scholarly journals Consolidation of Viscoelastic Soil With Vertical Drains for Continuous Drainage Boundary Conditions Incorporating a Fractional Derivative Model

2021 ◽  
Vol 8 ◽  
Author(s):  
Peishuai Chen ◽  
Jiacheng Li ◽  
Minghua Huang ◽  
Dejie Li
Keyword(s):  
Boundary Conditions ◽  
Fractional Derivative ◽  
Inversion Method ◽  
Numerical Inversion ◽  
Soft Ground ◽  
Large Area ◽  
Vertical Drains ◽  
Fractional Derivative Model ◽  
Continuous Drainage ◽  
Consolidation Settlement

In geotechnical engineering, vertical drainage is the most economical method for accelerating the consolidation of a large area of soft ground. In this study, we analyze the viscoelasticity of the soil and the actual drainage conditions on the top surface of the soil, and then we introduce continuous drainage boundary conditions and adopt a fractional derivative model to describe the viscoelasticity of the soil. With the use of a viscoelasticity model, the governing partial differential equation for vertical drains under continuous drainage boundary conditions is obtained. With the application of the Crump numerical inversion method, the consolidation solution for vertical drains is also obtained. Further, the rationality of the proposed solution is verified by several examples. Moreover, some examples are provided to discuss the influence of interface drainage parameters on the top surface of soil and the viscoelasticity parameters of soil on the consolidation behavior of vertical drains. The proposed method can be applied in the fields of transport engineering to predict the consolidation settlement of a foundation reinforced by vertical drains.

scholarly journals Improved Double-Layer Soil Consolidation Theory and Its Application in Marine Soft Soil Engineering

2019 ◽  
Vol 7 (5) ◽  
pp. 156 ◽  
Author(s):  
Deqiang Chen ◽  
Junhui Luo ◽  
Xianlin Liu ◽  
Decai Mi ◽  
Longwang Xu
Keyword(s):  
Boundary Conditions ◽  
Double Layer ◽  
Soft Soil ◽  
Foundation Engineering ◽  
Soil Consolidation ◽  
Consolidation Theory ◽  
Continuous Drainage ◽  
Consolidation Settlement ◽  
Soil Foundation ◽  
Soft Soil Foundation

Marine soft soil foundation is a double-layer foundation structure with a crust layer and soft substratum. Moreover, it is common that there are various forms of drainage. Accordingly, based on Terzaghi’s consolidation theory and the continuous drainage boundary conditions theory of controllable drainage conditions, an improved double-layer soil consolidation theory considering continuous drainage boundary conditions was proposed. To improve the computational efficiency and accuracy, the Laplace transform and the Stehfest algorithm was used to deduce the numerical solution of the improved double-layer soil consolidation theory considering continuous drainage boundary conditions and to compile a computer program. Subsequently, the theory was validated and analyzed by the degenerated model of the perfectly permeable boundary conditions and the semi-permeable boundary conditions, respectively, which showed that this theory has higher accuracy. Simultaneously, the analysis of double-layer consolidation settlement under continuous drainage boundary conditions for marine soft soil foundation of Guangxi Binhai Highway was carried on. The result showed that the consolidation settlement calculated by the improved double-layer consolidation theory presented is basically consistent with the field measurement results, and that the correlation coefficient between them is higher. Accordingly, the research results can provide useful basic information for marine soft foundation engineering.

scholarly journals Non-Instantaneous Impulsive Boundary Value Problems Containing Caputo Fractional Derivative of a Function with Respect to Another Function and Riemann–Stieltjes Fractional Integral Boundary Conditions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 130
Author(s):  
Suphawat Asawasamrit ◽  
Yasintorn Thadang ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Caputo Fractional Derivative ◽  
Fractional Integral ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Nonlinear Alternative

In the present article we study existence and uniqueness results for a new class of boundary value problems consisting by non-instantaneous impulses and Caputo fractional derivative of a function with respect to another function, supplemented with Riemann–Stieltjes fractional integral boundary conditions. The existence of a unique solution is obtained via Banach’s contraction mapping principle, while an existence result is established by using Leray–Schauder nonlinear alternative. Examples illustrating the main results are also constructed.

scholarly journals Modeling ramp-hold indentation measurements based on Kelvin–Voigt fractional derivative model

2018 ◽  
Vol 29 (3) ◽  
pp. 035701 ◽  
Author(s):  
Hongmei Zhang ◽  
Qing zhe Zhang ◽  
Litao Ruan ◽  
Junbo Duan ◽  
Mingxi Wan ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Fractional Derivative Model

Can a Time Fractional-Derivative Model Capture Scale-Dependent Dispersion in Saturated Soils?

Ground Water ◽  
2017 ◽  
Vol 55 (6) ◽  
pp. 857-870 ◽  
Author(s):  
Rhiannon M. Garrard ◽  
Yong Zhang ◽  
Song Wei ◽  
HongGuang Sun ◽  
Jiazhong Qian
Keyword(s):  
Fractional Derivative ◽  
Saturated Soils ◽  
Fractional Derivative Model ◽  
Time Fractional Derivative

Kelvin-Voigt versus fractional derivative model as constitutive relations for viscoelastic materials

AIAA Journal ◽  
1995 ◽  
Vol 33 (3) ◽  
pp. 547-550 ◽  
Author(s):  
Lloyd B. Eldred ◽  
William P. Baker ◽  
Anthony N. Palazotto
Keyword(s):  
Fractional Derivative ◽  
Constitutive Relations ◽  
Viscoelastic Materials ◽  
Fractional Derivative Model

Fractional BVPs with strong time singularities and the limit properties of their solutions

2014 ◽  
Vol 12 (11) ◽  
Author(s):  
Svatoslav Staněk
Keyword(s):  
Boundary Conditions ◽  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Existence Result ◽  
Continuous Operator ◽  
Nonlinear Alternative ◽  
Time Singularities

AbstractIn the first part, we investigate the singular BVP $$\tfrac{d} {{dt}}^c D^\alpha u + (a/t)^c D^\alpha u = \mathcal{H}u$$, u(0) = A, u(1) = B, c D α u(t)|t=0 = 0, where $$\mathcal{H}$$ is a continuous operator, α ∈ (0, 1) and a < 0. Here, c D denotes the Caputo fractional derivative. The existence result is proved by the Leray-Schauder nonlinear alternative. The second part establishes the relations between solutions of the sequence of problems $$\tfrac{d} {{dt}}^c D^{\alpha _n } u + (a/t)^c D^{\alpha _n } u = f(t,u,^c D^{\beta _n } u)$$, u(0) = A, u(1) = B, $$\left. {^c D^{\alpha _n } u(t)} \right|_{t = 0} = 0$$ where a < 0, 0 < β n ≤ α n < 1, limn→∞ β n = 1, and solutions of u″+(a/t)u′ = f(t, u, u′) satisfying the boundary conditions u(0) = A, u(1) = B, u′(0) = 0.

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