ = 10−4. Microscopic tests revealed that the incorporation of CCR and RHA helped to promote the hydration reaction, and the generated hydration products such as calcium silicate hydrate were able to enhance the integrity and compactness of the CRSC. The results of this research putfward solid foundation for the application of CCR-RHA in the modification of soft soil.

Study on the Permanent Deformation and Dynamic Stress–Strain of Coarse-Grained Subgrade Filler under Cyclic Loading

Using coal gangue as a subgrade filler will produce good benefits, and its application prospects are very broad. It is of great engineering and scientific value to study the improvement method and dynamic characteristics of coal gangue subgrade filler under traffic load. Combining the properties of coal gangue material, fly ash and lime and soil were added to improve the bearing behavior of coal gangue subgrade filler. Then, a compaction test was carried out using the principle of orthogonal experimental design. By analyzing the compaction test results, the optimal proportion of each additive was obtained. A large-scale dynamic triaxial test was carried out with the proportion of each admixture in the maximum dry density group in the compaction test. Based on the dynamic triaxial test results, the effect of confining pressure on the permanent strain was analyzed, the analysis model of permanent deformation and cycle number of traffic loading was proposed, and the correctness of the model was verified. In addition, a modified Hardin–Drnevich model was established, which can describe the dynamic stress–dynamic strain curve of coal gangue subgrade filler under traffic load, and then, the dynamic modulus and damping ratio were analyzed.

Investigation of Small Strain Dynamics in Modified Aeolian Sand under Vibration Triaxial Conditions

By utilizing vibration triaxial tests, this study analyzed the effects of various factors, such as confining pressure, consolidation ratio, and silt content on the elastic modulus and damping ratio of silt-modified aeolian sand under conditions of minor deformation. The results indicate that with increasing confining pressure and consolidation ratio, the dynamic elastic modulus of improved aeolian sand gradually increases, while the damping ratio decreases progressively. The dynamic elastic modulus growth rate of untreated aeolian sand demonstrates a positive correlation with confining pressure, while the corresponding rate for the modified aeolian sand by adding cement and silt exhibits an inverse correlation with confining pressure. As dynamic strain increases, the dynamic elastic modulus decreases and approaches a stable value. The damping ratio rises at a diminishing rate and eventually stabilizes as dynamic strain continues to increase. The dynamic stress-strain backbone curve of the modified aeolian sand follows a theoretical hyperbolic model, while the small strain dynamic behavior is consistent with the Hardin-Drnevich model.

Study on the effects of drying–wetting cycles on the dynamic elasticity modulus of weathered red sandstone soil

In this paper, the effect of drying–wetting cycles on the dynamic elasticity modulus of weathered red sandstone soil was studied based on a series of unconsolidated undrained dynamic triaxial tests under different confining pressures and with the help of the Hardin–Drnevich model. The main results from this work as follows: (1) Hardin–Drnevich model can well express the hyperbolic behaviors of dynamic backbone curves of the weathered red sandstone soil exposed to drying–wetting cycles. (2) Both the maximum dynamic elasticity modulus and the dynamic elastic modulus of the weathered red sandstone soil decreased linearly with numbers of drying–wetting cycles under a certain confining pressure. The dynamic elasticity modulus decreased non-linearly with the increase of dynamic strain. (3) The maximum dynamic elastic modulus of the weathered red sandstone soil decreased by 19.62% to 70.91%, 21.16% to 71.07%, and 29.53% to 77.36%, respectively after 3 to 12 drying–wetting cycles under confining pressures of 100, 200, and 300 kPa. The rate at which the maximum dynamic elastic modulus decreases is basically the same under different confining pressures.

Dynamic shear modulus and damping ratio of marine silt improved with wasted steel slag

In this article, steel slag was added into the marine silt to improve its dynamic properties. The characteristics of marine silt that can be studied by XRD, BET surface area, SEM, and FTIR were first described. Then, the influence of the sample density, water content, waste steel slag content, and the confining pressure on the dynamic shear modulus G and damping ratio λ was discussed by conducting resonant column tests. The results illustrated that the dynamic characteristics of the marine silt-steel slag admixtures were considerably improved. Additionally, G increased with the increasing steel slag content and λ increased with the decreasing steel slag content. Moreover, a dynamic model of the admixtures was developed based on the Hardin–Drnevich model. Furthermore, by comparing the dynamic characteristics of the admixtures with Nanjing sand, Fujian sand, Kiyohoro silty clay, and Wenzhou marine clay, it was found that the improved admixtures may be a more suitable geofiller in geotechnical engineering.

Shaking table test and numerical simulation of free field in sand-sawdust mixed soil

The sand-sawdust mixture has been frequently used in the shaking table test because it is easy to adjust the shear wave velocity of model soil by changing the sawdust content. In this paper, the dynamic properties and the seismic responses of the free field in sand-sawdust mixture as well as the boundary effects of the laminar shear model box were investigated using a series of shaking table tests. The influences of different constitutive models on to the seismic response analysis of the model soil were studied by comparing the numerical results with the experimental results. The comparison shows that the boundary effect mainly influences the model soil within 0.75 times of the soil depth from the box boundary and the impact decreases with the increasing of soil depth. The natural frequency and acceleration amplification factor of the field decrease with the increasing amplitude of the ground motion. The comparison of the seismic response results for different constitutive models of the Hardin-Drnevich, Ramberg-Osgood, and Davidenkov models using the one-dimensional equivalent linearization method indicated that the combination of Davidenkov and Hardin-Drnevich model could improve the accuracy of seismic response for sand-sawdust mixed soil.

Mechanical Properties and Engineering Applications of Special Soils—Dynamic Shear Modulus and Damping of MICP-Treated Calcareous Sand at Low Strains

Calcareous sand deposits are widespread along the shoreline in tropical and subtropical regions. Microbially induced calcite precipitation (MICP) treatment is a new method for improving the soil’s stiffness and strength. The small-strain shear modulus and damping ratio of MICP-treated calcareous sand, two critical parameters for predicting the dynamic behavior of soil, are little known. This study conducts a series of resonant column tests to investigate the dynamic characteristics of MICP-treated calcareous sand, emphasizing the influence of treatment duration and confining stress on the stiffness and damping characteristics. It analyzes the relationship between the initial dynamic shear modulus and unconfined compressive strength. In addition, empirical relationships between the reference shear strain and treatment duration or confining stress are provided. The results show that the normalized shear modulus G/G0 of MICP-cemented calcareous sand has a higher strain sensitivity than that of untreated sand, and the Hardin–Drnevich model can describe its attenuation pattern. The effective confining stress σc affects the degradation characteristics of the dynamic shear modulus of MICP-treated calcareous sand with a low cementation level; however, its impact decreases as the treatment duration increases. There is a linear relationship between the reference shear strain and confining stress. While the relationship between the reference shear stain and treatment duration is a power law.

Dynamic Characteristics of Rubber Reinforced Expansive Soil (ESR) at Positive and Negative Ambient Temperatures.

Using tire waste rubber reinforced expansive soil (ESR) can modify its poor engineering characteristics. The damping properties of ESR at different temperatures may vary dramatically. Two kinds of rubber Ra (large particle size) and Rb (small particle size) are mixed with expansive soil according to gradient ratio. The backbone curves, dynamic shear modulus, and damping ratio of expansive soil in varying temperature fields of 20 °C, −5 °C, and −15 °C are investigated. The Hardin-Drnevich model can well fit the backbone curves of ESR specimens in various temperature fields. Dynamic triaxial results show that 5–10% Ra rubber can withstand higher shear stress in all temperature fields; Rb rubber can increase the dynamic shear modulus of expansive soil and reach the peak value with 10% rubber content. The damping ratio can be significantly improved by using 10% Ra rubber at room temperature, while the ESR damping ratio in a temperature field of −5 °C does not change significantly with increasing shear strain or even decreases; Ra increases the damping ratio of expansive soils in the temperature field of 15 °C while small particle size Rb decreases the damping ratio of expansive soils. The experimental results validate the effectiveness of ESR in the frozen soil area. In an engineering sense, local temperature needs to be considered to use an appropriate ESR, which can provide effective seismic isolation and damping.

Study on Modified Dynamic Constitutive Model for Calcareous Sand considering Particle Breakage

Calcareous sand is special sand widely distributed in the South China Sea, which is characterized by the irregular particle shape, high porosity, easy-breaking, etc. Through a series of dynamic triaxial tests, this paper will study the influence of particle breakage on the dynamic deformation characteristics of calcareous sand and explore a modified dynamic constitutive model considering particle breakage suitable for calcareous sand. The research shows that the dynamic deformation characteristics of calcareous sand can be described by the Hardin-Drnevich model. The maximum dynamic shear modulus and average effective stress of calcareous sand obey Janbu empirical formula, with approximate a linear relationship. Through screening experiment, it is found that there is a linear relationship between particle crushing rate and effective confining pressure. On the basis of Hardin-Drnevich, the dynamic constitutive model of calcareous sand considering the influence of particle breakage is established by introducing relative crushing rate Br and constitutive model parameters. By comparing with the experimental data, it is found that the relative error between the calculated value and the experimental value of the model is no more than 12%, and the average error is no more than 8%, indicating that the modified dynamic constitutive model can better predict the dynamic characteristics of calcareous sand.

Effect of Wetting and Drying Cycles on the Dynamic Properties of Compacted Loess

This paper investigates the dynamic properties of compacted loess under wetting and drying (W‐D) cycles. A series of tests were conducted on compacted loess samples, namely, the soil dynamic triaxial test and the scanning electron microscopy (SEM) test. The test results showed that the dynamic stress‐strain relationship of the compacted loess under the action of W‐D cycles accords with the Hardin–Drnevich model. The initial dynamic shear modulus (G0) and the maximum dynamic shear stress (τy) of the compacted loess first decreased and then increased with the number of W‐D cycles (n) increasing. The damping ratio (λ) increased linearly with the dynamic strain (εd) increasing in the semilogarithmic coordinate. The defined change rate of the damping ratio (η) first increased and then decreased with the n increasing. The macrostructure and microstructure characteristics of samples in the process of W‐D cycles indicate that the increasing number of pores in the humidifying process and the cracks on the surface and inside of samples during dehumidification lead to the structural damage and dynamic properties reduction of compacted loess. The main reasons for structure strengthening and dynamic properties increasing are that soil particle structure develops to mosaic structure, pore structure develops to uniform small pore, and matrix suction makes soil sample tend to be dense.

Study on mechanical behaviours of rail fasteners and effects on seismic performance of urban rail viaduct

The mechanical properties of rail fasteners play a key role in rail-structure interaction of urban rail viaduct. To reduce vibration and noise, the damping materials such as rubber cushion pads are used as the assemble parts of the rail fasteners in urban rail viaduct. The use of the damping materials causes the mechanical behaviours of rail fasteners to be different from the traditional ones whose longitudinal stiffness can be simplified as linear elastic, elastic–plastic or bilinear models. It is important to capture the mechanical behaviours of the rail fastener for accurately predicting the nonlinear seismic response of urban rail viaduct. In this paper, the quasi-static and dynamic cyclic tests of three kinds of commonly used rail fasteners (Type WJ-2A, Type DTIII2, and Type ZX-3) in China urban rail transit were conducted to explore the mechanical behaviours of rail fasteners. On this basis, the Hardin-Drnevich model is used to simulate the nonlinear behaviours of rail fasteners. Analysis results showed that the Hardin-Drnevich model could describe the quasi-static and dynamic cyclic response of Type WJ-2A and Type DTIII2 rail fasteners with reasonable accuracy, while its prediction accuracy for Type ZX-3 rail fasteners are relatively lower than others. Moreover, the Hardin-Drnevich model can predict the nonlinear dynamic response of Type WJ-2A fastener under earthquake loading very well. The calibrated parameters of Hardin-Drnevich model were used to the rail fasteners in the nonlinear seismic response analysis of the practical urban rail viaduct, and that were compared with that using idealized elastic–plastic model of the rail fastener. Comparison results demonstrated that, the mechanical constitutive relations of the rail fastener have obvious effects on the seismic performance of rail viaduct, and the effects are more distinct in the longitudinal direction than in the transversal direction.

DYNAMIC PROPERTIES OF RIGID POLYURETHANE FOAM IN CYCLIC TRIAXIAL TESTS

The aim of this study is to clarify the dynamic properties of rigid polyurethane foam. A method for renovating a deteriorated bridge as a lightweight embankment was proposed. The space underneath a bridge is filled with polyurethane to support the upper structure. In this case, the upper structure of the bridge is considerably heavier than the polyurethane. Therefore, it is important to examine the seismic behavior of this new lightweight embankment. However, the dynamic deformation characteristics of polyurethane have not been clarified previously. In this study, stress-controlled cyclic triaxial tests based on JGS0542-2009 are used to evaluate the effect of the confining stress and the presence of a rigid layer on the dynamic properties of rigid polyurethane foam. As a result, the shear modulus of rigid polyurethane foam increases with increasing confining stress regardless of the absence of the rigid layer. The shear modulus of polyurethane with the rigid layer is lower than that of polyurethane without the rigid layer. The value of shear modulus of rigid polyurethane foam was measured in the range of approximately 1.6~3.2MPa. Moreover, the stiffness degradation and of rigid polyurethane foam are in good agreement with the Hardin-Drnevich model.

Dynamic properties of the mucky clay improved with the steel slag and the rubber particles

To make full use of advantages of waste steel slag and old rubber particles, the steel slag and rubber particles were mixed into the mucky clay to form the mucky clay-steel slag-rubber particles admixtures (MCSRA) to improve the engineering properties of mucky clay. Dynamic tests have been carried out by resonant column apparatus to investigate the influence of steel slag content, rubber particle content, rubber particle size and confining pressure on small-strain dynamic shear properties of MCSRA. The results showed that the dynamic properties of MCSRA were significantly improved compared with those of the mucky clay. It also revealed that as steel slag content increased, the shear modulus increased and the damping ratio decreased. In addition, as rubber particle content and rubber particle size increased, the shear modulus decreased and the damping ratio increased, and as confining pressure increased, the shear modulus increased and the damping ratio decreased. Moreover, an improved dynamic model was built based on the Hardin-Drnevich model to describe the dynamic performance of MCSRA. By comparing the dynamic characteristics of MCSRA with those of the mucky clay-steel slag admixtures, the Fujian standard sand and the Nanjing fine sand, the MCSRA could be applied to replace the mucky clay improved with the steel slag and Nanjing fine sand in some practical engineering.

Experimental investigation of dynamic shear behavior of typical silt sand in Rudong Offshore Wind Farm

The dynamic properties of typical silt sand in offshore wind farm are closely related to the stability of offshore wind farm foundations. This study investigates the dynamic behavior of typical silt sand in Rudong offshore wind farm of Jiangsu province based on dynamic triaxial testing and resonant column testing. Specifically, the dynamic properties including dynamic modulus, damping ratio, dynamic strength, dynamic strain, dynamic pore water pressures and stress-strain relationship of the silt sand are studied. It is found that the accumulated strain and pore pressure continuously increase with the increased cyclic number, which eventually leads to liquefaction failure. Soil specimen with a higher confining pressure is more likely to reach liquefaction with a lower number of loading cycles. It is also found that the Hardin-Drnevich model can be used to reflect the mechanism of the effect of confining pressure on the dynamic behavior of the silt sand. The dynamic shear modulus and damping ratio decrease and increase exponentially with the increase of shear strain, respectively.

An Experimental Study of the Dynamic Shear Modulus and Damping Ratio of Calcareous Sand in the South China Sea

Lan, J.; K.C., D.; Hu, L., and Gao, Y., 2021. An experimental study of the dynamic shear modulus and damping ratio of calcareous sand in the South China Sea. Journal of Coastal Research, 37(5), 964–972. Coconut Creek (Florida), ISSN 0749-0208. The marine deposits in the South China Sea are characterized by an abundance of calcareous sand. The dynamic characteristics and properties of this sand are important for potential engineering seismic analysis and infrastructure development in this oil- and gas-rich region. The present study aims to investigate the dynamic shear modulus and damping ratio of typical calcareous sand in the South China Sea. A series of dynamic triaxial tests under the strain control condition of cyclic loading were conducted, with a specific focus on the effects of relative density and confining pressure. The normalized dynamic shear modulus increases with the increase in confining pressure, and the shear modulus–shear strain relationship can be adequately described with the well-known Hardin-Drnevich model. However, the influence of confining pressure tends to decline in the sand samples of high initial relative density. Overall, the variations in the damping ratio as affected by confining pressure or relative density are not very significant. The experimental results were assessed and found to be reasonably consistent with some of the previously reported results in the literature.

Experimental study on static and dynamic mechanical properties of phosphogypsum.

Phosphogypsum (PG) is a solid waste product of the wet-process phosphoric acid industry that accumulates in large amounts on the ground, forming PG ponds. In recent years, the amount of PG produced and discharged into ponds has increased significantly with the increase in the market demand for phosphate fertilizers. To enrich the basic knowledge of PG properties and provide basic data for the stability analysis of PG dams, a series of laboratory geotechnical tests, including permeability tests, compressibility tests, triaxial shear tests, and dynamic triaxial tests, were conducted in this study. During the preparation of the test samples, solubility and high-temperature dehydration of PG were considered. The results indicated that PG exhibits medium compressibility and medium to weak permeability characteristics. The stress-strain curves of the triaxial shear tests were divided into three typical stages: initial deformation stage, strain hardening stage, and destruction stage. With increasing dry density and consolidation confining pressure, both the shear strength and deformation modulus significantly increased. The relationship between the deformation modulus and confining pressure gradually changed from linear to logarithmic with increasing density. The liquefaction resistance curves (CSR-NL curves) of PG were expressed by power functions. With increasing dry density, the curves shifted higher and became steeper. Compared with the Hardin-Drnevich model, the Davidenkov model was found to be more suitable for describing the relationship between the dynamic shear modulus ratio and damping ratio of PG and the dynamic shear strain. Furthermore, compared with those of tailings and natural soils, the engineering mechanical properties of PG were relatively poor, which may be related to its uniform particle distribution and neat particle stacking structure.

Study on Dynamic Characteristics of Unsaturated Strongly Weathered Sericite Schist Residual Soil

Sericite schist residual soils are widely distributed on the shallow surface of western Yunnan, and most of them are in an unsaturated state. In order to study its dynamic characteristics, a resonance column tester was used to target the strongly weathered unsaturated sericite schist residuals in the Dali Railway. The soil carries out dynamic characteristic test to study. The results show that the confining pressure has a great influence on the dynamic characteristics of the specimen, the dynamic shear modulus increases with the increase of the confining pressure, the phenomenon that the damping ratio decreases with the increase of shear strain is more obvious. Using the Hardin-Drnevich model can better fit the dynamic shear modulus with shear strain. The application of the improved linear equation can better describe the relationship and analyse its mechanism.

Nonlinear dynamic behavior of laterally loaded composite caisson-piles foundation under scour conditions

A simplified method for predicting the nonlinear dynamic response of composite caisson-piles foundation (CCPF) under scour conditions is proposed. The Hardin-Drnevich model is employed to represent the nonlinear soil reactions. Stress history is also considered to study the scour effect on the dynamic impedance of foundation. Then, harmonic vibration tests considering scour are conducted on a CCPF. It can be observed that the predicted trends of the CCPFs response agree with the experimental data, which verifies the reliability of the method. Then, a case study is investigated to evaluate the effects of stress history, scour depth and soil nonlinearity on the dynamic response of the foundation. The results show that soil nonlinearity has a close relationship with the lateral dynamic displacement of foundation, and it will result in a slight reduction in the resonant dimensionless frequency of the CCPFs. Additionally, with increasing scour depth, a remarkable decrease in the dynamic impedances is produced when soil nonlinearity is considered. Compared with soil nonlinearity, stress history is found to have greater influence on the displacement of the CCPFs, especially in the low frequency range. Finally, a discussion is conducted on the relationships between the resonant frequency of the CCPFs and the scour depth.