Fractional Burgers models in creep and stress relaxation tests

Okuka, Aleksandar; Zorica, Dušan

doi:10.1016/j.apm.2019.09.035

Cited by 31 publications

(31 citation statements)

References 26 publications

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“…The strain curve at this stage displayed typical nonlinear properties, and it was difficult to accurately describe its creep properties by using traditional models, such as the Kelvin and Maxwell models [ 40 ]. For soils that exhibit typical nonlinear viscoelastic solid-liquid coupling, the existing nonlinear viscoelastic theory does not accurately describe the creep properties, so the linear viscoelastic theory is often needed for precise exploration and analysis [ 41 ]. According to the creep curve properties of samples, Burgers model was proposed to study the creep properties of paddy soil, which belonged to linear viscoelastic model, and its mechanical model was shown below ( Fig 5 ).…”

Section: Resultsmentioning

confidence: 99%

Effects of moisture content and tillage methods on creep properties of paddy soil

et al. 2021

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The rheological properties parameters of paddy soil affect the interaction between the tillage tools and soil, thus influencing the operation quality and power consumption. In order to study the effects of tillage methods and moisture content on the rheological properties parameters of paddy soil in the middle and lower reaches of the Yangtze River, uniaxial compression creep tests of paddy soils with four moisture contents under no tillage (moisture contents: 26.71%, 24.52%, 23.26%, 21.28%) and plough tillage (moisture contents: 26.77%, 25.55%, 23.40%, 20.56%) were carried out using a TMS-PRO texture analyzer. The creep properties curves obtained from the tests, and the rheological constitutive equation of paddy soil under compression was established by Burgers viscoelastic model. Respectively, the quantitative change rules of creep properties of paddy soil with different moisture contents under different tillage methods and the correlation between these parameters were explored. The results showed that the moisture content under the three-year plough tillage and no tillage methods had significant influence on the rheological properties parameters of paddy soil (P < 0.05). The instantaneous elastic modulus, delay elastic modulus, and viscosity coefficient of the two paddy soils (no tillage and plough tillage soils) decreased with the increase of moisture content. However, the variation rules of relaxation time and delay viscosity coefficient with moisture content differed between these two paddy soils. Specifically, the strain rate of the two paddy soils decreased as moisture content decreased, where the total strain combines elastic strain, viscous strain, and viscoelastic strain. The initial strain rate and steady strain rate of the plough tillage paddy soils were lower than that of the no tillage paddy soils. The established creep model equation could be used to obtain viscoelastic rheological parameters of paddy soil in a wide range. The fitting equations between rheological parameters and moisture content were introduced into Burgers model, and the coupling equations between creep deformation and moisture content and time were derived, which could be used to predict the creep properties and deformation behavior of paddy soil in a certain range of no tillage and ploughed field. Overall, this study has a certain theoretical significance for the development and improvement of paddy soil rheology theory, and can also provide theoretical basis and technical support for the research of agricultural machinery design optimization, field water, soil conservation, soil tillage and compaction related simulation analysis in the middle and lower reaches of the Yangtze River.

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Section: Resultsmentioning

confidence: 99%

Effects of moisture content and tillage methods on creep properties of paddy soil

et al. 2021

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“…In addition, the long-term deformations of the actual full-size tunnel anchors of the Xingkang suspension bridge were evaluated by adopting an empirical method. [20], as illustrated in Figure 18.…”

Section: Numerical Calculationmentioning

confidence: 97%

In Situ Creep Model Testing for the Tunnel Anchor Foundation of Xingkang Suspension Bridge in Luding of China

Luo

Cheng

et al. 2020

Advances in Civil Engineering

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Due to the limitations of geography and geology, cast concrete tunnel anchors were used to provide counterforces for Xingkang Suspension Bridge foundation at the left bank of Daduhe River. In this study, the in situ creep tests were conducted on two model tunnel anchors at a scale of 1:10 near the real working anchor site. Thus, the long-term deformation of the real working tunnel anchors installed at the bridge foundation could be determined from the creep test of model tunnel anchors. The creep tests were conducted under three different loads and lasted for 102.2 h, 167.5 h, and 189.4 h, respectively. The model anchor, the surrounding rock, and their interface were all monitored and measured during the creep testing. In addition, the numerical calculation, in which the Burger creep constitution was used for describing the surrounding rock and the Mohr–Coulomb criterion for describing the concrete anchor, was performed to further evaluate the long-term stability of the real working tunnel anchors. The numerical calculations are in good agreement with the laboratory testing results, and the creep deformations of the anchor and the surrounding rock have the same order of magnitude. The results show that the tunnel anchor and surrounding rock of Xingkang Bridge are in a stable creep state under the three different loads.

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“…for the second class of Burgers models. Since σ (g) sr = a3 b , see [28,Eq. (57)], the wave propagation speed (44) is exactly the wave propagation speed (8) that is obtained in [22] for the constitutive models having fractional differentiation orders not exceeding one.…”

Section: After Inverting Fourier and Laplace Transforms In (35)mentioning

confidence: 99%

“…Functions Φ σ and Φ ε , given by (33) in the case of the first, or by (34) in the case of the second model class, are never zero for Re s > 0. Namely, it is well-known that function Φ ε , except for s = 0, does not have other zeros in the principal Riemann branch arg s ∈ (−π, π) , while for function Φ σ it is proved in [28] that if it has zeros, then they lie in the left complex half-plane.…”

Section: A Justification For Using the Fourier Inversion Formulamentioning

confidence: 99%

“…Considering the interval [0, 1] , the highest fractional differentiation orders of stress and strain are equal, which also holds true for the orders from interval [1,2] . The responses in creep and stress relaxation tests for Models I -VIII are examined in [28]. Recall, creep compliance ε cr (relaxation modulus σ sr ) is the strain (stress) history function obtained as a response to the stress (strain) assumed as the Heaviside step function.…”

Section: Introductionmentioning

confidence: 99%

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Fractional Burgers wave equation

2019

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Thermodynamically consistent fractional Burgers constitutive models for viscoelastic media, divided into two classes according to model behavior in stress relaxation and creep tests near the initial time instant, are coupled with the equation of motion and strain forming the fractional Burgers wave equations. Cauchy problem is solved for both classes of Burgers models using integral transform method and analytical solution is obtained as a convolution of the solution kernels and initial data. The form of solution kernel is found to be dependent on model parameters, while its support properties implied infinite wave propagation speed for the first class and finite for the second class. Spatial profiles corresponding to the initial Dirac delta displacement with zero initial velocity display features which are not expected in wave propagation behavior.

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Fractional Burgers models in creep and stress relaxation tests

Cited by 31 publications

References 26 publications

Effects of moisture content and tillage methods on creep properties of paddy soil

Effects of moisture content and tillage methods on creep properties of paddy soil

In Situ Creep Model Testing for the Tunnel Anchor Foundation of Xingkang Suspension Bridge in Luding of China

Fractional Burgers wave equation

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