Small Strain Effects Research Articles

Evaluation of deformation for two-dimensional (2D) and three-dimensional (3D) braced excavation in clays with centrifuge modelling and numerical analysis

This study presents an improved in-flight strutting system for centrifuge modelling. Based on the centrifuge model test data, the mobilizable strength design (MSD) method was revised. The modified MSD method extends to the prediction of three-dimensional (3D) deformations in retaining walls due to excavation activities. Initially, an improved in-flight excavation tool used in centrifuge tests was employed to investigate the impacts of staged excavation on the characteristics of wall displacement and ground settlement in two-dimensional (2D) braced excavation. Subsequently, 2D and 3D finite element analyses, calibrated against the centrifuge test data and considering the small strain effect, were conducted to assess the performance of wall displacement, ground settlement, and movement of the underground soil induced by the braced excavation. Moreover, this research proposes a straightforward predictive model based on the modified MSD, specifically for calculating the deformation along the length of retaining walls in 3D braced excavations. The insights and the modified MSD method given in this study may facilitate the design of foundation pit projects, especially when the 3D effects are an essential detail to be considered in these projects.

Comparison of two small-strain concepts: ISA and intergranular strain applied to barodesy

The intergranular strain concept (IGS) and intergranular strain anisotropy formulation (ISA) are state of the art extensions to describe small-strain effects. The main conceptional difference between ISA and IGS is the purely elastic strain range introduced by ISA. In addition, the ISA formulation used in this article includes an additional state variable in order to reduce accumulation effects for cyclic loading with a larger number of repetitive cycles. Barodesy is enhanced here with ISA to improve its small-strain predictions. The performance of this new model is compared with barodesy enhanced with IGS. It turned out that the small-strain extensions do not negatively influence predictions under monotonic loading. Differences between ISA and ISG are only remarkable for very small-strain cycles and even there they are negligible for certain parameter values.

AVISA: anisotropic visco-ISA model and its performance at cyclic loading

In this work, a constitutive model able to capture the strain rate dependency, small strain effects and the inherent anisotropy is proposed considering the influence of the overconsolidation ratio (OCR). Small strain effects are captured by using an extended ISA plasticity formulation (Fuentes and Triantafyllidis in Int J Numer Anal Methods Geomech 39(11):1235–1254, 2015). The strain rate dependency is reproduced by incorporating a third strain rate mechanism (in addition to the elastic and hypoplastic strain rate). A loading surface has been incorporated to define a three-dimensional (3D) overconsolidation ratio and to account for its effects on the simulations. Experimental investigations using Kaolin Clay and Lower Rhine Clay with horizontal bedding plane have shown that under undrained cycles of small strain amplitudes (<10^{-4}), the effective stress path in the p–q space is significantly inclined towards the left upper corner of the p - q plane. Consequently, a transversely (hypo)elastic stiffness has been successfully formulated to capture this behaviour. The performance of the model has been inspected by simulating the database of approximately 50 cyclic undrained triaxial (CUT) tests on low-plasticity Kaolin Clay (Wichtmann and Triantafyllidis) considering different deviatoric stress amplitudes, initial stress ratios, displacement rate, overconsolidation ratio and cutting direction. Furthermore, 4 CUT tests conducted on high-plasticity Lower Rhine Clay were simulated, whereby the influence of the displacement rate, as well as the deviatoric stress amplitude, has been analysed. The simulations showed a good congruence with the experimental observations.

Simple analytical solutions of one-equation modelling for steady/decaying homogeneous turbulence sensitized to small strain

This study presents a simple mathematical solution describing the turbulent kinetic energy in steady or decaying homogeneous turbulence sensitized to small strain. Small strain is found to have little effect on the anisotropy of decaying homogeneous turbulence, which is consistent with a previous experiment. The effect of small strain on dissipation in the governing equations of turbulent kinetic energy is examined using the standard k-ε model. Two temporal profiles, namely a constant profile and a linear profile, with small strain are used. The steady homogeneous turbulence is maintained by linear forcing, as previously reported. This study mainly focuses on the effects of small strain on the turbulence time scale. When the magnitude of the small strain is small, the effects on the turbulence time scale can be negligibly small, especially for a constant profile. Based on this result, the governing equations for steady or decaying homogeneous turbulence sensitized to small strain can be reduced to simple linear equations. The analytical solution of these equations, a simple exponential function, is the same for the two types of homogeneous turbulence.

Small strain effect on the mechanical vibration behavior of cross-linked functionalized carbon nanotubes with polyethylene: A molecular-dynamics study

Based on the classical molecular-dynamics (MD) simulations, the vibrational behavior of cross-linked functionalized carbon nanotubes (CNTs) with polyethylene (PE) chains is studied under the applied mechanical tensile and compressive strains. So, different distribution patterns, namely mapped and wrapped distribution patterns are chosen. According to the results, it is seen that natural frequency of cross-linked functionalized CNTs reduces in which this reduction increases by increasing the weight percentage of attached chain. Under tensile strain, it is observed that the frequency of functionalized CNTs increases. Moreover, it is observed that the frequency shifts rise by increasing the applied tensile strain. By contrast, the compressive strain results in higher reductions in natural frequency of functionalized CNTs which considerably rises by increasing the applied strain. Moreover, it is shown that as the weight percentage of cross-linked functionalized CNTs increases, the sensitivity of the frequency shift to the applied tensile and compressive strains decreases and increases, respectively.

Numerical-based theoretical analysis on the decay of homogeneous turbulence affected by small strain based on constant and linear strain variations

This study clarifies the effects of small strain on the decay of homogeneous turbulence by focusing on the temporal profile of the small strain. Small strain is defined in such a way as to not affect the anisotropy of the homogeneous turbulence. We apply the framework of the standard k–ε model to examine the effects of small strain. Constant and linearly varying small strains are studied. The effects of linearly varying small strain are found to be greater than those of constant strain. To discuss the results, we derive an analytical solution that describes the effects of the two types of small strain. Although the form of the analytical solutions is the same for constant and linearly varying strains, the coefficients used in the analytical solutions, for which an equation is also obtained, differ. The difference observed in the effects of the two types of small strain is thus caused by the difference in coefficient.

A multivariate adaptive regression splines model for estimation of maximum wall deflections induced by braced excavation

With rapid economic growth, numerous deep excavation projects for high-rise buildings and subway transportation networks have been constructed in the past two decades. Deep excavations particularly in thick deposits of soft clay may cause excessive ground movements and thus result in potential damage to adjacent buildings and supporting utilities. Extensive plane strain finite element analyses considering small strain effect have been carried out to examine the wall deflections for excavations in soft clay deposits supported by diaphragm walls and bracings. The excavation geometrical parameters, soil strength and stiffness properties, soil unit weight, the strut stiffness and wall stiffness were varied to study the wall deflection behaviour. Based on these results, a multivariate adaptive regression splines model was developed for estimating the maximum wall deflection. Parametric analyses were also performed to investigate the influence of the various design variables on wall deflections.

The Small Strain Effects to the Shear Strength and Maximum Stiffness of Post-Cyclic Degradation of Hemic Peat Soil

The Small Strain Effects to the Shear Strength and Maximum Stiffness of Post-Cyclic Degradation of Hemic Peat Soil

A simple prediction model for wall deflection caused by braced excavation in clays

Deep excavations particularly in deep deposits of soft clay can cause excessive ground movements and result in damage to adjacent buildings. Extensive plane strain finite element analyses considering the small strain effect have been carried out to examine the wall deflections for excavations in soft clay deposits supported by retaining walls and bracing. The excavation geometry, soil strength and stiffness properties, and the wall stiffness were varied to study the wall deflection behavior. Based on these results, a simple Polynomial Regression (PR) model was developed for estimating the maximum wall deflection. Wall deflections computed by this method compare favorably with a number of field and published records.

The application of a small strain model in excavations

The importance of soil small strain effect on soil-structure behavior was investigated by researchers in last decades. The finite element method (FEM) is always used to predict the excavation behavior, whereas there are not many soil models available to consider this effect in analysis. This paper introduces a simple small strain soil model—hardening small-strain (HSS) in PLAXIS 8.5 and exhibits its application in excavation problems via studying the history of two cases. The analyses also use two familiar soil models: hardening-soil (HS) model and Mohr-Coulomb (MC) model. Results show that the HSS predicts more reasonable magnitudes and profiles of wall deflections and surface settlements than other models. It also indicates that the small strain effect relies on the strain level which is induced by excavation.

Characterization of the dynamic strain response of lead magnesium niobate based ferroelectric relaxor using a fiber optic interferometer

A high resolution optical technique is described which allows for the direct measurement of the dynamic strain response of ferroelectric relaxors. A fiber optic interferometer with strain resolution ≤10-11 (1Hz bandwidth) is utilized to probe the small strain effects in a (Pb(Mg1/3Nb2/3)O3)0.859-(PbTiO3)0.137-(SrTiO3)0.004 ferroelectric relaxor. The total macroscopic strain in the material is assumed to depend both linearly (piezoelectric term) and quadratically (electrostrictive term) on the applied electric field thereby allowing for the characterization of the material as a function of both ac and dc fields. The strain response of the material is monitored at the fundamental (f = 22kHz) and at the second harmonic. The effective piezoelectric and electrostrictive coefficients are computed as a function of temperature from the ac and dc scans and compared to the ones obtained from the low frequency sideband technique (LFST). The maximum value of the dynamic (f = 22 kHz) effective electrostrictive coefficient measured at T = 48°C was found to be 6.4 × 10-16 (m2/V2). The effective piezoelectric coefficient is found to decrease as the temperature increases while the effective electrostrictive coefficient has a maxima near 48°C. At room temperature the material is found to contain a remnant field which decreases as the temperature increases.

Inhomogeneous dynamic strain characteristics of ferroelectric relaxors

Abstract We utilize a high resolution fiber optic (FO) interferometer to measure the dynamic small strain effects in relaxor ferroelectrics. The dynamic strain response of both a PZT and PMN based relaxor ferroelectric is characterized as a function of the applied electric field containing both ac and dc components. Using this technique we have found that relaxor ferroelectrics ferroelectrics exhibit a residual strain signal which cannot be understood by the scalar strain-polarization relationship (e = QP2). The effects of large residual strain signal on the performance of high resolution low frequency fiber optic voltage sensors are discussed.

Observation of residual strain in dynamically excited electrostrictors

We measured the dynamic small strain effects in electrostrictive ceramics with a high resolution fiber optic interferometer. The dynamic strain response of both a lead magnesium niobate (PMN) and a lead zirconate titanate (PZT)-based electrostrictive ceramic exhibited a residual signal which cannot be understood by the simple scalar strain-polarization relationship, e+QP2. The magnitude of the residual signal decreased as a function of increasing temperature indicating that the residual strain signal has origins in the remnant electric polarization of the material. The magnitude of the residual strain was generally higher for the PZT-based electrostrictor than for the PMN based sample. The observed residual strain signal represents a novel phenomenon previously unseen in the dynamical strain response of electrostrictive ceramics.