## 4 Influence on Time-Dependent Deformation Based on the Proposed Extensive Model  
In this chapter, the extensive DuCOM, which was tackled and verified in the previous chapters, is coupled with COM3, with evaluation of time-dependent deformation for a long time being carried out through the integrated analysis (Figure 5, Part C)  
As illustrated in Figure 1, (A) DuCOM and (B) COM3 are linked with (C) the multiscale constitutive model. In DuCOM, pores are classified into interlayer, gel and capillary pores, according to sizes, formation process and whether or not the pore space is available for precipitating cement hydrates. Their thermodynamic moisture states in micro-pores can be calculated by the basic components of DuCOM and transferred to the constitutive model. The constitutive model is based on the rheological model of solidifying cluster proposed by [PERSON], et al. [28]. Although the brief explanation to estimate time-dependent deformation is described in the introduction, the detail modeling and mathematical formulations are explained in [1; 28]. For example, the dashpot viscosity and plastic strain limit are tailored for association with pore saturation. It is assumed that dry, empty pores may rapidly reach converged plasticity while liquid-filled pores may exhibit slow viscous flow. As creep deformation in the submerged state is smaller than when dry, and since lower humidity causes greater creep, larger ultimate plastic strain is assumed under severe drying conditions in the model. Figure 26 shows the comparative results of drying creep under different relative humidities at 20 \({}^{\circ}\)C between the past experiment [31] and the analysis by using (a) \"Original DuCOM\"-COM3 or (b) \"Extensive DuCOM\"-COM3. Both (a) and (b) analyses provided good results to simulate the long-term experiments regardless of the relative humidity. As the W/C of the experiment corresponds to 49%,  
Figure 24: Comparison of weight loss based on the extensive model (W/C = 35%, 55%) [28]. Figure 25: Comparison of weight loss based on the extensive model (W/C = 60%) [29]. the reduction factor \(w_{red}\) in the extensive model keeps 1.0 during the loading time, leading to similar results except for the influence of the modification of the original multicomponent hydration model (Figure 5, Part A). Similarly, Figure 27 shows the comparative results of basic creep under different temperatures without drying [32]. It was confirmed that the analysis (b) shows better agreement than (a), specifically in the case of T = 71 \({}^{\circ}\)C. This seems to be caused by the higher saturation degree of gel pores in (b), resulting from stagnation of hydration with the extensive modeling for a low W/C mixture. The higher the environmental temperature, the more remarkably the stagnation effect appears, leading to mitigation of basic creep. Consequently, the large discrepancy in (a) which was seen at higher temperature is greatly improved in (b). In addition, assuming application of the extensive model to a practical mass concrete structure, predictive simulations over 100 years were conducted before and after the extensive modeling. It was assumed in the analysis that the mixture is the same as Reference [27], OPC, W/C = 30% and the boundary condition is continuously sealed at 20 \({}^{\circ}\)C just after casting. The comparative results are presented in Figure 28. In the case of the extensive model, the reduction factor \(w_{red}\) begins to work at the 1.5-year age (about 550 days) and after that excessive hydration in the fine micro-pore structures is mitigated. As a result, it was suggested that the differences of the inner average relative humidity and the shrinkage between before and after the extensive modeling are 20% and 400u, respectively, at the 100-year age. Of course, this validity should be checked in the future due to scarcity of monitoring data currently available on practical low W/C structures with a long history.