Early-age stress analysis of a concrete diaphragm wall through tensile creep modeling

Abstract

This paper reports a recent large-scale experimental investigation on early-age stress evolution in a deep underground concrete diaphragm wall. To evaluate the early-age stress induced by hydration temperature rise, autogeneous shrinkage and reinforcement restraint, both laboratory tests and in situ large-scale model wall test are performed. The laboratory tests include concrete adiabatic temperature rise, autogeneous shrinkage and restraint test. The in situ model wall simulates continuous and sliding design options for the external and inner layers with thermal and strain sensors installed in the inner layer. The restraint test results are interpreted via tensile creep modeling and an algorithm is conceived to calibrate the concrete tensile creep law. With the identified creep law, a thermomechanical analysis is performed on the model wall to calculate the concrete temperature and stress evolution at early age. The identified tensile creep law is furthermore validated by the numerical results and in situ measurements. Furthermore, the early-age stress analysis is performed on the full-scale diaphragm wall. Comments on the concrete tensile creep law and the diaphragm wall design option are given in the end.

Appendix: Parameter identification algorithm of tensile creep

Discretize the time domain from zero tensile instant t ₀ to the expected end t _end . For our analysis, t ₀ = 15.0 h and t _end  = 336 h. The time interval is equal to 1.0 h. The parameter identification is summarized as follows:

• (a) Determine the search ranges and steps for tensile creep parameters,

  $$\left\{\begin{array}{l}\phi_{0}: [\phi_{0}^{min},\phi_{0}^{max}], \Updelta\phi_{0}\\ d:[d_{min},d_{max}], \Updelta d \\p:[p_{min}, p_{max}], \Updelta p \\ \end{array}\right.$$

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• (b) Select a parameter group [$\bar{\phi}_0,\bar{d},\bar{p}$] from the above search ranges, calculate the incremental creep strain from t ₀ to t _end through Eq. 16,

  $$ \begin{aligned} \displaystyle{\Updelta_n^{n+1}\epsilon_{cr}}&=\displaystyle {\bar{\phi}_0\sum^{n-1}_{i=0}\bigg\{\frac{\sigma'(t_{i,\frac{1}{2}})}{E(t_{i,\frac{1}{2}})} t_{i,\frac{1}{2}}^{-\bar{d}}\big[(t_{n+1}-t_{i,\frac{1}{2}})^{\bar{p}}-(t_{n}-t_{i,\frac{1}{2}})^{\bar{p}}\big]\Updelta t_i^{i+1}\bigg\}}\\& \displaystyle{+\bar{\phi}_0 \frac{\sigma'(t_{n,\frac{1}{2}})}{E(t_{n,\frac{1}{2}})}t_{n,\frac{1}{2}}^{-\bar{d}}\bigg(\frac{\Updelta t_n^{n+1}}{2}\bigg)^{\bar{p}}}\Updelta t_n^{n+1} \end{aligned} $$

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• (c) Calculate the accumulated integral error η _in and absolute error η _ab for this parameter group,

  $$ \eta_{in}=|\epsilon_{cr}^f-\sum\limits^{t_{end}}_{t_n=t_0}\Updelta_n^{n+1} \epsilon^c_{cr}|/\epsilon_{cr}^f,\eta_{ab} =\hbox{Max} |\Updelta_n^{n+1}\epsilon_{cr}^f-\Updelta_n^{n+1} \epsilon^c_{cr}| $$

  (28)

  with $\epsilon_{cr}^{f,c}$ signifying respectively the fitted and calculated tensile creeps.

• (d) Go to (b) until all the parameters groups are calculated. Then find the optimized parameter group by fixing the numerical tolerances for integral and absolute errors $\bar{\eta}_{in,ab}$,

  $$ \eta_{in} \le \bar{\eta}_{in},\quad \eta_{ab} \le \bar{\eta}_{ab} $$

  (29)

• (e) If multiple groups are available from the above selection, decrease the tolerances $\bar{\eta}_{in}, \bar{\eta}_{ab}$ until only one group is left.