ORCID ID: K. Liu (

To investigate the behaviour of recycled aggregate concrete (RAC) under combined compression and shear stresses, 75 hollow cylinder specimens prepared with various replacement ratios of recycled coarse aggregate (RCA) were tested with a self-designed loading device. The results showed that the failure pattern was similar for RAC with different replacement ratios of RCA. The ultimate shear stress improved with an increasing axial compression ratio of less than 0.6 and declined after exceeding 0.6. A modified failure criterion for RAC with normal strength under combined compression and shear stresses was proposed. A new procedure to predict the shear strength for RAC beams without stirrups was developed based on the proposed failure criterion, showing a better correlation with the experimental results than the predictions calculated by GB50010, Eurocode 2, fib Model Code 2010 and ACI 318-11.

As sustainable development has become a common concern of mankind, the use of sustainable materials in the construction industry has gained in popularity. With the rapid development of the construction industry, environmental issues, such as the excessive exploitation of natural aggregates and the increasing amount of construction and demolition debris, are increasingly pressing. As a viable way to address demolition waste, recycled aggregate concrete (RAC) can help provide a sustainable construction material and has received considerable attention in many countries over the last several decades (

In practical engineering, reinforced concrete elements are frequently subjected to combined compression and shear stresses rather than the uniaxial compression or tension stress state, such as prestressed elements, beams, two-way slabs and shell roofs (

Compared with current studies on conventional concrete, few studies have been conducted for RAC under combined stresses (

Crushed gravel with a maximum diameter of 19 mm from a local ready-mix concrete plant was used as the natural coarse aggregate (NCA). The parent concrete prepared for the recycled coarse aggregate (RCA) in this programme was made from an abandoned concrete frame in the laboratory (2 years old, with concrete compressive strength of 30 MPa). The waste concrete was first manually broken into pieces that were smaller than 150 mm. After screening all other materials and debris, the pieces were further crushed in a mini jaw crusher. The crushed RCA was between 4.75 and 19 mm. The particle size distribution of NCA and RCA satisfied the GB/T 14685-2011 (

Physical properties of NCA and RCA

Type | Apparent density (kg/m^{3}) |
Water absorption (% weight) | Crushing value index (%) | Residual mortar content (% weight) |
---|---|---|---|---|

NCA | 2700 | 0.6 | 2.6 | – |

RCA | 2687 | 6.68 | 12 | 41 |

There is still no standard mix design method for RAC mixture design. Generally, a standard method of mixture design for conventional concrete is adopted in which the NCA is replaced by RCA at different proportions. Three accepted aggregate replacement methods are direct weight replacement, direct volume replacement (DVR) and equivalent mortar volume (EMV) replacement (

Mixture proportions

ID | Cement (kg/m^{3}) |
Water (kg/m^{3}) |
Sand (kg/m^{3}) |
NCA (kg/m^{3}) |
RCA ^{a}
^{3}) |
---|---|---|---|---|---|

NAC | 413 | 215 | 635 | 1081 | 0 |

RAC30 | 413 | 215 | 635 | 757 | 345 |

RAC50 | 413 | 215 | 635 | 541 | 574 |

RAC70 | 413 | 215 | 635 | 325 | 804 |

RAC100 | 413 | 215 | 635 | 0 | 1148 |

The mass for pre-soaked RCA.

The tested specimens consist of hollow cylinders with a 207 mm outside diameter, 126 mm inside diameter and 650 mm height. The cylinders were cast on a shaking table in a longitudinal position in a split steel mould with a demountable polyethylene core. After 24 h, the specimens were demoulded and then cured under normal conditions (20 ± 2°C and 95% relative humidity).

To load the torque, the end of the cylinder was changed to square shape. The surfaces of both ends with a length of 100 mm was pockmarked by an electric drill, and then four steel bars were plugged into the holes with a diameter of 12 mm made at the quartering point 50 mm from the end. High-strength non-shrinking grouting material was used to fill the square mould and strengthen the ends. Both ends of the cylinders were strengthened by two layers of glass fibre-reinforced polymer wrap to avoid premature failure during the test. The details for the specimen are shown in

Details for the specimen (a) Blueprint (b) Physical map.

A total of 75 cylinders were prepared, 15 for each mixture. Meanwhile, twelve cubes with a side length of 100 mm were made as the control specimens for each mixture to test the compressive strength and split tensile strength.

Test results for control specimens

ID | Cubic compressive strength _{cu} (MPa) |
Axial compressive strength |
Split tensile strength (MPa) |
---|---|---|---|

NAC | 45.63 | 34.68 | 2.89 |

RAC30 | 34.31 | 26.08 | 2.23 |

RAC50 | 33.33 | 25.33 | 1.69 |

RAC70 | 30.79 | 23.40 | 1.69 |

RAC100 | 30.17 | 22.93 | 1.97 |

The axial compressive strength was calculated according to GB50152 (

The test setup is shown in

Test setup (a) Schematic drawing (b) Physical map.

The force-control method was used during the whole loading programme. An axial compressive loading was applied first to a predetermined level to give compressive stress _{x} of 0, 0.2, 0.4, 0.6 or 0.8 times the axial compressive strength _{c}. The axial compressive stress was held constant and the torque was then applied monotonically in step loading system until failure occurred. The shear strain was tested by two strain rosettes, adhered to the surface of the specimen and consisting of an axial strain gauge, a lateral one and a diagonal one with an angle of 45°. Two tilt sensors were placed at the side of the specimen to monitor the torque angle and make sure a uniform rotation direction. In addition, the torque was recorded by the electro hydraulic servo system automatically in each loading step.

The failure patterns for all mixtures were similar. The five typical failure modes for RAC100 series are illustrated in _{x} / _{c} increased, the angle _{x} / _{c} of 0.8.

Typical failure modes for RAC100 series.

A previous study indicated that the shearing stress of a hollow cylinder can be assumed as a linear distribution along the thickness (

where _{0°} = axial strain, με; _{45°} = diagonal strain, με; and _{90°} = lateral strain, με.

The typical shear stress versus shear strain curves are listed in

A summary of shear stress

_{x}/_{c} |
ID | ||||
---|---|---|---|---|---|

NAC | RAC30 | RAC50 | RAC70 | RAC100 | |

0 | 2.24 | 1.97 | 2.45 | 1.82 | 1.79 |

2.31 | 2.33 | 1.80 | 1.78 | 1.80 | |

2.22 | 1.95 | 1.74 | 1.93 | 1.88 | |

0.2 | 3.96 | 3.64 | 3.95 | 3.31 | 3.46 |

4.67 | 3.89 | 3.98 | 3.34 | 3.96 | |

4.07 | 3.52 | 2.62 | 4.40 | 2.43 | |

0.4 | 5.11 | 4.36 | 4.76 | 2.91 | 3.80 |

5.88 | 3.92 | 4.32 | 4.70 | 4.31 | |

5.27 | 4.45 | 3.44 | 5.06 | 4.00 | |

0.6 | 6.24 | 5.76 | 5.85 | 4.76 | 5.28 |

6.32 | 6.14 | 5.89 | 5.45 | 4.17 | |

4.97 | 5.23 | 5.42 | 5.29 | 4.19 | |

0.8 | 5.01 | 5.02 | 4.79 | 5.24 | 3.80 |

— ^{a} |
4.28 | 4.34 | 4.50 | 4.32 | |

— | 5.12 | — | — | — |

‘—’ represents missing data.

Shear stress versus shear strain curves. (a) NAC (b) RAC30 (c) RAC50 (d) RAC70 (e) RAC100.

Under the plane stress condition, the combined compression and shear stresses state can be transformed to a tensile–compression stress state (

Transformation between two stress states.

where _{1} = principal tensile stress, MPa; and _{2} = principal compressive stress, MPa.

The angle _{2} and the longitudinal axis can be calculated as follows [

It can be seen from

Based on

Average Ratios between predictions and experimental results

ID | Failure criteria | |||
---|---|---|---|---|

Leon | Twin shear stress | Kupfer | Bresler | |

NAC | 1.40 | 1.27 | 1.08 | 1.04 |

RAC30 | 1.19 | 1.15 | 0.89 | 0.93 |

RAC50 | 1.01 | 0.91 | 0.78 | 1.03 |

RAC70 | 0.98 | 0.91 | 0.75 | 1.01 |

RAC100 | 0.93 | 0.84 | 0.74 | 1.03 |

Based on the previous analysis, Bresler theory was selected to establish the failure criterion for RAC under combined compression and shear stresses in plane stress space. To make a failure criterion suitable for both NAC and RAC with normal strength, a unified formula was proposed based on experimental results and can be expressed as follows [

where

where

_{c} increased with the increasing _{c} was still larger than that of NAC.

Comparison between test results and predictions of proposed failure criterion. (a) NAC (b) RAC30 (c) RAC50 (d) RAC70 (e) RAC100.

The failure criterion is an effective approach to determine the capacity of reinforced concrete structures under various conditions of loading. As an indication of the possibility of applying the proposed failure criterion for RAC, a method for calculating the shear strength of normal RAC beams without stirrups was developed. The following conventional assumptions were made in advance:

Concrete cannot resist tension.

Failure occurred by the destruction of concrete in the shear–compression zone.

The shear strength of the RAC beam _{beam} was provided by three parts: concrete _{c}, aggregate interlock capacity _{a}, and dowel resistance of the longitudinal reinforcement

Distribution of internal force for a simply supported beam.

To simplify the process, the average shear stress _{m} and direct stress _{m} were used for representing the real stress state, and the force equilibrium equation can be expressed as follows [

where _{ξ} = depth of the shear–compression zone, mm; σ_{s}= tensile stress of longitudinal reinforcement, MPa; _{0} = distance from extreme compression fibre to centroid of longitudinal reinforcement, mm. _{a} and _{s} can be expressed by the following equation (

where μ was a proportionality. For concrete beams without stirrups, _{ξ}, which can be expressed as follows [

where _{s} for the longitudinal bar can be calculated by the following formula (

Once _{s} was obtained, _{m} can be determined by _{m}. Then, _{c} was obtained from _{beam} was determined by

_{beam} of 20 beams exhibiting shear compression failure (_{pre}. In addition to the method proposed in this paper, GB50010 (

Ratios between _{per} and _{beam} of selected beams

Investigator | Specimen ID | RCA Replacement ratio | _{per}/_{beam} |
||||
---|---|---|---|---|---|---|---|

Proposed failure criterion | GB50010 | Eurocode 2 | fib Model Code 2010 | ACI 318-11 | |||

Zhang et al. (2007) | LC-2.5-0 | 0% | 1.20 | 0.97 | 0.47 | 0.76 | 0.24 |

LR-2.5-1 | 100% | 1.46 | 0.97 | 0.48 | 0.78 | 0.24 | |

LC-1.5-0 | 0% | 0.74 | 0.41 | 0.17 | 0.23 | 0.14 | |

LR-1.5-1 | 100% | 1.07 | 0.51 | 0.24 | 0.45 | 0.18 | |

LR-1.5-0.3 | 30% | 0.90 | 0.42 | 0.19 | 0.27 | 0.15 | |

LR-1.5-0.5 | 50% | 0.91 | 0.42 | 0.18 | 0.26 | 0.15 | |

LR-1.5-0.7 | 70% | 1.00 | 0.44 | 0.21 | 0.33 | 0.16 | |

Fathifazl et al. (2009) | EM-1.5N | 63.5% | 1.04 | 0.66 | 0.35 | 0.59 | 0.33 |

EM-2N | 63.5% | 0.97 | 0.70 | 0.44 | 0.83 | 0.36 | |

EV-1.5N | 74.3% | 0.94 | 0.72 | 0.36 | 0.66 | 0.33 | |

EV-2N | 74.3% | 1.06 | 0.82 | 0.43 | 0.87 | 0.35 | |

Ni et al. (2010) | BH0 | 0% | 0.67 | 0.80 | 0.38 | 0.67 | 0.36 |

BH25-1 | 25% | 0.83 | 0.85 | 0.37 | 0.69 | 0.37 | |

BH25-2 | 25% | 0.90 | 0.92 | 0.40 | 0.54 | 0.40 | |

BH25-3 | 25% | 0.82 | 0.84 | 0.37 | 0.74 | 0.36 | |

BH50-1 | 50% | 0.96 | 0.82 | 0.40 | 0.54 | 0.37 | |

BH50-2 | 50% | 0.90 | 0.77 | 0.38 | 0.64 | 0.35 | |

BH50-3 | 50% | 0.94 | 0.80 | 0.40 | 0.56 | 0.37 | |

BH75-1 | 75% | 0.96 | 0.82 | 0.41 | 0.53 | 0.38 | |

BH75-3 | 75% | 0.96 | 0.81 | 0.41 | 0.53 | 0.38 |

The behaviour of RAC under combined compression and shear stresses was investigated experimentally in this paper. The following conclusions are drawn:

The failure patterns for all mixtures were similar. As the axial compressive stress increased, the angle of the diagonal crack to the longitudinal axis gradually decreased.

The ultimate shearing stress and shear stiffness increased with increasing axial compression ratio when the ratio was below 0.6 and declined when the ratio exceeded 0.6.

A modified failure criterion for both NAC and RAC under combined compression and shear stresses was proposed, showing good matching with the test results.

A new method for determining the shear strength of RAC beams without stirrups was developed based on the failure criterion, showing a good correlation with the test results.

1. Leon theory

Leon (

where _{t} and _{c} are the numerical values of the uniaxial tensile and compressive strengths, respectively.

2. Twin shear stress criterion

The twin shear stress theory was proposed by Yu et al. (

where _{13}= the maximum principle shear stress; _{12}, _{23}= the other two principle shear stresses, _{h} = hydrostatic pressure; and _{h}. The parameters

Where _{bc} is the biaxial compressive strength. In addition,

Therefore, the twin shear stress theory can be described in the principal stress space:

The twin shear stress theory can then be transformed as follows:

Where

3. Kupfer criterion

Kupfer et al. (

This can be rewritten in terms of the applied stresses _{x} and

4. Bresler theory

Bresler et al. (

where _{oct} is octahedral shear stress; _{oct} is octahedral normal stress; _{1}, _{2} and _{3} are parameters.

This can be rewritten in terms of the applied stresses _{x} and

Where

The work described in this paper was supported by a grant from the National Natural Science Foundation of China (grant number 51278151).