Viscoelastic Analysis of Flexible Pavements Embedded with Controlled Low-Strength Material Bases Using Finite Element Method

This paper presents finite element analysis of 4-layered flexible pavements embedded viscoelastic asphalt concrete (AC) top layer and controlled low-strength materials (CLSM) sublayers as well as graded crushed stone subgrades layers. Two-dimensional deformation assumption is employed. Time-dependent stress-strain relations are treated using Laplace transform based on correspondence principle. Collocation method is employed for inversion of Laplace transformed results into time-domain results. A typical layered pavement is analyzed in which relaxation modulus of top viscoelastic asphalt layer is expressed in Prony series. Two kinds of CLSMs, i.e., CLSM-B80/30% and CLSM-B130/30% are compared with graded crushed stones and AC used for base materials. Time-domain responses of vertical displacement, vertical stress and horizontal stress at the bottom of AC layer are compared. The steady state vertical settlements using CLSM bases (B80/30% and B130/30%) are smaller than that using graded crushed stones even considering viscoelastic behavior of asphalt layer and show to be good materials employed as base substitutes for graded crushed stone in flexible pavement design. Introduction Flexible pavements have been widely employed in highway engineering for a long time and recently an effective rapid pavement construction had been achieved by using the controlled low strength materials (CLSM) [1, 2]. CLSM is a kind of flowable fill defined as self-compacting cementitious material that is in a flowable state at the initial period of placement and has a specified compressive strength of 1200 psi or less at 28 days or is defined as excavatable if the compressive strength is 300 psi or less at 28 days [3]. The special features of CLSM include: durable, excavatable, erosion-resistant, self-leveling, rapid curing, flowable around confined spacing, wasting material usage and elimination of compaction labors and equipments, etc. The authors also conducted some preliminary studies on engineering properties of CLSM [4] and the numerical analyses on static and free vibration analysis of CLSM bases in flexible pavements [5, 6]. It is well known that asphalt mixtures have special viscoelastic behavior [7]. Its mechanical response exhibits time and rate dependency. Numerical schemes combined with finite element models and Laplace transform method or time-incremental skills have been applied for flexible pavement analysis [8-10]. This study is aimed at viscoelastic analysis of 4-layered flexible pavements using finite element method. The top layer is considered as Hot Mix Asphalt (HMA) which is modeled as viscoelastic materials; while 4 kinds of base materials are employed, i.e., graded crushed stones, CLSM-B80/30%, CLSM-B130/30% and AC. Comparison study is performed on the comparison of time responses of vertical displacement, vertical stress and horizontal stress located at top of base layer. Finite Element Modeling of 4-Layered Flexible Pavements The calculation of displacements, stresses and strains caused by vehicles loads in pavements is a Advances in Engineering Research (AER), volume 102 214 Second International Conference on Mechanics, Materials and Structural Engineering (ICMMSE 2017) This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). Copyright © 2017, the Authors. Published by Atlantis Press. difficult task. Finite element methods can be employed for multilayered elastic/viscoelastic analysis based on correspondence principle. The stress-strain relationship of a viscoelastic material can be expressed as a form of convolution integrals for stress formulation or strain formulation as t t E d t E t t ∂ ∂ ⊗ = ∂ ∂ • − = ∫ ε τ τ ε τ σ ) ( ) ( ) ( 0 (1a) t t D d t D t t ∂ ∂ ⊗ = ∂ ∂ • − = ∫ σ τ τ σ τ ε ) ( ) ( ) ( 0 (1b) for uniaxial stress state, where E (t) is the relaxation modulus, D(t) is the creep compliance, t is the current time, is a temporal variable starting from the beginning of loading. Taking Laplace transform of Eq. (1) we have ) ( ˆ ) ( ˆ ) ( ˆ s s E s s ε σ • = (2) Thus based on correspondence principle in the theory of linear viscoelaticity we can replace E by ) ( ˆ s E s in FEM for stiffness formulation in the theory of elasticity. ) ( ˆ ) ( ˆ ) ( ˆ s F s X s K = (3) where, ) ( ˆ s X and ) ( ˆ s F are systematic nodal displacement vector and force vector, respectively; and the stiffness matrix in the Laplace transformed domain is expressed as dV B s D B s K T V ] )][ ( ˆ [ ] [ ) ( ˆ ∫ = (4) The calculation of displacements, stresses and strains in Laplace transform domain is the same as for elastic analysis. The relaxation modulus for a viscoelastic material can be expressed as the Prony series