Effects of creep recovery on the fracture properties of concrete

Highlights

• Creep recovery model was proposed to analyze the time-dependent behavior of concrete.

• Variations of stress in concrete during the creep recovery process were obtained.

• Stress relaxation caused the increase of initial cracking and peak loads of concrete.

• Static fracture toughnesses can reflect crack resistance of creep recovery concrete.

Abstract

To study the influence of creep recovery on the fracture properties of concrete, the pre-notched specimens were firstly subjected to three-point bending (TPB) loading at 60% peak load (P_max) over 30 days. Afterwards, the load was removed and the creep recovery tests were performed for 1, 2, 3 and 15 days, respectively. Thereafter, the quasi-static TPB tests were conducted on the creep recovery specimens. The deformation versus time curves, initial cracking load (P_ini), peak load and fracture energy in the quasi-static TPB tests after creep recovery were obtained. Also, the numerical analyses were conducted by combining with the Norton-Bailey model to investigate the stress variations at the crack tip and the time-dependent behaviour of concrete. By comparing the fracture parameters for the specimens with and without undergoing creep recovery, the effects of creep recovery on the fracture characteristics of concrete were assessed. The results showed that during the creep stage, the stress relaxation generated at the crack tip due to viscoelastic characteristics of concrete enlarged the deformation. In contrast, the reversed stress would occur at the crack tip during the recovery stage, and its relaxation over the time contributed to the time-dependent deformation during the creep recovery stage. By comparing with the specimens under the quasi-static TPB loading, P_ini and P_max for the creep recovery specimens would increase, and the increments slowed down over the recovery time. However, the increases in P_ini and P_max for the creep recovery specimens could not enhance the initial and critical fracture toughnesses and these toughnesses were approximately equal to those under the quasi-static tests.

Introduction

Concrete gravity dams in service are usually subjected to long-term loading due to its function of storing water, where time-dependent creep behaviour exists in the concrete structures. Creep in concrete leads to stress redistributions, cracking and increased deformation, which may negatively affect the long-term serviceability and sustainability of the concrete dams. In contrast, when the water level drops, the concrete of gravity dams will enter the creep recovery stage and instantaneous recovery occurs after unloading [1], [2]. The recovery of the creep deformation is only part of the initial creep deformation, while the rest part remains unrecoverable [3], [4]. Together with the recovery of the creep deformation, the stress field in concrete will change in the recovery process. Considering the safety of the gravity dams in service, the effects of creep recovery on the crack resistance of concrete should be further explored so that the residual life of the dams can be comprehensively evaluated.

So far, the creep recovery behaviour of concrete has attracted much attention of academic and engineering communities. Creep behaviour of concrete can be classified as linear and nonlinear deformations depending on load levels. In general, linear viscoelastic behaviour of concrete occurs under low sustained loading. In contrast, under high sustained loading, the concrete exhibits nonlinear viscoelastic behaviour because of crack initiation, propagation and their interaction with the viscoelasticity of concrete [5], [6]. For the creep recovery behaviour, the previous studies mainly focused on the effects of stress levels [6], concrete compositions including cement types [7], coarse aggregate [8], blast furnace slag [9] and polystyrene aggregate [10], and concrete strength [4] on the time-dependent behaviour. These investigations showed that the variations of the creep recovery deformation for concrete under compression and tension were similarly associated with the stress levels but hardly affected by the concrete compositions. Under high sustained loading, the recovery of creep deformation of the concrete consisted of crack closure and recovery creep deformation [3], while under low sustained loading, the linear viscoelastic characteristic of concrete would govern the recovery of creep deformation. The recovery of creep deformation was only part of the creep deformation and a large portion of the creep deformation was irretrievable. In addition, extensive investigations have been conducted to analyse the mechanisms of the creep recovery of concrete. The study by Davies [11] demonstrated that the variations of the creep and the recovery of the creep deformation were the same, where the increments of the creep and the recovery of the creep deformations were caused by the identical stresses with the opposite signs. For the unrecoverable creep deformation, Su et al. [2] and Rossi et al. [6] considered that it was caused by the accumulated micro-damage during the creep process. In contrast, Tang et al. [10] and Davies [11] stated that closure of voids in concrete, and viscous flow and swelling of the cement-paste occurring in the creep process were irreversible. Qian and Kawashima [12] stated that the viscoelastic fluid deformation of concrete occurring in the creep process caused unrecoverable creep deformation. Above-mentioned explanations did not show clear mechanism of creep recovery. Creep and stress relaxation are known to be interrelated in viscoelastic materials like concrete [13], [14], and the relationship between stress relaxation and creep can be characterised by an exact analytical expression. Stress relaxation in concrete leads to stress redistributions. In particular, for the pre-notched three-point bending (TPB) concrete beams subjected to long-term loading, the stress concentration existed at the tip of the pre-prepared notch [15], [16]. The stress at the crack tip significantly decreased in the creep process due to the effect of stress relaxation. The stress relaxation occurring at the crack tip is local effect, while the creep deformation could be considered as structural effect. Similarly, during the creep recovery stage, the stress around the crack tip also influenced with the recovery of creep deformation [17]. However, the relation between the recovery of the creep deformation and the stress variation is not explicit. Therefore, to reasonably apprehend the creep recovery of concrete, it is necessary to quantitatively investigate and assess the variations of the stress and deformation of concrete during the creep recovery process.

Meanwhile, the fracture parameters, such as the initial fracture toughness$K_{\text{IC}}^{\text{ini}}$, the unstable fracture toughness $K_{\text{IC}}^{\text{un}}$ and the fracture energy G_f, are generally considered as the material properties, which represent the fracture resistance and characteristics of concrete. Some investigations have been performed on the creep fracture properties of concrete [18], [19], [20], [21], [22]. Omar et al. [20] studied the variations of the creep fracture characteristics of concrete by conducting the TPB tests on the creep specimens, and the results indicated that the long-term loading almost had no effect on the residual capacity of creep specimens. However, according to the researches by Saliba et al. [21], [22], P_max and G_f of concrete slightly increased after experiencing the creep process. This phenomenon was explained by the strengthening of the compressive zone of the TPB specimens in the creep process. In addition, Dong et al. [16] studied the creep fracture properties of concrete. According to the experimental and numerical results, they considered that the increments in P_ini and P_max of concrete were caused by the stress relaxation at the crack tip during the creep process. Accordingly, when the effects of stress relaxations were considered, the calculated$K_{\text{IC}}^{\text{ini}}$and$K_{\text{IC}}^{\text{un}}$of the creep specimens were approximately equal to those under quasi-static conditions. In the case of creep recovery, the stress at the front of the crack tip would be accompanied by the recovery of the creep deformation [17], [23], and affected the fracture behaviour of concrete. For assessing the cracking resistance of creep recovery concrete, it is necessary to perform further studies on the fracture characteristics of creep recovery concrete so that the fracture properties of concrete structures can be assessed accurately. Furthermore, the applicability of the fracture criteria with respect to Kini IC and Kun IC under quasi-static conditions should be clearly clarified when they are used in the fracture analyses on concrete subjected to creep recovery.

To comprehensively understand the creep behaviour of concrete, many investigations have been conducted to analyse the time-dependent behaviour of concrete. Barpi and Valente [24], [25] simulated the tertiary creep of concrete by employing the viscous rheological element to reveal the time-dependent behaviour in the fracture process zone (FPZ), and the obtained lifetime and load–displacement relationship from numerical analyses showed a good agreement with those from the experimental investigation. Zhou [26] also simulated the fracture process of concrete under sustained loading by introducing the Maxwell model to reflect the time-dependent behaviour in FPZ. Luzio [27] investigated the time-dependent fracture of concrete by employing the modified micro-plane model to characterise the viscoelasticity of the FPZ and un-cracked concrete. These studies presented successful modelling concepts for the tertiary creep of concrete under sustained loading. However, the investigations on the effects of creep recovery on the fracture behaviour of concrete are limited. Therefore, it is necessary to investigate the fracture properties of concrete after creep recovery and assess the effects of creep recovery on the fracture behaviour of concrete.

In line with this, the aim of this research is to study the creep recovery behaviour of concrete and its effects on the fracture characteristics of concrete. First, the TPB creep tests were carried out on the pre-notched concrete specimens at 60%P_max over 30 days. Thereafter, the creep recovery tests were performed over different recovery durations. After the creep recovery tests, the specimens were subjected to quasi-static TPB loading until failure. The creep recovery deformation versus time curves, the initial cracking load and the peak load were obtained in the tests. In addition, by combining with the Norton-Bailey model, the time-dependent behaviour and the stress intensity factor (SIF) of the concrete subjected to the creep recovery were analysed numerically. Finally, the effects of creep recovery on the fracture parameters of concrete were assessed.