Experimental and Numerical Studies on the In-Plane Shear Behavior of PVC-Encased Concrete Walls

Abstract

The effective application of lightweight stay-in-place concrete forms for casting shear walls subjected to wind and seismic loading is of particular concern to practitioners. Insufficient technical data available for new kinds of wall systems, such as Polyvinyl Chloride (PVC) form walls, hinder their implementation in construction practice. To that end, an effective experimental and numerical campaign was launched at Western Sydney University to investigate the structural performance of PVC form walls when subjected to in-plane shear loading. A set of push-out specimens was designated to conduct monotonic in-plane shear tests until failure. All failure phenomena, capping strengths, and ductility capacities were monitored. Test results indicated that the embedded PVC latticed webs could efficiently protect the concrete web from sudden crushing and improve ductility capacity and failure pattern of the specimens. Nonlinear finite element analysis on test specimens was also conducted and good correlation with experiment results was achieved.

1 Introduction

The common construction technique of stay-in-place (SIP) concrete forms delivers low installation costs and high speed of construction. A novel SIP form, cast with high-strength fabrics, was developed by Li and Yin [1] and its composite action with inner concrete was studied. Both finite element (FE) analyses and experimental lab works were conducted by various researchers to explore the performance of SIP encasements under mechanical and thermal loading conditions [2,3,4]. The application of cold-formed sections in the off-site manufacturing of SIP forms was studied by Wu et al. [5]. The so-called Insulated Concrete Forms (ICF) were extensively employed to cast either squat or slender walls and their structural composite action with the concrete core were mostly studied under monotonic and cyclic loading regimes [6,7,8,9,10]. A novel stackable Polyvinyl Chloride (PVC) SIP form was introduced to cast concrete walls even with complex geometries [11,12,13], as shown in Fig. 1. As the PVC form engages with the inner concrete, the new design represents a departure from traditional solid concrete core in responding to in-plane shear loads. Therefore, the in-plane shear behavior of PVC form walls needs to be explored through experimental and numerical studies. In this paper, we present in-plane shear behavior of PVC form walls using experimental tests on push-out specimens as well as FE analysis.

Fig. 1

Geometry of PVC form

2 Methods and Results

2.1 Test Outline

A total of three PVC form wall push-out specimens were tested to failure to acquire a better understanding of the in-plane shear capacity and ductility with the influence of PVC encasement. Further, one push-out wall specimen was cast using the traditional form to be enabled for direct comparison with PVC form walls. The geometry of specimens along with the test parameters are, respectively, shown in Fig. 2 and in Table 1. These tests were performed to investigate the effects of vertical and horizontal reinforcement ratio, wall thickness, and the PVC encasement. Constants were concrete compressive strength and steel yield stress. Concrete compressive strength and steel tensile yield stress were, respectively, 40 and 550 MPa. A 10,000 kN servo hydraulic machine was employed to apply vertical force parallel to the shear surface. Figure 3 Shows photographs of PVC and traditional form walls secured in the testing rig. Linear Potentiometers (LPs) were employed to measure vertical displacement that occurred along the shear plane. The location of LPs at the top and bottom face of specimens is shown in Fig. 4.

Fig. 2

Geometry of specimens

Table 1 Push-out test specimens

Fig. 3

Specimens in testing rig

Fig. 4

Instrumentation of specimens

2.2 Test Results

Qualitative observations of the response of PVC form specimens were recorded during the tests. Most of the observations were visual including crack initiation, growth, and propagation, as well as excessive deformation through PVC encasements. Figure 5 shows the failure shapes of PVC form and traditional form concrete specimens. In Fig. 5a, it is identified while the slip occurred due to concrete failure along shear plane, the excessive deflection in PVC encasement took place due to outward dilatation of concrete. As seen in Fig. 5b, the concrete crushing near the bottom corner close to the shear plane is mostly attributed to substantial slip along the shear plane. In Fig. 5c, inclined shear cracking near the shear plane as well as crushing and spalling of the concrete is associated with failure at shear plane. More specifically, this failure occurred abruptly accompanied with explosive sound. Figure 6 depicts force-slip relationships pertinent to different specimens. As seen, specimens cast with PVC forms demonstrate substantially high ductility compared to one cast with the traditional form. The major reason is the confining action of PVC encasement to protect concrete core against dominating premature spalling off. Further, the higher in-plane shear strength of the traditional form specimen is attributed to the thickness and amount of vertical and horizontal reinforcement.

Fig. 5

Phenomena of failure a excessive deformation of PVC encasement in a PVC form specimen b concrete crushing at the bottom face in a PVC form specimen c diagonal concrete crushing in traditional form specimen

Fig. 6

Force-slip behavior of different specimens

2.3 FE Simulation

In this study, the Abaqus program [14] was employed for FE analyses. The proper selection of constitutive material model played an important role in verifying FE models against experiments. Three built-in material models including Concrete Damaged Plasticity (CDP), Crushable Foam (CF) [20], and J₂ Plasticity were used, respectively, to model concrete, PVC encasement, and horizontal/vertical reinforcements. The ascending and descending branches of uniaxial stress–strain curves in compression pertinent to CDP model were assumed as follows [15]:

$$\begin{aligned} \sigma _{c} = & \left( {1 - H\left[ {\left| {\varepsilon _{c} } \right| - \left| {\varepsilon _{{c1}} } \right|} \right]} \right)\frac{{\kappa .\eta - \eta ^{2} }}{{1 + \left( {\kappa - 2} \right).\eta }}f_{{cm}} \\ & + H\left[ {\left| {\varepsilon _{c} } \right| - \left| {\varepsilon _{{c1}} } \right|} \right]\left[ {\frac{{2 + \gamma _{c} f_{{cm}} \varepsilon _{{c1}} }}{{2f_{{cm}} }} + \gamma _{c} \varepsilon _{c} + \frac{{\gamma _{c} \varepsilon _{c}^{2} }}{{2\varepsilon _{{c1}} }}} \right]^{{ - 1}} \\ \end{aligned}$$

(1)

where

$\sigma_{c}$ = compression stress in (MPa)

$\varepsilon_{c}$ = compression strain

$$\eta = \varepsilon_{c} /\varepsilon_{c1}$$

$$\kappa = E_{ci} /E_{c1}$$

$\gamma_{c}$ = constant crushing energy [16]

$$\gamma_{c} = \frac{{\pi^{2} f_{cm} \varepsilon_{c1} }}{{2\left[ {g_{cl}^{*} - \frac{1}{2}f_{cm} \left( {\varepsilon_{c1} \left( {1 - \beta_{c} } \right) + \beta_{c} \frac{{f_{cm} }}{{E_{c} }}} \right)} \right]}}$$

$g_{cl}^{*}$ = volume specific localised crushing energy

$\varepsilon_{c1}$ = strain at maximum compressive stress

$E_{ci}$ = tangent modulus = $10^{4} f_{cm}^{1/3}$ in (MPa)

$f_{cm}$ = characteristic compressive strength

$E_{c1}$ = secant modulus from the origin to the peak compressive stress

$H$ = Heaviside function

The concrete stress–strain relation in uniaxial tension consisted of a linear phase up to tensile strength, followed by a nonlinear strain softening phase that depended on the specimen geometry. The stress-crack opening relation can be expressed as [17, 18]

$$\begin{aligned} \sigma _{{ct}} \left( w \right) = & \left\{ {\left[ {1 + \left( {\frac{{c_{1} w}}{{w_{c} }}} \right)^{3} } \right]\exp \left( { - \frac{{c_{2} w}}{{w_{c} }}} \right) - \frac{w}{{w_{c} }}\left( {1 + c_{1} ^{3} } \right)\exp \left( { - c_{2} } \right)} \right\}{\text{~}}f_{{ctm}} {\text{~~~}} \\ & c_{1} = 3,{\text{~~}}c_{2} = 6.93 \\ \end{aligned}$$

(2)

where

$\sigma_{ct}$ = tensile stress in (MPa)

$w = l_{t} \varepsilon_{ct}^{ck} = l_{t} \left( {\varepsilon_{ct} - \sigma_{ct} /E_{ci} } \right)$ = crack opening in (mm)

$w_{c} = 5G_{F} /f_{ctm}$ = crack opening when $\sigma_{ct} = 0$ in (mm)

$G_{F} = 0.073f_{cm}^{0.18}$ = fracture energy in (N/mm)

$f_{ctm} = 0.3f_{cm}^{2/3}$ = tensile strength in (MPa)

$\varepsilon_{ct}$ = tensile strain

$l_{t}$ = characteristic length in FE modelling

$\varepsilon_{ct}^{ck}$ = cracking strain

List of parameters used for CDP model calibration was presented in [19]. To capture nonlinear behavior of the PVC encasement, parameters of the CF model were calibrated against test results as reported in [11]. To establish yield surface for J₂ Plasticity constitutive law, steel Young’s modulus, Poisson’s ratio, yield stress, ultimate stress, and ultimate strain was, respectively, assumed as 200 GPa, 0.3, 550 MPa, 650 MPa, and 0.05. Figure 7 shows the comparison between failure phenomena obtained from the experiment and FE simulations. The equivalent plastic strain was chosen from FE analysis to represent localization of damage. As seen, the FE simulation reasonably replicates the failure modes triggered and evolved across the PVC encasement and concrete core. As shown in Fig. 8, there is a good correlation between experimental results and those obtained from FE analysis.

Fig. 7

a A photo of excessive deformation on PVC encasement b localized plastic deformation on PVC encasement obtained from the FE c a phot of concrete crushing at the bottom end d damage evolution at the bottom end obtained from FE

Fig. 8

Comparison between FE and test results

3 Conclusion

Push-out experimental lab tests were conducted to explore in-plane shear capacity of PVC form concrete walls under monotonic loading. Further, a numerical FE model was established to predict the shear behavior of the walls. Experimental observations revealed gentler failure phenomena for PVC form walls compared to the one cast using the traditional form. It was also concluded that PVC encasement provided confinement pressure against concrete outward dilation and therefore enhanced ductility capacity was observed. Further, the established FE model showed correlative results with those obtained from experiments.