Small-strain Modulus Research Articles

Damage constitutive model of fly ash–cementitious iron tailings powder under small strain

With the vigorous development of industrial economy, the production capacity and level have been significantly improved, but at the same time, a large amount of iron tailings, fly ash and a series of bulk solid waste materials have been accumulated. These industrial wastes have caused serious impact on the ecological environment. How to deal with them effectively is an urgent problem that needs to be solved. The aim of this study was to investigate the effect of cement and fly ash compound admixtures on the mechanical properties of iron tailings powder (ITP). Hence, different mixing ratios of cement and fly ash were used to prepare two kinds of ITP-based materials. A range of uniaxial compressive strength (UCS), resonance column (RC), scanning electron microscopy and X-ray diffraction tests were conducted to investigate the roles of cement, fly ash and curing age in ITP solidification. A random one-dimensional damage model was imported to study the damage evolution of ITP materials using the UCS and RC test results, which showed that cement and fly ash enhanced the unconfined compression strength and small-strain stiffness of ITP. When 5–10% fly ash content was used as a substitute for 10% cement, the unconfined compressive strength and small-strain modulus of cement–fly ash–ITP increased with curing age. The microstructure and mineralogy analysis confirmed that fly ash enhanced the strength of the material. Overall, the damage constitutive model effectively represented the randomness of the compressive strength and stress–strain relationship of ITP materials under unconfined conditions.

Bender element sensor technology to quantify local stiffness enhancement of geogrid-stabilized aggregate specimens

Geogrids improve pavement performance and extend lifespan by making the unbound aggregate base/subbase course stiffer. Extruded (i.e., punched and drawn) geogrids are widely used in pavement applications. This paper presents an experimental evaluation of multi-axial extruded geogrids with various aperture shapes for pavement applications. The study quantified modulus enhancement ratio and identified the extent of the geogrid-stiffened zone. Two types of aggregates (i.e., crushed limestone and partially crushed gravel), commonly used in Illinois for base or subbase course, were utilized. Repeated load triaxial tests were conducted on 6-in. diameter and 12-in. height cylindrical specimens instrumented with embedded shear wave transducers in the form of Bender Element (BE) sensors. The BE pairs were horizontally placed at three different heights above the geogrid. Resilient moduli of the aggregate samples were determined following the AASHTO T 307 standard test procedure. Concurrently, the localized small-strain moduli at different heights above the midheight of the specimen were determined from the shear wave velocities computed according to the first arrival times from the BE sensors recorded at the end of the application of each stress state. The results reveal that resilient modulus tests do not capture the geogrid effects, while BE sensors can quantify the local stiffness enhancement due to a geogrid, and the extent of the geogrid-stiffened zone. Results show that the multi-axial geogrids provided a 45% increase in small strain modulus for both aggregate types in the vicinity of the geogrid.

VALORIZATION OF DREDGED SEDIMENTS FROM DAMS IN PAVEMENT DESIGN

Introduction: This study is part of research aimed at valorizing dredged sediments through the development of formulations for use in road engineering. The purpose of the study was to determine if the materials selected for pavement layers comply with road design standards, in particular, with specific requirements for density, grain size, plastic properties, organic matter, and mechanical performance. Methods: To determine the physical-chemical and mechanical characteristics of the dredged sediments obtained from samples taken from the Bakhadda dam located in western Algeria’s semi-arid climate, the sediments were treated with binders in small amounts (3% lime (L), 6% cement (C)) for reuse in road construction. The study focused on the evolution of physical and mechanical characteristics of the treated sediments, including LL, PI, VBS, immediate bearing index (IBI%), UCS, tensile strength Ϭt, as well as small strain modulus ESS and large strain modulus E50. The results showed that adding lime and cement to the dredged sediments improved their strength, as evidenced by the increased compressive strength (UCS) over time for the samples containing different amounts of binders (3%L, 6%C, and 3%L + 6%C). Additionally, the effect of the water content on the mechanical properties of the formulations was demonstrated. The study showed that the strength increased when the water content decreased.

Assessment of small strain modulus in soil using advanced computational models

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Shear strength and modulus of mine waste rock – Large scale laboratory testing results

This paper presents the sampling and laboratory testing results of mine waste rock consisting of limestone, siltstone, and intrusive materials collected from the Ok Tedi open pit mine in Papua New Guinea. The laboratory tests included specific gravity measurements, index testing, large-scale direct shear tests using a 720 mm square direct shear apparatus, large-scale consolidation tests using a 550 mm diameter consolidation apparatus, and shear wave velocity tests conducted on compressed waste rock samples. The obtained strength values, as well as small and larger strain modulus values, were subsequently compared with existing literature data from the literature. These findings can serve as a valuable reference for mine waste materials with similar lithology, particle size distribution, and stress condition, particularly in the context of static and seismic slope stability designs.

Compressibility and small strain stiffness characteristics of silt-hematite mixtures

Iron mining waste is disposed of near mines and forms iron ore (hematite) tailings dams. Furthermore, the distinctive characteristics of hematite particles can affect the geotechnical properties of soil. This study aimed to experimentally examine the compressibility and small-strain stiffness of silt-hematite mixtures. Silt-hematite mixtures were prepared in an oedometer cell at a fixed relative density with different hematite contents (0% to 100% in weight). Vertical displacements and loads were measured with the oedometer, and shear and compression waves were measured using bender and piezo-disk elements, respectively. The results showed that the void ratio and compressibility increased, while the constrained modulus decreased with increasing hematite content as hematite formed porous aggregate owing to high van der Waals forces. The elastic wave velocities (Vs and Vp) and small-strain moduli (Gmax and Mmax) increased with increasing hematite content owing to hematite's high stiffness and coordination number. Furthermore, the elastic wave velocities of high hematite-content specimens were practically constant at low-stress levels (<20 kPa), because of the van der Waals forces being greater than the skeletal forces. This study suggests that the geotechnical properties of hematite-containing soils, hematite-coated soils, and iron ore tailings soils can be evaluated by the hematite ratio.

Degraded Ballast Stiffness Characterization Using Bender Element Field Sensor and PANDA® Penetrometer

The progressive degradation of railway ballast over time increases the degree of ballast fouling and poses significant drainability concerns leading to frequent maintenance activities. To avoid such issues, an effective and continuous characterization of the physical properties of the ballast layer is deemed necessary. This paper introduces the combined use of a bender element (BE) piezoelectric field sensor and a PANDA® dynamic cone penetrometer for periodic evaluations of ballast condition over the traffic use. To simulate various levels of ballast degradation, box tests were conducted using a dolomitic ballast material compacted in a laboratory-sized testbed with fouling indices ranging from zero to 39%. BE sensor pairs were embedded in the ballast layer to calculate the small strain modulus behavior of the ballast assessed through shear wave velocity measurements under different confinement conditions. Strength profiles of the ballast at different fouling levels were also measured using the PANDA® penetrometer. Experimental findings from both test methods indicate the existence of a dense state of ballast linked to a certain fouling index that maximized stiffness and strength characteristics of the tested ballast in dry condition. Accordingly, the potential use of BE field sensors embedded within in-service ballasted track coupled with periodic penetration testing can be a viable approach to evaluate ballast layer degradation. Various void packing conditions associated with ballast fouling levels can be linked to important ballast layer modulus and strength behavior. Further, such smart sensing of ballasted track behavior can provide long-term performance monitoring solutions for ballast cleaning and maintenance scheduling.

Effect of Salt on Dynamic Mechanical Behaviors of Polyampholyte Hydrogels

Understanding the dynamic mechanical behaviors of tough hydrogels with ionic dynamic bonds in saline solution is crucial for applications, particularly in the biomedical field. In this work, using polyampholyte hydrogels, dually crosslinked with a primary network from covalent crosslinkers and/or trapped entanglements, and a dynamic network from ionic bonds, as a model system, we investigate the salt effect on rheological response and mechanical behaviors. Through a systematic study on one gel without a chemical crosslinker and one gel with a chemical crosslinker, we demonstrate that the salt effect on mechanical properties, including small-strain moduli, large deformation energy dissipation, and fracture stretch ratio, can be effectively converted into frequency or strain rate dependences following the time–salt superposition principle. Accordingly, we access a wide range of observation time scales from 10–11 to 102 rad/s at room temperature, covering three regimes: (I) the high-frequency plateau regime from the dynamic and primary networks, (II) the viscoelastic regime from sticky Rouse motion of ionic associations, and (III) the low-frequency plateau regime from the primary network. Moreover, we disclose an in-depth understanding of the entanglement’s behavior in the long-timescale regime III. This work not only provides a guide to biological applications of hydrogels in saline environments but also gives important insights into the toughening mechanism via dynamic bonds in other systems with dually crosslinked structures.

Effect of size and strain rate on particle strength and stress–strain properties of rockfill materials

The stress-strain properties of the rockfill materials under cyclic loading conditions are critical for the seismic safety analysis of dams. However, due to the effect of size and strain rate, the parameters obtained from the scaled laboratory tests may not accurately calculate the earthquake response. In the presented study, a novel approach has been developed to infer the prototype parameters based on the single particle strength. Firstly, a series of particle crushing tests with different sizes and loading rates were conducted. The results show that as the strain rate increases, the particle strength enhances and the size effect on particle strength gradually weakens. According to the established particle strength model, it is assumed that two specimens have homothetic particle size distributions and the same compaction, and is geometrically similar, then the size effect relations on macroscopic stress and strain tensors can be derived, a set of monotonic and cyclic triaxial tests are used to validate the approach. Furthermore, the effect of particle size and strain rate on the equivalent linear model is determined, the small-strain modulus parameter K obtained from the laboratory test should be modified. This study provides a reference to the engineering design and seismic safety evaluation of high rockfill dams.

Stiffness decay characteristics and disturbance effect evaluation of structured clay based on in-situ tests

The structure of the sedimentary clay influences its mechanical behavior in non-negligible ways. This paper proposes an effective approach for investigating the in-situ stiffness characteristics from shear modulus and strain decay curves (G–γ curves) based on self-boring pressuremeter and seismic dilatometer tests. To evaluate the excavation disturbance effects on the structured clay, the stiffness parameters from pre-bored pressuremeter tests are compared with the results of self-boring pressuremeter tests. The result indicates that the complete in-situ G–γ curves can be acquired by integrating the strain-dependent tangent shear modulus Gt from self-boring pressuremeter tests and the small-strain modulus G0 from seismic dilatometer tests. Simultaneous observations of the G–γ curves with hyperbolic shapes in semi-logarithmic coordinates at the same strain scale show the similarity of the stiffness decay mode of the soil at different depths. The increase in the measured values of Gt and G0 with depth can be attributed to the improved consolidation pressures and cemented strength in the structured clay. Additionally, the G/G0–γ curves measured by the in-situ tests generally agree well with the results predicted by the Stokoe model. The excavation disturbance weakens the stiffness of the structured clay, as evidenced by Gt from the pre-bored pressuremeter data being significantly smaller than that from self-boring pressuremeter tests at the same depth. Based on quantitative analysis, the disturbance degree computed from the measured results has a low sensitivity to the soil depth and a strong negative correlation with the strain level of the soil. This study provides an effective method for predicting the stiffness parameters of structured soil based on in-situ tests.

Correlating failure strength with wave velocities for cemented sands from the particle-level analysis

Measurement of elastic wave velocities allows engineers to effectively characterize and monitor the stiffness and strength development of the cemented soils. Several correlations between elastic wave velocity and strength, as well as correlations between small-strain modulus and strength, have been proposed for different materials. However, since the physical justification of the stiffness-strength correlation is not fully understood, criticisms and diverse views still exist. This study derived the analytical correlation between the elastic wave velocity (or small-strain stiffness) and the unconfined compressive strength of cemented soil, based on a simple cubic packing of coated equal-sized spheres. The analytical derivation suggested a one-parameter power function between the strength and the wave velocity or stiffness, with the power index of 4 and 2 for wave velocity and stiffness, respectively. To verify the derived correlation model, a first-hand laboratory database was used. Factors affecting the correlations are also discussed.

Shear modulus of ionomer interlayer: Effects of time, temperature and strain rate

The transparent ionomer material SentryGlas® or SG for short is widely used as interlayers in laminated glass and is also a potential adhesive in laminated connection. The material’s shear modulus is of practical interest before glass breakage because it allows a shear transfer between glass components. Due to the viscoelasticity behaviour of the material, its modulus is significantly dependent on the working conditions. This work investigates the effects of temperature, time, and strain rate on SG’s shear small-strain modulus from the point of practical application. The shear property at room temperature is obtained from the results of shear tests. Based on the viscoelastic theory, the time and temperature dependence within the actual application range is quantitively determined from DMA measurements. The glass transition temperature associated with modulus decline is then recalibrated. The effect of strain rate is also qualitatively measured. Finally, the time-temperature dependent equations of shear modulus are applied to numerical simulation of a long-term loading test on framed ionomer interlayer laminated glass.

Cyclic fatigue failure of TPU using a crack propagation approach

Thermoplastic polyurethane elastomers (TPU) are stretchable, tough, wear resistant and easily processable soft materials. Especially because of their recyclability, TPUs can be suitable candidates to replace rubbers in several applications such as damping, footwear and cable coatings. However, their capacity to operate under cyclic loads over many cycles was rarely investigated, mainly due to their complex strain-dependent morphology and viscoplastic character. Additionally, the absence of chemical crosslinks results in a certain degree of creep and plastic deformation when TPUs are cyclically strained, questioning how to unambiguously define fracture mechanics variables such as the energy release rate G, typically used to evaluate fatigue crack growth in chemically crosslinked elastomers. We show that, when TPUs are cyclically loaded up to the same value of maximum stretch, their stress-stretch curve changes with the number of applied cycles, but eventually achieves a steady-state. We propose a suitable methodology to evaluate the cyclic fatigue resistance in TPUs, based on a fracture mechanics approach with some additional treatments to account for the higher tendency to creep of TPUs than thermoset rubbers. Comparing the obtained results of TPU with those for classical filled rubbers with a similar small strain modulus, we underline the excellent toughness and cyclic fatigue resistance of TPUs, opening new opportunities in their use for applications requiring to resist to crack propagation under cyclic loading at large strains.

Laboratory Studies of Small Strain Stiffness and Modulus Degradation of Warsaw Mineral Cohesive Soils

The shear modulus and normalized shear modulus degradation curve are the fundamental parameters describing soil behavior. Thus, this article is focused on the stiffness characteristic of 15 different Warsaw cohesive soli represented by the parameters mentioned above. In this research, standard resonant column tests were performed in a wide shear strain range, from a small one, where soil behaves like an elastic medium, to a medium one, where soil has an unrecoverable deformation. Collected data allows the authors to create empirical models describing stiffness characteristics with high reliability. The maximum shear modulus calculated by the proposed equation for Warsaw cohesive soil had a relative error of about 6.8%. The formula for normalized shear modulus estimated G/GMAX with 2.2% relative error. Combined empirical models for GMAX, and G/GMAX allow the evaluation of Warsaw cohesive soil’s shear modulus value in a wide shear deformation range, with a very low value of the relative error of 6.7%.

Effects of Relative Humidity During Curing on Small-Strain Modulus of Cement-Treated Silty Sand

This study investigated the effects of relative humidity ( $$R_{h}$$ ) or total suction condition during curing on small-strain shear modulus (G0) of a cement-treated silty sand using free-free resonant frequency tests (FFR). The moduli were determined on samples cured at different suctions corresponding to three $$R_{h}$$ values of 7%, 75%, and 100%, in both unsoaked and soaked conditions. Soil–water retention curves (SWRCs), and unconfined compression strength (UCS) were also determined along with x-ray diffraction (XRD) analysis. The cement-treated SWRCs showed a much flatter slope than the non-treated ones, and the air-entry suction increased with cement content. The values of G0 increased with cement content and curing time. The highest modulus was achieved in 75% $$R_{h}$$ curing condition. The 7% $$R_{h} $$ condition resulted in a significant drop in modulus, even close to the non-treated G0 for the 2% cement case. At the same UCS value, the soaked cement-treated samples had higher modulus than the non-treated ones in the unsoaked condition, indicating that the effect of suction on modulus was smaller than the effect of cementation. XRD analysis revealed a greater availability of C3S in 7% $$R_{h}$$ curing condition at 7-day curing period suggesting that the hydration process was still not complete, which explained the decrease in G0 in this curing condition.

The Ring-Pull Assay for Mechanical Properties of Fibrous Soft Tissues - An Analysis of the Uniaxial Approximation and a Correction for Nonlinear Thick-Walled Tissues.

The ring-pull test, where a ring of tissue is hooked via two pins and stretched, is a popular biomechanical test, especially for small arteries. Although convenient and reliable, the ring test produces inhomogeneous strain, making determination of material parameters non-trivial. To determine correction factors between ring-pull-estimated and true tissue properties. A finite-element model of ring pulling was constructed for a sample with nonlinear, anisotropic mechanical behavior typical of arteries. The pin force and sample cross-section were used to compute an apparent modulus at small and large strain, which were compared to the specified properties. The resulting corrections were validated with experiments on porcine and ovine arteries. The correction was further applied to experiments on mouse aortic rings to determine material and failure properties. Calculating strain based on centerline stretch rather than inner-wall or outer-wall stretch afforded better estimation of tissue properties. Additional correction factors were developed based on ring wall thickness H, centerline ring radius R c , and pin radius a. The corrected estimates for tissue properties were in good agreement with uniaxial stretch experiments. The computed corrections improved estimation of tissue material properties for both the small-strain (toe) modulus and the large-strain (lockout) modulus. When measuring tensile strength, one should minimize H/a to ensure that peak stress occurs at the sample midplane rather than near the pin. In this scenario, tensile strength can be estimated accurately by using inner-wall stretch at the midplane and the corrected properties.

The Influence of Model Assumptions on the Dynamic Impedance Functions of Shallow Foundations

The influence of model assumptions on the dynamic impedance functions of shallow foundations is investigated using finite elements in two studies. The first investigates the effects of model assumptions in different combinations including embedment of the foundation, variation of modulus with depth, and permanent load acting on the foundation. The second study is a parametric analysis investigating the effects of permanent load at varying soil depths and with different soil modulus coefficients. Shallow foundations in strata of frictional soil on top of bedrock are considered. Small-strain modulus and modulus reduction relationships are used in an iterative process to update the modulus due to the permanent load. The results show that model assumptions can have a large influence on impedance functions. The static stiffness coefficients differ, in some instances by more than 100%. The impedance functions, normalized with the static stiffness coefficients match each other well in the pre-resonance frequency range. However, in the frequency range above the fundamental frequency, the normalized impedance functions show a large variation. Further, the results show that the influence of the permanent load is largest in the case of shallow and stiff soil strata, both regarding normalized impedance functions as well as the static stiffness coefficient, which can be increased up to 67%. The change in fundamental frequency was however minimal.

Exploration of a mechanistic model for the quantification of the resilient modulus using free-free resonant column testing

Resilient modulus (MR ) is one of the key properties used to characterise and quantify the mechanical behaviour of soil materials for pavement design purposes. Standard MR test procedures are often complex, lengthy, and cost-prohibitive for most routine daily applications. Therefore, correlative models relating to easy-to-obtain basic soil index properties, such as the Atterberg limits, have been historically used to predict and estimate MR ; such index properties, however, are not always effective for obtaining correct MR values. Alternatively, the California bearing ratio (CBR) and nonlinear stress–strain constitutive models have also been used to estimate MR . The work presented in this paper proposes the implementation of an enhanced hyperbolic constitutive model (eHCM) for the estimation of MR based on small-strain modulus measurements from the free-free resonant column (FFRC) test. The proposed approach aims to circumvent some of the challenges and complexity associated with the lengthy MR laboratory testing. Using the Texas flexible pavements and overlays database (namely the DSS) as the data source, the research methodology included: (a) formulating and developing the eHCM, (b) estimating MR values using the eHCM model along with FFRC test measurements, (c) calibrating and validating the eHCM model using modulus measurements obtained through conventional MR testing, and (d) establishing statistical correlations between eHCM model parameters and routinely measured soil properties. Ten in-service highway test sections from the DSS, encompassing both granular (flex) base and raw subgrade soil materials, were used for the study. From the corresponding results and findings, the eHCM model was found to be satisfactory in terms of adequately quantifying the mechanical behaviour of granular base and subgrade soil materials, yielding coefficient of variation values comparable to the literature. Overall, the proposed eHCM model indicated promising potential as a viable alternative, surrogate, and/or supplement for rapid MR estimation based on simple and inexpensive field or laboratory small-strain modulus testing such as the FFRC.

Anisotropic small-strain stiffness of calcareous sand affected by sample preparation, particle characteristic and gradation

Sands exhibit a directional diversity in shear modulus at small strains, reflecting the anisotropic stiffness behaviour in the structure. In this paper, sample preparation method, particle shape and particle size are considered as parameters to produce samples with various initial fabric. Five preparation methods, namely, air and water pluviation, dry and moist tamping and dry funnel deposition are used to reconstitute the samples. The stiffness anisotropy of calcareous sand and Mol silica sand is quantified by the small-strain modulus G0 measured in horizontal and vertical planes with the bender element technique in triaxial tests. Test results show that calcareous sands behave as an elastic homogeneous continuum material at small strains. Calcareous samples prepared by the air pluviation method possess the highest anisotropic ratios. The lowest stiffness anisotropy exists in the samples prepared by moist tamping and dry funnel deposition methods. Compared with the anisotropic ratios of the air pluviation samples from the literature, the notably higher values for the calcareous sand in this study are attributed to the lower sphericity. In addition, less prominent stiffness anisotropy is found in calcareous sands with smaller particle sizes (D50).

Stiffness Decay in Structured Soils by Seismic Dilatometer

The small-strain stiffness modulus G0 is not directly applicable to evaluate deformation in most practical engineering problems, and therefore, nonlinear soil behavior curves have been developed in terms of Young modulus E or shear modulus G. These curves were successfully obtained for sedimentary soils, while for residual soils, the available data from intertional community is still scarce. Residual soils are considered structured soils and often classified as problematic soils since they do not fit into the behavior of remolded or unstructured soils. In fact, the role of bonding and fabric affects both the strength and the stiffness of the soil. This article illustrates the use of the seismic dilatometer test (SDMT) for the determination of in situ stiffness decay curves with strain level (G-γ curves or similar) in a granitic residual soil of the Northeastern region of Portugal (Guarda), showing its adequacy to solve these kinds of problems. In situ and laboratory tests were performed on these granitic residual soils. The adopted approach relies on the ability of SDMT to provide a small-strain modulus G0 (from the shear wave velocity Vs) and a “working strain” modulus GDMT (derived from the constrained modulus MDMT in accordance with the theory of elasticity). Thus, in situ G-γ decay curves were tentatively constructed by fitting curves through these two points using a hyperbolic model. However, it was observed that the results obtained by the hyperbolic model for the cemented soils are not satisfactory. Based on the SDMT parameters, a logistic curve was derived for the reproduction of reference stiffness curves obtained from the triaxial test results.