Finite element analysis of controlled low strength materials

Abstract

Controlled low strength materials (CLSM) are flowable and self-compacting construction materials that have been used in a wide variety of applications. This paper describes the numerical modeling of CLSM fills with finite element method under compression loading and the bond performance of CLSM and steel rebar under pullout loading. The study was conducted using a plastic-damage model which captures the material behavior using both classical theory of elasto-plasticity and continuum damage mechanics. The capability of the finite element approach for the analysis of CLSM fills was assessed by a comparison with the experimental results from a laboratory compression test on CLSM cylinders and pullout tests. The analysis shows that the behavior of a CLSM fill while subject to a failure compression load or pullout tension load can be simulated in a reasonably accurate manner.

Keywords

CLSM / finite element method / compressive strength / pullout / numerical modeling / plastic damage model

Introduction

Controlled low strength material (CLSM) is defined by the ACI 229R [¹] as a flowable self-compacting cementitious material that has a specified 28-day compressive strength of 8.3 MPa (1200 psi) or less. CLSM is a mixture of soil or aggregate, cement, fly ash, water, and sometimes chemical admixtures. CLSM, also known as flowable fill, can be used as a replacement for compacted backfill and is defined as excavatable if the 28-day compressive strength is 2.1 MPa (300 psi) or less.

Compared with conventional earth fill materials that require controlled compaction in layers, CLSM has several inherent advantages for use in construction, including: ease of mixing and placement, ability to flow into hard-to-reach places, self-leveling characteristics, rapid curing, incompressibility after curing, which reduce equipment needs, labor costs, and associated inspections [²]. Moreover, the CLSM makes use of environment-friendly materials, such as fly ash or foundry sand, within its mixture, thereby reducing the demands on landfills where these materials might otherwise be deposited [³,⁴]. CLSM is a multipurpose construction material that has been used in a wide variety of applications that are well documented in the literature. Among the many applications of CLSM, the following are the most important [¹]: backfill for building excavations, utility trench, and retaining walls; structural fill for footings, road bases, and utility bedding; and void-filling for underground structures. A survey by Trejo et al. [⁴] indicated that 42 out of 44 state DOTs have specifications to use CLSM as a construction material.

Research studies in CLSM have mostly been focused on the use of various industrial by-products and waste materials as major or supplementary constituents of the mixture [⁵]. Very little research has been done to investigate the feasibility of using numerical modeling to study the behavior of CLSM in different applications. Schmitz et al. [⁶] conducted finite element analyses to determine the lateral pressures generated by CLSM on retaining walls. Blanco et al. [⁷] employed finite element method to simulate and define the mechanical requirements of CLSM for the backfill of a narrow trench.

This paper describes the finite element analyses performed to evaluate the following: failure behavior of CLSM fills under compression loading, bond performance of the CLSM, and steel rebar under pullout loading. Concrete structures often undergo extensive cracking before failure. Many theories and computational approaches are available in the literature to simulate fracture with meshfree and finite element methods [⁸–¹⁵]. More advanced numerical investigations on evolving cracks in quasi-brittle materials can be found in Refs. [¹⁶–²¹]. However, in this study the objective is to illustrate the general failure patterns under compression and pullout tension loads. The study utilizes the analytical framework of a plastic damage model in Abaqus [²²] in which the compressive and tensile behavior of the material must be specified by strain softening and damage evolution functions. The capability of the finite element approach for the analysis of CLSM fills was assessed by a comparison with the experimental results from a laboratory compression test on CLSM cylinders and pullout tests. The objective is to present a rational procedure, via the finite element method, to simulate the behavior of CLSM fills for different applications.

Experimental testing

Compression tests

Compressive strength is the main important design parameter for many CLSM applications. Cylindrical specimens were prepared and tested following the instructions on ASTM D 4832 [²³]. The selected CLSM fill for this study with the ingredients listed in Table 1 had a compressive strength of 206 kPa. Load-controlled unconfined compressive strength test was employed using a relatively low-load capacity computerized testing machine at a constant rate to attain the stress-strain behavior of the CLSM. The typical setup for the compression test is shown in Fig. 1. Similar to concrete, there were two main modes of failure commonly observed in the testing of CLSM cylinders, shear band failure and conical type shear failure, see Fig. 1.

Pullout test

CLSM is much lower in strength than concrete and so its bond performance to steel rebar is identified as a critical area of concern for CLSM applications. The bond strength was evaluated by a pullout test using a wooden box of 0.61 m × 0.61 m × 0.91 m divided into four equal partitions. Four rebars, 12.7 mm diameter with the embedment length of 0.91 m, were placed and secured in the center of each partition (Fig. 2), the box was then filled with the same CLSM fill with compressive strength of 206 kPa. As shown in Fig. 2, a simple frame was made over the box to set up the loading device and instrumentations. After curing, the tension load was applied gradually to each rebar and the slip was measured.

Finite element modeling of compression test on CLSM cylinders

Behavior of the CLSM is similar to that of other quasi-brittle materials such as concrete, rock, and ceramics, and therefore, a material model developed for quasi-brittle materials is considered. Besides, the model input parameters must be obtainable from uniaxial test experiments. Based on these requirements, the Concrete Damaged Plasticity model proposed by Lubliner et al. [²⁴] and extended by Lee and Fenves [²⁵] has been chosen for the present study. Modeling of the material behavior has been performed with the finite element software Abaqus [²²] where an implementation of the proposed plastic damage model is available.

In the plastic damage model, stiffness degradation due to the damage is embedded in the plasticity part of the model. An independent scalar (isotropic) damage variable d is used to describe the irreversible damage that occurs during the fracturing process. The initial undamaged state and total loss in strength of the material are indicated by d = 0 and d = 1, respectively. Any intermediate value indicates a partially damaged state. The material parameters required for the model are categorized into three types, namely elasticity, plasticity, and damage. In the elastic zone, from the experimental stress-strain response, Young’s modulus of 22.6 MPa and yield stress of 134.3 kPa were determined and Poisson’s ratio was assumed to be 0.19. Four parameters, {{\displaystyle \sigma }}_{\mathrm{b}\mathrm{0}}/{{\displaystyle \sigma }}_{\mathrm{c}\mathrm{0}}, K_c, y, and ε, are required to define the yield surface and flow potential function of the plasticity part.

The yield surface for this model as proposed by Lubliner et al. [²⁴] is based on modifications of the classical Mohr-Coulomb plasticity (Fig. 3(a)):

F={\displaystyle \frac{\mathrm{1}}{\mathrm{1}-\alpha }}\left(\overline{q}-\mathrm{3}\alpha \overline{p}+\beta \left({\tilde{\epsilon }}^{\mathrm{p}\mathrm{l}}\right)\langle {{\displaystyle \widehat{\overline{\sigma }}}}_{\max }\rangle -\gamma \langle -{{\displaystyle \widehat{\overline{\sigma }}}}_{\max }\rangle \right)-{{\displaystyle \overline{\sigma }}}_c\left({{\displaystyle \tilde{\epsilon }}}_{\mathrm{c}}^{\mathrm{p}\mathrm{l}}\right)，

with

\alpha ={\displaystyle \frac{({{\displaystyle \sigma }}_{\mathrm{b}\mathrm{0}}/{{\displaystyle \sigma }}_{\mathrm{c}\mathrm{0}})-\mathrm{1}}{\mathrm{2}({{\displaystyle \sigma }}_{\mathrm{b}\mathrm{0}}/{{\displaystyle \sigma }}_{\mathrm{c}\mathrm{0}})-\mathrm{1}}}，\beta ={\displaystyle \frac{{{\displaystyle \overline{\sigma }}}_{\mathrm{c}}\left({{\displaystyle \tilde{\epsilon }}}_{\mathrm{c}}^{\mathrm{p}\mathrm{l}}\right)}{{{\displaystyle \overline{\sigma }}}_{\mathrm{t}}\left({{\displaystyle \tilde{\epsilon }}}_{\mathrm{t}}^{\mathrm{p}\mathrm{l}}\right)}}(\mathrm{1}-\alpha )-(\mathrm{1}+\alpha )，\gamma ={\displaystyle \frac{\mathrm{3}(\mathrm{1}-{{\displaystyle K}}_{\mathrm{c}})}{\mathrm{2}{{\displaystyle K}}_{\mathrm{c}}-\mathrm{1}}，}

where {{\displaystyle \widehat{\overline{\sigma }}}}_{\max } is maximum principal stress, {{\displaystyle \overline{\sigma }}}_{\mathrm{c}} is uniaxial compressive stress, {{\displaystyle \overline{\sigma }}}_{\mathrm{t}} is uniaxial tensile stress, \bar{p} is effective hydrostatic pressure, \bar{q} is equivalent effective deviatoric stress, {\tilde{\epsilon }}^{\mathrm{p}\mathrm{l}} is equivalent plastic strain. {{\displaystyle \sigma }}_{\mathrm{b}\mathrm{0}}/{{\displaystyle \sigma }}_{\mathrm{c}\mathrm{0}} is the ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress (the typical value is 1.16); K_c is the ratio of the second stress invariant on the tensile meridian to that on the compressive meridian (the typical value is 2/3) [²²].

Assumption of the non-associated flow rule in the plastic damage model requires a separate flow potential to determine the direction of plastic flow. The flow potential G accepted for this model is the Drucker-Prager hyperbolic function:

G=\sqrt{{(ϵ{{\displaystyle \sigma }}_{\mathrm{t}\mathrm{0}}\tan \psi )}^{\mathrm{2}}+{{\displaystyle \overline{q}}}^{\mathrm{2}}}-\overline{p}\tan \psi

where y is the dilation angle measured in the p-q plane and it controls the orientation of the flow potential function G, see Fig. 3(b). It is not possible to obtain y directly from the results of the experiments. It was set to 35° by applying the inverse modeling approach in comparing the simulated and the experimentally measured stress-strain curves [²⁶]. s_t0 is the uniaxial tensile stress at failure, taken from the user-specified tension stiffening data; and ϵ is the eccentricity of the flow potential, that defines the rate at which the function approaches the asymptote (the flow potential tends to a straight line as the eccentricity tends to zero) (the default value is 0.1), see Fig. 3(b). Parameters \overline{p} and \bar{q} are hydrostatic pressure and von Mises equivalent stress, respectively. The details of the mathematical formulation of the plastic damage model are given in the Abaqus theory and analysis manual [²²].

For plasticity and damage, the compressive and tensile behavior of the material must be specified by strain softening and damage evolution functions. The strain softening curve is provided by tabular data in the material model in the form of yield stress as a function of inelastic strain. The inelastic strain is identified by subtracting the elastic strain corresponding to the undamaged material from the total strain. The damage evolution curve is given as damage parameter d and the corresponding inelastic strain at certain points in the softening zone of the experimental stress-strain curve. The corresponding damage parameter d is determined from the varying slope (E) and the initial stiffness (E₀) as d= 1 – E/E₀. Accordingly, the material parameters for the strain softening and damage evolution response of the specified CLSM was determined from the experimental compression tests and summarized in Table 2. Tensile behavior of the CLSM was defined by a linear strain softening function which was estimated from the compressive strength. In general, the ratio of the direct tensile strength to compressive strength ranges from about 0.07 to 0.11 [²⁷].

A three dimensional solid finite element model was employed to simulate the CLSM cylinders under unconfined compressive loading. The cylinders were modeled by 8-node linear brick with reduced integration hourglass control elements (C3D8R). To simulate different modes of failure, different boundary conditions were applied to the CLSM cylinders. Figures 4–5 shows the distribution of the stiffness degradation (damage) variable d at maximum compressive stress and at failure. This distribution is similar to the modes of failure frequently observed in the testing of CLSM cylinders.

As illustrated in Fig. 4, cylinders with fixed ends (laterally constrained ends) exhibit a symmetric conical type shear failure mode at the center of the cylinder. To stimulate the unsymmetrical shear failure, one end was set free for lateral displacements, see Fig. 5. Capped end conditions were also analyzed to determine the effect of frictional lateral end constraints on cylinder’s failure response. Two caps with solid elements were modeled to contact the two ends of the cylinder with friction coefficient of 0.3. As a result of the simulation, the CLSM cylinder fails with unsymmetrical shear bands, see Fig. 5(c). It was observed that the location of the shear band changes with the change of the friction between pads and the cylinder.

The simulation results and effect of mesh size and dilation angle on the stress-strain behavior are presented and compared with the experimental results in Fig. 6. As shown in Fig. 6, the proposed model can capture the peak stress and the softening branch of the axial stress-strain curve in an acceptable accuracy. Due to the fracture energy criterion of Hillerborg et al. [²⁸] in the plastic damage model [²²], the effect of mesh size on the simulated stress-strain behavior is negligible. The dilation angle of 35° shows quite good agreement with the experiment. It can be concluded that the plastic-damage model with the identified material parameters is capable of simulating the stress-strain response and visualizing the failure of a CLSM fill.

Finite element modeling of pullout tests

A three dimensional finite element discrete model was employed to simulate the pullout tests and assess the bond strength. The finite element analysis software Abaqus [²²] was used for the analysis. The same plastic damage model and material properties described before were used to model the CLSM. Geometry and boundary conditions used in the finite element simulation were consistent with the pullout test in Fig. 2. Both the CLSM fill and steel rebar were modeled by 8-node linear brick with reduced integration elements (C3D8R). Very fine mesh was used in the vicinity of the interaction and is coarsened toward the outer surface boundary in order to reduce the computational time. A portion of the mesh adopted for the zone of steel bar-CLSM interaction is shown in Fig. 7.

A surface-based cohesive contact behavior with damage was used to simulate the bonding of steel and CLSM, which is considered an efficient and simple methodology to represent the interfacial deterioration. The theory of the contact behavior is based on the traction-separation law for surfaces. This theory describes the interfacial contact with an initial linear elastic behavior until the achievement of the maximum bond stress (interfacial shear strength, t_max) and then a decreasing branch (here is considered exponential function) which reproduce the progressive degradation of the interface stiffness after the strength peak, as described by Fig. 8. The slope of elastic portion before the shear strength is referred to as interface stiffness. The details of the mathematical formulation for the surface-based cohesive contact model are given in the Abaqus theory and analysis manual [²²]. For the pullout test, purely shear cohesive contact (along the direction of the pullout load) was considered. Based on the experimental bond strength-slip response for the specified CLSM, interface shear stiffness and shear strength was determined as 0.35 N/mm³ and 0.45 MPa, respectively.

Frictional resistance was not considered in the model assuming that its effect was implicitly present in the horizontal shear property of the cohesive contact due to the fact that it was derived directly from the pullout test. The normal interaction was modeled using the Hard Contact option [²²] which minimizes penetration of the steel elements into the surrounding CLSM at the contact interface. In a displacement control mode, a prescribed displacement imposed at the free end of the rebar, applied in the pullout direction, which generated a force used to pull the rebar for a certain distance. The load was applied in small increments to overcome numerical instability difficulties that can occur when a large load is applied suddenly. Quasi-static response was obtained using Abaqus/Explicit module software. The explicit dynamic solution procedure was chosen because it is most accurate in applications where brittle behavior dominates. As a result of the simulation, damage of the surrounding CLSM matrix due to the contact interaction with the steel rebar at maximum bond stress is presented in Fig. 9. Damage in the matrix during pullout process is not distributed uniformly through the whole length of the matrix, but tends to be localized at some regions.

Accuracy of the simulation was assessed by comparison with the measurements obtained in the pullout test. As shown in Fig. 10, the numerical result is in good agreement with the experiment and therefore the adapted cohesive bond model can effectively simulate the bond behavior of CLSM and steel and reproduce the pullout force.

To determine the effects of bar size on the bond strength, results of numerical pullout tests for bar sizes ranging from Nos. 4 to 10 (bar diameters ranging from 12.7 to 32 mm) are compared in Fig. 10. Numerical results indicate that the bond capacity decreases slightly with increasing bar size because the rebar has less CLSM cover due to the larger diameter. The bond capacity of the model with No. 10 bar is 83% of that of the model with No. 4 bar.

Conclusions

In this paper, a numerical study was performed to simulate the failure behavior of CLSM fills under compression loading, and the bond performance of the CLSM and steel rebar under pullout loading.

The behavior of the CLSM was modeled using a plastic-damage model which captures the material behavior using both classical theory of elasto-plasticity and continuum damage mechanics. The finite element modeling of the standard compression tests demonstrated the capability of the material model for a realistic prediction of the failure patterns in the CLSM cylinders and stress-strain response.

Bond performance was studied with the experimental pullout tests and simulated using the finite element method. The bonding between steel and CLSM was modeled using a surface-based cohesive contact behavior with damage. The numerical result was in good agreement with the experimental data. Numerical simulation of pullout tests indicated that the bond capacity of CLSM decreases slightly with increasing bar size.

References

[1] ACI 229R. Controlled Low-Strength Materials. Farmington Hills, MI: American Concrete Institute, 2013

[2] Alizadeh V. The sustainable application of fly ash in bridge abutments. Geo-Chicago 2016: Sustainable Materials and Resource Conservation, Geotechnical Special Publication (GSP), 2016, 272: 159–166

[3] Najafi F T, Tia M. Use of accelerated flowable fill in pavement section. Final Report-Vol. 1. 2004

[4] Trejo D, Folliard K J, Du L. Sustainable development using controlled low-strength material. In: Proceedings of International Workshop on Sustainable Development and Concrete Technology, 2004, 231–250

[5] Sheen Y N, Huang L J, Wang H Y, Le D H. Experimental study and strength formulation of soil-based controlled low-strength material containing stainless steel reducing slag. Construction & Building Materials, 2014, 54: 1–9

[6] Schmitz M E, Parsons R L, Ramirez G, Zhao Y. Use of controlled low-strength material as abutment backfill. Report No. K-TRAN: KU-02–6. 2004

[7] Blanco A, Pujadas P, Cavalaro S, Aguado A. Methodology for the design of controlled low-strength materials application to the backfill of narrow trenches. Construction & Building Materials, 2014, 72: 23–30

[8] Amiri F, Anitescu C, Arroyo M, Bordas S P A, Rabczuk T. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics, 2014, 53(1): 45–57

[9] Areias P, Rabczuk T, Camanho P P. Finite strain fracture of 2D problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics, 2014, 72: 50–63

[10] Rabczuk T, Akkermann J, Eibl J. A numerical model for reinforced concrete structures. International Journal of Solids and Structures, 2005, 42(5–6): 1327–1354

[11] Rabczuk T, Belytschko T. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799

[12] Rabczuk T, Belytschko T. Application of particle methods to static fracture of reinforced concrete structures. International Journal of Fracture, 2006, 137(1–4): 19–49

[13] Rabczuk T, Belytschko T. Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343

[14] Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455

[15] Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures. Engineering Fracture Mechanics, 2008, 75(16): 4740–4758

[16] Areias P, Msekh M A, Rabczuk T. Damage and fracture algorithm using the screened Poisson equation and local remeshing. Engineering Fracture Mechanics, 2016, 158: 116–143

[17] Areias P, Rabczuk T, Dias-da-Costa D. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 2013, 110: 113–137

[18] Areias P, Rabczuk T. Steiner-point free edge cutting of tetrahedral meshes with applications in fracture. Finite Elements in Analysis and Design, 2017, 132: 27–41

[19] Ghorashi S Sh, Valizadeh N, Mohammadi S, Rabczuk T. T-spline based XIGA for fracture analysis of orthotropic media. Computers & Structures, 2015, 147: 138–146

[20] Ren H, Zhuang X, Cai Y, Rabczuk T. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476

[21] Ren H, Zhuang X, Rabczuk T. Dual-horizon peridynamics: A stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 762–782

[22] Abaqus analysis user’s manual. Dassault Systèmes, Version 6.14, 2014

[23] ASTM D4832. Standard Test Method for Preparation and Testing of Controlled Low Strength Material (CLSM) Test Cylinders. West Conshohocken, PA: American Society for Testing and Materials, 2010

[24] Lubliner J, Oliver J, Oller S, Oñate E. A plastic-damage model for concrete. International Journal of Solids and Structures, 1989, 25(3): 299–326

[25] Lee J, Fenves G. Plastic-damage model for cyclic loading of concrete structures. Journal of Engineering Mechanics, 1998, 124(8): 892–900

[26] Jankowiak T, Tomasz L. Identification of parameters of concrete damaged plasticity constitutive model. Foundations of Civil and Environmental Engineering, 2005, 6: 53–69

[27] Mindess S, Young J F, Darwin D. Concrete. Upper Saddle River, NJ: Pearson Education Inc., 2003

[28] Hillerborg A, Modéer M, Petersson P E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research, 1976, 6(6): 773–781

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature