An Extended Damage Plasticity Model for Shotcrete: Formulation and Comparison with Other Shotcrete Models

Abstract

The aims of the present paper are (i) to briefly review single-field and multi-field shotcrete models proposed in the literature; (ii) to propose the extension of a damage-plasticity model for concrete to shotcrete; and (iii) to evaluate the capabilities of the proposed extended damage-plasticity model for shotcrete by comparing the predicted response with experimental data for shotcrete and with the response predicted by shotcrete models, available in the literature. The results of the evaluation will be used for recommendations concerning the application and further improvements of the investigated shotcrete models and they will serve as a basis for the design of a new lab test program, complementing the existing ones.

Keywords: constitutive model; experimental data; numerical simulation; shotcrete; tunnel advance.

Figure 1

(a) Illustration of the time transformation function $\tau \left(t\right)$ (black curve) versus time t (straight gray line); (b) Evolution of the Young’s modulus $E\left(t\right)$, based on $v\left(t\right)$ and $v\left(\tau \right(t\left)\right)$, and comparison with experimental data by Huber [15].

Figure 2

Evolution of the Young’s modulus: (a) Results of the calibration of the shotcrete models based on test data of test series 5 by Huber [15]; (b) Validation of the shotcrete models by means of the data of test series 1 to 4 in [15].

Figure 3

Evolution of the uniaxial compressive strength: (a) Results of the calibration of the shotcrete models based on test data of test series 5 by Huber [15]; (b) Validation of the shotcrete models by means of the data of test series 1 to 4 in [15].

Figure 4

Evolution of the total strain in shrinkage tests: (a) Results of the calibration of the shotcrete models based on test data of test series 4 by Müller [17]; (b) Validation of the shotcrete models by means of the data of test series 3 in [17].

Figure 5

Evolution of the total strain in creep tests on unsealed specimens: Results of the calibration of the shotcrete models based on the test data from creep test series 4/2, load step 1, by Müller [17].

Figure 6

Evolution of the total strain in creep tests on unsealed specimens: Validation of the shotcrete models by means of the test data from creep test series 4/2 by Müller [17].

Figure 7

Evolution of the total strain in creep tests on unsealed specimens: Validation of the shotcrete models by means of the test data from creep test series 4/1 by Müller [17].

Figure 8

Evolution of the total strain in creep tests on unsealed specimens: Validation of the shotcrete models by means of the test data from creep test series 3 by Müller [17].