An inverse problem to simulate the transport of chloride in concrete by time–space fractional diffusion model

Figures & data

Figure 1. Schematic diagram of chlorides diffusion in concrete. 

Figure 2. The experimental data compared with present model.  

Table 1. The estimated parameters according to related parameters from Ref. [54].

concrete	$C_s$	$D_e$	ε	α	β	${\lambda }_1$	${\lambda }_2$
OPC-30	0.89031	0.04579	0.123	1.00000	1.98043	1	0.86691
OPC-40	1.06521	0.12096	0.145	1.00000	1.88568	1	0.97801
OPC-50	1.13956	0.20736	0.153	1.00000	1.89366	1	0.93214
OPC-60	1.35490	0.45792	0.179	1.00000	1.88595	1	1.00000
FA35-40	1.16886	0.02592	0.157	0.88945	2.00000	0.95562	1
Slag20-40	1.04577	0.06566	0.142	1.00000	1.97989	1	0.87744
Slag35-40	1.02538	0.0432	0.139	1.00000	2.00000	1	1

Table 2. Convergence rate and CPU time of OPC-30 for the process of searching optimal parameters.

$\overline{\epsilon }$	τ (day)	Iterations	Standard error	CPU time (s)
0.05	1	3	0.0418	40
0.025	1	5	0.0238	62
0.0151	1	7	0.0143	98
0.0151	5	11	0.0147	22
0.0151	10	19	0.0150	15

Figure 3. Influence of  t and depth on the chloride diffusion.

Figure 4. Influence of p on the chloride diffusion. 

Figure 5. Influence of  Cs on the chloride diffusion.  

Figure 6. Influence of ϵ on the chloride diffusion. 

Figure 7. Influence of fractional derivatives on the chloride diffusion. 

Qiao C, Ni W, Wang Q, et al. Chloride diffusion and wicking in concrete exposed to NaCl and mgCl 2 solutions. J Mater Civ Eng. 2018;30(3):04018015.

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