3D Numerical Modeling of Rigid Inclusion-Improved Soft Soils Under Monotonic and Cyclic Loading—Case of a Small-Scale Laboratory Experiment

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1

Typos and grammar errors should be eliminated in the work. Please check the whole paper carefully.

The authors have carefully checked the typos and grammar errors.

2

What are the limits of applicability or implementation? Any limitations should be included in the article. This helps a reader a lot during the application.

This paragraph is added now in the conclusion part:

The hypoplastic model is a sophisticated model that requires many parameters, some of them are not physical ones and some others are connected. Besides, the adjusting procedure for the parameter’s determination requires a lot of procedures and interrelationships. In this study, due to the lack of laboratory tests some of the required parameters for the intergranular strain concept are assumed. To obtain more accurate results in the numerical analysis, a more accurate calibration of all the input parameters should be done by back analysis of complementary laboratory tests.

3

A table that can summarize/compare the results will be very helpful.

Tables 5 and 6 are added in the article to compare the results in the manuscript:

The two loading cases are compared in Table 5. The pile efficiency in both tests is similar. It means that the cyclic loading range considered does not significantly affect the soil arching development.

A comparison of the two cyclic loading types is presented in Table 6. As it can be seen, the cumulative settlements in the test C2 represent only one third of the C1 test ones. It is because when the loading increases to 30 kPa, the soil pre-consolidation is updated. The following cyclic loading in the C2 test ranges from 10 to 20 kPa and is then within the elastic region. This results in less cumulative settlements induced in test C2 than in C1.

Table 6 also shows that the cumulative settlements obtained considering the CYsoil constitutive model are remarkably higher than the experimental ones after 50 load cycles. They are doubled for C1_D100 and, tripled for C2_D100. The pre-consolidation pressure is not updated in the CYsoil model and its cap still enlarged gradually under the loading cycles number. The cumulative settlements obtained considering the HYP model coincide well with the experimental data in both C1_D100 and C2_D100 tests in terms of values and shape. The HYP model allows to better simulate a preloaded soil in terms of load transfer mechanisms and cumulative settlements, after the first loading cycle. It is due to the fact that after a preloading of 30 kPa, the load cycles in test C2 are in the elastic strain range. The intergranular strain concept permits to simulate them accurately.

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1

Please, under what norms/laws was the experiment done?

The sentences are introduced for explaining why the experiment is done:

The French national project (ASIRI, 2012) studied the soft soil improvement by rigid inclusions technique. However, this research project was mainly concentrated on the system behavior subjected to static loadings. Structures under cyclic loading are commonly encountered in practice. The experiments were done to better understand the soft soil improved by rigid inclusions under monotonic and cyclic loading.

2

Please, give clearer explanations to the numerical results.

Some sentences are added to clarify explanations of the numerical results:

Figure 9 depicts the variation of the soil arching, in terms of pile efficacy, with respect to the load cycles number in the C1_D100 test. In general, the pile efficacy decreases as the number of cyclic loading increases. This tendency was also presented in the study of Heitz et al. (2008), in which the arching ratio reduced from 76% to 56% for 700 load cycles. This can be explained by the grain rearrangement which occurs during the cyclic loading.

As can be seen, the cumulation of settlement with the number of loading cycles is figured out, but the cumulation per cycle reduces gradually with the following cycles, which leads to a decline in the rate of cumulative settlement. The cumulative settlement equals 6 mm after 10 cycles followed by an increase of 4 mm after the following 40 cycles. There is a good accordance between the HYP model and the experimental data in terms of the cumulative settlement. The numerical results of the HYP model for the LTP are more accurate than the CYsoil ones in terms of the cumulative settlements. Considering the non-linearity response in the unloading-reloading process allows the constitutive model to better evaluate the cumulative settlements.

Table 6 shows that the cumulative settlement obtained by the CYsoil model is remarkably higher than that obtained by the experimental one after 50 load cycles, doubled in C1_D100, and tripled in C2_D100. The pre-consolidation pressure is not updated in the CYsoil model and its cap enlarged gradually under the loading cycles number. The cumulative settlement acquired by the HYP one coincides well with the experimental data in both C1_D100 and C2_D100 tests for the value and shape. The HYP model allows to simulate preconsolidated soil in terms of load transfer mechanisms and cumulative settlements, after the first load cycle. This is because after a preloading of 30 kPa, the load cycles in test C2 are in the elastic strain range. The intergranular strain concept permits to simulate them accurately.

3

In the method of research, a more detailed procedures should be give for easy replication of the experiment to confirm the authentication and scientific development of this research.

This article is not dedicated to detail the experimental procedures. These procedures were already presented in Houda (2006) [6]. To clarify the detail of numerical procedures, the introduction part is rewritten, as:

The proposed numerical modeling is performed by the finite element method (FEM) using the ABAQUS software. A representative elementary volume model is suggested for reducing the calculation time. The hypoplastic constitutive model (HYP model) is applied for the load transfer platform (LTP).

The proposed numerical results are compared to the experimental data and the previous numerical results of Houda. The cyclic response of the systems is shown in terms of soil arching and settlements. The decrease in pile efficacy and the cumulative settlements are exhibited. Also, the HYP model in the study permits to better simulate the soil arching mechanisms inside the LTP than the CYsoil model in Houda’s research and permits to obtain a good concordance between the proposed numerical results and the experimental data.