# Behaviour of Lightweight Concrete Wall Panel under Axial Loading: Experimental and Numerical Investigation toward Sustainability in Construction Industry

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

#### 1.1. Sustainable Aspect of Agricultural Waste

#### 1.2. Research on OPS Concrete

#### 1.3. Concrete Wall Subjected to Axial Loading

#### 1.4. Design Guide and Research of Concrete Wall

#### 1.5. Research Significance

#### 1.6. Objective

## 2. Experimental Program

#### 2.1. Materials

#### 2.2. Wall Specimens

#### 2.3. Experimental Setup and Instrumentation

## 3. Finite Element Model

#### 3.1. Material Model of Concrete

^{3}. The ${\beta}_{1}$ parameters of ascending and descending branches are determined from Equations (6) and (7), respectively. The comparison of stress-strain curves determined from the experimental test and the empirical model is shown in Figure 5a. The curve computed from the empirical model is close to the experimental. This confirmed that the empirical model is able to capture the actual stress-strain behavior of OPS based lightweight self-compacting concrete. Thus, this empirical stress-strain model was used for the parametric study of wall with varying compressive strength and elastic modulus. For the compressive stress strain input in CDP, the total strains of the raw stress-strain curve are converted into inelastic strain [58] by using Equation (9), and these are shown in Figure 5a. In addition, the compression damage parameters [58] are determined by using Equation (10). Five parameters comprising dilation angle, eccentricity, ${\sigma}_{b0}/{\sigma}_{c0}$ ratio, K

_{c}, and viscosity are required to be inputted in the CDP model. The parameters used are summarized in Table 5.

#### 3.2. Material Model of Steel

#### 3.3. Model Description

#### 3.4. Summary

## 4. Results and Discussion

#### 4.1. Experimental Results and Analysis

#### 4.1.1. Failure Mode

#### 4.1.2. Load Deflection

#### 4.1.3. Deflection Corresponding to Ultimate Failure Load

#### 4.1.4. Ultimate Failure Load

_{cal}/P

_{exp}ratio of the ACI equation varies from 0.38 to 0.58. The underestimation of the ACI equation is mainly due to the assumption made by the ACI equation that loading is applied within the eccentricity of t/6. The experiments in this research were carried out with concentric loading. Therefore, the underestimation made by the ACI equation proves that it is not suitable to determine the ultimate load of concrete wall with other eccentricities. As for the AS 3600 design equation, the P

_{cal}/P

_{exp}ratio varies from 0.46 to 0.61. The ultimate strength of concrete wall loaded at different values of eccentricity can be determined by the AS 3600 equation. However, this equation still underestimates the ultimate strength of lightweight wall without reduction factor, as shown in this research. The comparisons of experimental and calculated results have highlighted that the AS 3600 equation has the limitation in which the equation is conservative, and no parameter is allowed for lightweight concrete wall. Among the design equations from the three standards, Eurocode 2 gives load estimation with the best accuracy. The P

_{cal}/P

_{exp}ratio varies from 0.91 to 0.66. However, the Eurocode 2 equation becomes less accurate when the slenderness ratio is increased. Nevertheless, this design equation takes into consideration parameters similar to AS 3600 but appears to show better results accuracy when compared to AS 3600. Unfortunately, similar to the other three standards, Eurocode 2 does not have a parameter to consider the effect of the material property of lightweight concrete.

#### 4.2. Effect of Specimen Size

#### 4.3. FEA Model Validation

_{FEA}/P

_{exp}ratio for the purpose of comparison. The comparison indicates that the P

_{FEA}/P

_{exp}ratios ranged from 1.03 to 1.05 for the experimental results of this study. The P

_{FEA}/P

_{exp}ratios of the benchmarked model [28,43] ranged from 0.9 to 1.12. Overall, P

_{FEA}/P

_{exp}ratio has mean value of 1.04 and standard deviation of 0.06. The comparison of results shows that the predicted ultimate axial capacity of FEA model is satisfactory, albeit with a slight overestimation. The slight discrepancies of FEA results are mainly due to the idealistic nature of the FEA model, including materials and boundary conditions [63]. The CDP model gives a more accurate prediction of the ultimate axial capacity of lightweight concrete wall compared to the results calculated using design equations of various design standards.

## 5. FEA Parametric Study

#### 5.1. Effect of Slenderness Ratio

#### 5.2. Effect of Eccentricity

#### 5.3. Effect of Compressive Strength

#### 5.4. Effect of Elastic Modulus

^{3}, and the FEA results are illustrated in Figure 11. The range of density studied has been chosen with consideration of the common density of OPS-based lightweight concrete [10] and encompasses lightweight, semi-lightweight, as well as normal-weight concrete. Decrease in elastic modulus with a constant low eccentricity and a low slenderness ratio results in a decrease in both ultimate axial capacity and axial strength ratio. It is noted that the P

_{fea}/P

_{2400}ratio decreases as the concrete elastic modulus decreases. At eccentricity of t/20 and slenderness ratio 23, by decreasing the elastic modulus from 18,713 to 10186 MPa, the axial strength decreases by 7%. The effect of elastic modulus reduction on axial capacity is more pronounced with increase of slenderness ratio. At eccentricity of t/20 and slenderness ratio of 50, the decrease in elastic modulus has resulted in 39% strength reduction. For higher values of eccentricity and a constant slenderness ratio, the axial capacity of the wall also decreases with a decrease in elastic modulus. For example, at a slenderness ratio of 23, when elastic modulus decreases from 18,713 to 10,186 MPa, the axial capacity decreases by 7%, 8%, and 13% for eccentricities of t/20, t/12, and t/6, respectively.

## 6. Proposed Design Equation

- The wall must contain minimum reinforcement in both vertical and horizontal directions as specified by the AS3600 standard;
- The loads are within the stress block of the section;
- The wall behaves as one-way wall under axial loading.

_{ua}/P

_{us2}values derived from the FEA results and Equation (21) are plotted against E, as shown in Figure 13f. The E variable is also represented by a power function raised to a fixed power of 0.48. This factor is calibrated from the results of the FE model by using regression analysis. The final design equation is depicted as Equation (22).

#### Equation Validation

_{cal}/P

_{exp}ratio of this study ranged from 0.88 to 1, while the P

_{cal}/P

_{exp}ratio from the published literature ranged from 0.8 to 1.14. The calculated results from the proposed equation are slightly conservative in predicting the axial strength of the lightweight concrete wall with all P

_{cal}/P

_{exp}ratios of less than 1. As shown in Table 10, none of the existing equations provide a good axial strength prediction for lightweight concrete wall. The proposed design equation gives better prediction of the axial capacity of lightweight concrete wall compared to the existing equations. It can be seen that the proposed equation gives an improved estimation of the axial strength of normal-weight concrete wall compared with the existing equations. For highstrength concrete wall, the axial strength prediction using Equation (22) shows slight overestimation for specimens OWHS3 and OWHS4 [43], with P

_{cal}/P

_{exp}ratios of 1.14 and 1.11, respectively. The compressive strengths of these specimens are 63 and 75.9 MPa, respectively, while the slenderness ratios are 35 and 40, respectively. As for the high-strength concrete walls of Fragomeni and Mendis [35], the calculated results from Equation (22) are slightly conservative with P

_{cal}/P

_{exp}ratios of 0.92, 0.96, and 0.89 for specimens 2b, 5b, and 6b, respectively. The compressive strengths of these specimens are 65.4, 59.7, and 67.4 MPa, respectively, whereas the slenderness ratios are 15, 20, and 25, respectively. These comparisons manifest that the proposed equation can give a good prediction of the ultimate capacity of the normal-weight high-strength slender wall. The comparisons demonstrate that the predicted results obtained have shown a good agreement with both the present and published experimental results.

## 7. Conclusions

- It is found that the axial load-deflection behavior of OPS-based LWSCC wall shows linear responses in the initial loading region, which are followed by nonlinear response up to ultimate failure load. The ultimate axial strength of lightweight wall decreases with an increase in the slenderness ratio.
- From the comparisons, it can be seen that the existing design equations from the standards provide conservative estimation with P
_{cal}/P_{exp}ratios ranging from 0.36 to 0.91 and are not suitable for use in lightweight concrete wall. None of them takes into consideration the material properties of lightweight concrete. - From the results of parametric study on the effects of slenderness ratio, it has been demonstrated that concrete wall is still capable of sustaining loading with a slenderness ratio more than 30, and the axial strength ratio decreases nonlinearly with the increase of slenderness ratio.
- Parametric study shows that the ultimate axial capacity increases nonlinearly with the increase of the compressive strength of concrete. Typically, the axial strength ratio can be decreased nonlinearly by 57% when compressive strength increases from 13.7 MPa to 80 MPa at constant eccentricity of t/6.
- From parametric study, the analysis has identified the elastic modulus as one of the key parameters determining the ultimate axial strength of concrete wall. Decrease in elastic modulus of concrete results in a reduced ultimate axial capacity of the wall and vice versa. Elastic modulus of concrete is the key parameter affecting the ultimate axial strength of lightweight concrete wall.
- A design equation based on the equivalent rectangular stress block concept and incorporated with statistical factors has been proposed, which takes into account the effects of the elastic modulus, slenderness ratio, eccentricity, and nonlinear compressive strength of concrete. The equation has been benchmarked against published data and found to be effective and versatile. With the consideration of concrete elastic modulus and relevant parameters, the proposed design equation is thought to be a more reliable and effective design aid for industrial application. The proposed design equation can be the basis for further development of the equation, taking into account more parameters such as wall openings and side restraints (two-way wall).
- Hence, considering its lightweight characteristics and self-compacting property, OPS-based LWSCC can be introduced as a sustainable solution for the construction industry to promote not only automation but also environmental conservation. The proposed design equation can serve as a practical design tool to provide insight into the strength of lightweight concrete wall used as an axial component for a sustainable building structure.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Specimen Details

References | Specimen | H × L × t (mm) | f′c (MPa) | Steel Ratio | fsy (MPa) | Failure Load (kN) |
---|---|---|---|---|---|---|

Saheb and Desayi [28] | WAR1 | 600 × 900 × 50 | 17.864 | 0.00173 | 297 | 484.27 |

WAR2 | 600 × 600 × 50 | 17.86 | 0.00 | 297 | 315.8 | |

WAR3 | 600 × 400 × 50 | 17.86 | 0.00 | 297 | 198.29 | |

WSR1 | 450 × 300 × 50 | 17.34 | 0.00 | 297 | 214.18 | |

WSR2 | 600 × 400 × 50 | 17.34 | 0.00 | 297 | 254.1 | |

WSR3 | 900 × 600 × 50 | 17.34 | 0.00 | 297 | 298.92 | |

WSTV2 | 600 × 900 × 50 | 20.14 | 0.00 | 286 | 535.07 | |

WSTV3 | 600 × 900 × 50 | 20.14 | 0.01 | 581 | 583.52 | |

WSTH2 | 600 × 900 × 50 | 19.6 | 0.00173 | 297 | 538.01 | |

Fragomeni and Mendis [35] | 2a | 1000 × 300 × 50 | 42.4 | 0.0025 | 450 | 231.8 |

2b | 1000 × 300 × 50 | 65.4 | 0.0025 | 450 | 263.5 | |

5a | 1000 × 500 × 40 | 35.7 | 0.0025 | 450 | 201.2 | |

5b | 1000 × 500 × 40 | 59.7 | 0.0025 | 450 | 269.2 | |

6b | 600 × 200 × 40 | 67.4 | 0.0031 | 450 | 178 | |

Doh and Fragomeni [43] | OWNS3 | 1400 × 1400 × 40 | 52 | 0.0031 | 610 | 426.7 |

OWNS4 | 1600 × 1600 × 40 | 51 | 0.0031 | 610 | 441.5 | |

OWHS3 | 1400 × 1400 × 40 | 63 | 0.0031 | 610 | 441.5 | |

OWHS4 | 1600 × 1600 × 40 | 75.9 | 0.0031 | 610 | 455.8 | |

Ganesan, Indira and Santhakumar [36] | OPCAR1 | 600 × 320 × 40 | 33.832 | 0.0088 | 415 | 230.53 |

GPCSR1 | 480 × 320 × 40 | 33.072 | 0.0088 | 415 | 256.18 | |

GPCAR1 | 600 × 320 × 40 | 33.072 | 0.0088 | 415 | 211.89 |

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**Figure 2.**Particle size distribution of OPS and river sand [54].

**Figure 4.**Detail of support condition: (

**a**) Schematic diagram, (

**b**) Experimental setup for T60 series, (

**c**) Experimental setup for T25 series.

**Figure 7.**Comparison between experimental and FEA failure mode (

**a**) T60-AR5.3SR23, (

**b**) T25 AR5.3SR23.

**Figure 8.**Comparison between FEA and experimental results: (

**a**) T60-AR5.3SR23, (

**b**) T25-AR3.1SR23 and T25-AR5.3SR23, (

**c**) T25-AR1.8SR17 and T25-AR1.8SR23.

**Figure 10.**Axial strength ratio versus slenderness ratio with different compressive strength: (

**a**) e = 0.05, (

**b**) e = 0.0833, (

**c**) e = 0.1667.

**Figure 11.**Axial strength ratio versus slenderness ratio with varying elastic modulus: (

**a**) e = 0.05, (

**b**) e = 0.0833, (

**c**) e = 0.1667.

**Figure 13.**Regression analysis for (

**a**) λ at e = t/20, (

**b**) λ at e = t/12, (

**c**) λ at e = t/6, (

**d**) parameter e, (

**e**) f′c, (

**f**) parameter E.

**Table 1.**Chemical properties of cement and fly ash [54].

Chemicals | Cement (%) | Fly Ash (%) |
---|---|---|

$\mathrm{Silicon}\text{}\mathrm{dioxide}\text{}\left({\mathrm{SiO}}_{2}\right)$ | 20.0 | 57.8 |

$\mathrm{Aluminium}\text{}\mathrm{oxide}\text{}\left({\mathrm{Al}}_{2}{\mathrm{O}}_{3}\right)$ | 5.2 | 20.0 |

$\mathrm{Ferric}\text{}\mathrm{oxide}\text{}\left({\mathrm{Fe}}_{2}{\mathrm{O}}_{3}\right)$ | 3.3 | 11.7 |

$\mathrm{Calcium}\text{}\mathrm{oxide}\text{}\left(\mathrm{CaO}\right)$ | 63.2 | 3.28 |

$\mathrm{Magnesium}\text{}\mathrm{oxide}\text{}\left(\mathrm{MgO}\right)$ | 0.8 | 1.95 |

$\mathrm{Sulfur}\text{}\mathrm{trioxide}\text{}\left({\mathrm{SiO}}_{3}\right)$ | 2.4 | 0.08 |

${\mathrm{K}}_{2}\mathrm{O}$ | - | 3.88 |

${\mathrm{TiO}}_{2}$ | - | 2.02 |

${\mathrm{Na}}_{2}\mathrm{O}$ | - | 0.30 |

Loss on ignition | 2.5 | 0.32 |

**Table 2.**Physical properties of aggregates [54].

Physical Property | River Sand | OPS |
---|---|---|

Specific gravity | 2.64 | 1.19 |

Water absorption (24 h) (%) | 1.1 | 18.11 |

Aggregate impact value (AIV) (%) | - | 4.2 |

**Table 3.**Concrete mix design [54].

Cement (kg/m^{3}) | Fly Ash (kg/m^{3}) | Water (kg/m^{3}) | Sand (kg/m^{3}) | OPS Aggregate (kg/m^{3}) | SP (kg/m^{3}) |
---|---|---|---|---|---|

312 | 208 | 161.2 | 715 | 455 | 8.6 |

Specimen | Height L (mm) | Width W (mm) | Thickness t (mm) | Average Compressive Strength (MPa) | Average Splitting Tensile Strength (MPa) | Nominal Density (kg/m^{3}) |
---|---|---|---|---|---|---|

T25-AR1.8SR17 ^{a} | 425 | 235 | 25 | 16.4 | 1.5 | 1829 |

T25-AR1.8SR23 ^{a} | 565 | 315 | 25 | |||

T25-AR3.1SR23 ^{a} | 565 | 185 | 25 | |||

T25-AR5.3SR23 ^{a} | 565 | 105 | 25 | |||

T60-AR5.3SR23 ^{b} | 1400 | 260 | 60 | 13.7 | 1.1 | 1823 |

^{a}T25 series specimens were from 1st batch of concrete.

^{b}T60 series specimens were from 2nd batch of concrete.

Parameters | Values |
---|---|

Elastic modulus (MPa) | 12,047 |

Poisson ratio | 0.2 |

Density (kg/m^{3}) | 1800 |

Dilation angle | 31° |

Eccentricity | 0.1 |

$\mathrm{Initial}\text{}\mathrm{biaxial}/\mathrm{uniaxial}\text{}\mathrm{ratio},\text{}{\sigma}_{c0}/{\sigma}_{b0}$ | 1.16 |

K_{c} | 0.667 |

Viscosity | 0.001 |

Fsy (MPa) | Fsu (MPa) | v |
---|---|---|

299 | 374 | 0.3 |

Specimens | Maximum Deflection, Δ (mm) | Specimen Height, H (mm) | Deflection Ratio, Δ/H |
---|---|---|---|

T25-AR1.8SR17 | 1.93 | 425 | 0.0045 |

T25-AR1.8SR23 | 2.97 | 565 | 0.0053 |

T25-AR3.1SR23 | 2.89 | 565 | 0.0051 |

T25-AR5.3SR23 | 2.46 | 565 | 0.0044 |

T60-AR5.3SR23 | 6.4 | 1400 | 0.0046 |

Specimens | Average Failure Load P_{exp} (kN) | Standard Deviation of Test Results | Average Axial Strength Ratio Pexp/f′cAg | ACI P _{cal} (kN) | AS P _{cal} (kN) | Eurocode 2 P _{cal} (kN) |
---|---|---|---|---|---|---|

T25-AR1.8SR17 | 78 | 2.25 | 0.78 | 40.83 | 44.6 | 63.51 |

T25-AR1.8SR23 | 85.59 | 1.8 | 0.64 | 39.81 | 46.42 | 66.33 |

T25-AR3.1SR23 | 51.2 | 1.31 | 0.65 | 23.43 | 27.31 | 39.01 |

T25-AR5.3SR23 | 27.32 | 0.6 | 0.68 | 10.46 | 12.52 | 18.06 |

T60-AR5.3SR23 | 155.06 | 2.25 | 0.71 | 60.03 | 71.07 | 101.97 |

Study | Specimen | P_{exp} (kN) | P_{FEA} (kN) | P_{FEA}/P_{exp} Ratio |
---|---|---|---|---|

Present Study | T25-AR1.8SR17 | 78 | 82.31 | 1.06 |

T25-AR1.8SR23 | 85.59 | 88.53 | 1.03 | |

T25-AR3.1SR23 | 51.2 | 53.55 | 1.05 | |

T25-AR5.3SR23 | 27.32 | 28.55 | 1.05 | |

T60-AR5.3SR23 | 155.06 | 159.68 | 1.03 | |

Saheb and Desayi [28] | WSR1 | 214.18 | 192.4 | 0.90 |

WSR2 | 254.1 | 246.87 | 0.97 | |

WSR3 | 298.92 | 319.1 | 1.07 | |

WSR4 | 373.65 | 409.67 | 1.10 | |

WSTV4 | 704.14 | 787.66 | 1.12 | |

WSTV7 | 463.28 | 430.94 | 0.93 | |

WSTH6 | 348.74 | 362.97 | 1.04 | |

Doh and Fragomeni [43] | OWNS3 | 426.7 | 462.25 | 1.08 |

OWNS4 | 441.5 | 443.63 | 1.00 | |

OWHS2 | 482.7 | 504 | 1.04 | |

OWHS3 | 441.5 | 462.45 | 1.05 | |

OWHS4 | 455.8 | 495.71 | 1.09 | |

Mean | 1.04 | |||

Standard Deviation | 0.06 |

Specimen | ACI | AS | EC 2 | Equation (22) | |
---|---|---|---|---|---|

P_{cal}/P_{exp} | P_{cal}/P_{exp} | P_{cal}/P_{exp} | P_{cal}/P_{exp} | ||

Present study | T25-AR1.8SR17 | 0.52 | 0.56 | 0.80 | 0.88 |

T25-AR1.8SR23 | 0.46 | 0.54 | 0.77 | 1.00 | |

T25-AR3.1SR23 | 0.45 | 0.53 | 0.75 | 0.97 | |

T25-AR5.3SR23 | 0.38 | 0.46 | 0.66 | 0.94 | |

T60-AR5.3SR23 | 0.39 | 0.46 | 0.66 | 0.97 | |

Saheb and Desayi [28] | WAR1 | 0.78 | 0.68 | 0.75 | 1.06 |

WAR2 | 0.80 | 0.70 | 0.77 | 1.08 | |

WAR3 | 0.85 | 0.74 | 0.81 | 1.14 | |

WSR1 | 0.62 | 0.54 | 0.64 | 0.88 | |

WSR2 | 0.65 | 0.56 | 0.62 | 0.88 | |

WSR3 | 0.66 | 0.57 | 0.52 | 0.89 | |

WSTV2 | 0.80 | 0.70 | 0.76 | 1.03 | |

WSTV3 | 0.73 | 0.64 | 0.70 | 0.94 | |

WSTH2 | 0.78 | 0.67 | 0.74 | 1.01 | |

Fragomeni and Mendis [35] | 2a | 0.92 | 0.79 | 0.67 | 0.87 |

2b | 1.25 | 1.07 | 0.91 | 0.92 | |

5a | 0.76 | 0.64 | 0.42 | 1.02 | |

5b | 0.95 | 0.80 | 0.52 | 0.96 | |

6b | 1.30 | 1.13 | 1.13 | 0.89 | |

Doh and Fragomeni [43] | OWNS3 | N.A. | N.A. | N.A. | 1.10 |

OWNS4 | N.A. | N.A. | N.A. | 0.99 | |

OWHS3 | N.A. | N.A. | N.A. | 1.14 | |

OWHS4 | N.A. | N.A. | N.A. | 1.11 | |

Ganesan, Indira and Santhakumar [36] | OPCAR1 | 0.81 | 0.70 | 0.70 | 0.81 |

GPCSR1 | 0.78 | 0.68 | 0.75 | 0.80 | |

GPCAR1 | 0.86 | 0.74 | 0.75 | 0.87 | |

Mean | 0.36 | 0.31 | 0.34 | 0.97 | |

Standard Deviation | 1.05 | 0.97 | 0.96 | 0.10 |

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## Share and Cite

**MDPI and ACS Style**

Rahman, M.E.; Ting, T.Z.H.; Lau, H.H.; Nagaratnam, B.; Poologanathan, K.
Behaviour of Lightweight Concrete Wall Panel under Axial Loading: Experimental and Numerical Investigation toward Sustainability in Construction Industry. *Buildings* **2021**, *11*, 620.
https://doi.org/10.3390/buildings11120620

**AMA Style**

Rahman ME, Ting TZH, Lau HH, Nagaratnam B, Poologanathan K.
Behaviour of Lightweight Concrete Wall Panel under Axial Loading: Experimental and Numerical Investigation toward Sustainability in Construction Industry. *Buildings*. 2021; 11(12):620.
https://doi.org/10.3390/buildings11120620

**Chicago/Turabian Style**

Rahman, Muhammad Ekhlasur, Timothy Zhi Hong Ting, Hieng Ho Lau, Brabha Nagaratnam, and Keerthan Poologanathan.
2021. "Behaviour of Lightweight Concrete Wall Panel under Axial Loading: Experimental and Numerical Investigation toward Sustainability in Construction Industry" *Buildings* 11, no. 12: 620.
https://doi.org/10.3390/buildings11120620