Ultra-high performance concrete is an advanced cement-based material with high strength and high durability. Due to the low water-binder ratio and high binder consumption of UHPC, the early shrinkage of UHPC during the setting and hardening process is larger than that of conventional concrete and high-strength concrete, which easily leads to the cracking of engineering structures and affects the performance of structures. Therefore, it is of great significance to study the early shrinkage characteristics of UHPC for the optimization of the material and the prediction of early cracking. In this paper, the effects of binder-sand ratio, water-binder ratio, different fiber types and contents and curing environment on the early shrinkage performance of UHPC were investigated, and the early shrinkage model of UHPC was established by combining BPNN and WOA-BPNN neural network.

In this study, a total of seven groups of specimens were set up, considering four control factors, i.e., the cement-sand ratio, water-binder ratio, curing environment and polypropylene fiber volume content. Each group consisted of four specimens with size of 25 mm×25 mm×280 mm (including three specimens for drying-shrinkage tests and one specimen for autogenous-shrinkage tests). The specimens were cured in a curing box with a temperature of (25±2) ℃ and a relative humidity of (98%±2%). At the same time, a control group was set up, which was cured in a natural environment with a temperature of (28±5) ℃ and a relative humidity of (60%±15%). The shrinkage deformation of the specimens was measured by a specific length meter at 0, 1, 2, 3, 4, 6, 8, 10, 12 h and 1.0, 1.5, 2.0, 2.5, 3.0, 4.0, 5.0, 6.0, 7.0, 9.0, 11.0, 14.0, 18.0, 21.0, 25.0, 28.0 d. Combined with BPNN and WOA-BPNN machine learning models, the measured data were trained with small samples, and finally a neural network model that can be used to predict the early drying and autogenous shrinkage performance of UHPC was obtained.

The early drying-shrinkage and autogenous-shrinkage of UHPC increased with an increase of the cement-sand ratio, and the MIC values of drying shrinkage and cement-sand ratio also increased. The early drying-shrinkage and autogenous-shrinkage of specimen with a cement-sand ratio of 1.2 increased by 108% and 60%, respectively, compared with specimen with a cement-sand ratio of 0.8. The early drying-shrinkage and autogenous-shrinkage of UHPC increased with a decrease of the water-binder ratio. The appropriate amount of polypropylene fiber and steel fiber mixture would limit the early shrinkage of UHPC. With an increase of polypropylene fiber content, the inhibitory effect on both the early drying-shrinkage and autogenous-shrinkage grew firstly and then weakened. The specimens with fiber content of 0.10 % exhibit the best inhibitory effect. The drying-shrinkage expressed a great correlation with the curing method, and the MIC value was 0.56. The correlation between the autogenous-shrinkage and curing method is small, and the MIC value is 0.27. The drying-shrinkage rate and self-shrinkage rate under dry curing conditions were 2.5 times and 1.2 times that under standard curing conditions, respectively.

The two machine learning (ML) algorithms were used in the shrinkage prediction and exhibit good accuracy. The WOA-BPNN algorithm expressed delightful predicted accuracy, whose R², RMSE and MAE for drying-shrinkage model are 0.959, 0.050 and 0.040, respectively, and R², RMSE and MAE for autogenous-shrinkage model are 0.896, 0.076 and 0.053, respectively. The predicted results indicated that the whale optimization algorithm could improve the ML model effectively.

The main conclusions of this paper are given as follows: 1) The fine aggregate has an inhibitory effect on the early drying-shrinkage and autogenous-shrinkage of UHPC. When the cement-sand ratio decreases from 1.2 to 0.8, the early drying-shrinkage and autogenous-shrinkage increase by 108% and 60%, respectively. 2) The early drying-shrinkage and autogenous-shrinkage of UHPC increase with a decrease of water-binder ratio, and the decrease of water-binder ratio leads to the advance of UHPC self-drying phenomenon. 3) The research found that the polypropylene fiber volume content of 0.10% exhibit the best inhibitory effect on the UHPC shrinkage. 4) The curing method had a great influence on its early drying-shrinkage and autogenous-shrinkage. The drying-shrinkage rate of specimens under dry curing condition is 2.5 times that under standard curing condition, and the autogenous-shrinkage rate of specimens under dry curing condition is 1.2 times that under standard curing condition. The early drying-shrinkage and autogenous-shrinkage predicted results of UHPC based on the WOA-BPNN neural network show nice accuracy and robustness compared to that of BPNN.