The commercial software ABAQUS (Dassault Systemes, 2012) is employed in this study. In consideration of the geometric properties of the geotextile mat dyke, two-dimensional plane strain model is set in the simulation. Full-section models are generated (see Figure 2A ). The bottom boundary of the model is restrained against vertical movement, while the vertical boundaries are retrained against horizontal movement (i.e. U _x = 0 for the left and right sides, and U _y = 0 for the bottom side). Figure 2B illustrated the FE model of the large geotextile mat dyke on the stiff-over-soft soil deposits.

Mohr-Coulomb model is used for the infill sand fill in the dyke, the underlying sand and clay of the foundation, in which five parameters are required: the cohesion (C), the friction angle (φ), Young’s modulus (E), Poisson’s ratio (ν), and the dilatancy angle (ψ). Considering its high permeability, the infill sand is assumed to be fully drained. For the soft clay in the foundation, undrained analysis is set up to account for its low permeability. The saturated unit weight of the fill sand and the ground sand layer are 19.5 kN/m³ and 21 kN/m³, respectively. The saturated unit weight of clay is 17 kN/m³. A conservative analysis is normally considered with undrained condition for soft clay. This is because clay consolidation normally has a minimal effect during the fast construction process of the dyke. The range of the undrained shear strength of clay is set from 2.5 kPa to 25 kPa. The stiffness ratio of E/S _u is kept as a constant of 500 (Tian et al., 2011; Zhou et al., 2013; Zhou et al., 2016). The parameters of all materials involved in this study are selected within practical ranges as shown in Table 1 . The ultimate elongation of the geotextile is defined as 10%. For the geotextile mats, they are modelled as a linear elastic material using 2D continuous truss element which can subject tensional force only. A penalty ratio is introduced to define the interaction between the soil and geogrids. A “hard contact” is adopted in the normal direction (i.e. no penetration is allowed), and penalty algorithm is used to define the tangential friction behaviour (see Dassault Systemes, 2012).

Based on the interface shear tests for all different contacts, friction coefficient of the interface between the infill sand and geotextiles is set as α_s = 0.6. The frictional coefficient of the interface between the layers of large geotextile mats (i.e. geotextile to geotextile) is set as α_g = 0.6. The frictional coefficient of the interface between geotextiles and the foundation is set as α_c = 0.5.

Modified direct shear tests were conducted to obtain these roughness parameters. It is to be noted that the parameters of roughness are obtained from laboratory test for the cases as shown in Figure 1B , which is within the practical arranges reported (Anubhav and Basudhar, 2010; Wang et al., 2022).

To simulate the construction process of the dyke, geotextile mat filled with sand are inactivated before the filling process in the numerical simulation. They are then activated layer by layer until the entire filling process is completed. The load of each mat layer is applied to the FE model when it is activated until the dyke collapses or the geotextiles break. The failure of underlying soft clay and the elongation strain of geotextile exceed 10% are the two criteria for defining the failure of a dyke. When one of these criteria is reached, the failure of the dyke is described with F _s = 1.

The above generated FE model is validated against the centrifuge testing data and numerical simulation results reported by Yan and Chu (2010). Table 1 (Group I) summarizes the parameters used in the validation cases. These previous results were carried out to examine the stability of a dyke on layered clay designed for the land reclamation at Tianjin Port, China. In their study, the foundation soil consisted of three layers of clay. The right side of Figure 3A shows the ultimate settlement contours of the dyke and the underlying soil. The left side of Figure 3A gives the results of this study. A good agreement on the soil settlement underneath the dyke can be found between the results by this study and the data reported by Yan and Chu (2010). In addition, the soil flow in the underly (displacement vector plot) as shown in Figure 3B also show close match between this study and the centrifuge testing results.

To explore the influence of the sand layer thickness below the dykes, t _s, on the failure mechanisms and the corresponding stability of the large geotextile mat dyke, one group of cases are modelled with varying the sand soil layer thickness t _s from 0 m to 10 m, and other parameters are maintained to be the same as t _c = 100 m, E = 20 Mpa, φ _s = 32°, C _s = 0.1 kPa, S _u = 10 kPa, W = 60 m, K = 1/2, J = 140 kN/m (Group III, in Table 1 ). The influence of the sand layer thickness on the limiting fill height of the dykes is shown in Figure 4A . It is clear that, with an increased sand soil layer t _s, the limiting fill height of the dyke increases almost linearly. Figure 4B shows the failure mechanisms of the dyke. A “global failure mechanism” in the foundation of the soil underneath the dyke is mobilized. As the thickness of the sand layer increases, the failure surface in the foundation develops deeper and the larger area of failure zone in the foundation soil is mobilized. A similar observation that the height of the failure zone is proportional to the stiffness of the foundation soil, was obtained from numerical and experimental studies (Rowe and Li, 2005). The bearing capacity of the foundation with sand-overlying-clay soil deposits was also analysed experimentally and numerically by Kenny and Andrawes (1997) and Zheng et al. (2016). It showed that increasing of thickness of the sand layer t _s below the dyke results in a higher bearing capacity.

In order to adapt to the different soil grounds and projects, the width of geotextile mat dykes ranges widely in practice. To further explore the influence of the sandbag width at the base of the dyke – W onto the stability of the large geotextile mat dyke, a group of cases with W = 20 ~ 100 m are conducted, while t _s = 5 m, t _c = 100 m, E = 20 Mpa, φ _s = 32°, C _s = 0.1 kPa, S _u = 10 kPa, K = 1/2, J = 140 kN/m, as tabulated in Group IV, Table 1 .

Figure 5 shows the relationship between the dyke width and the limiting fill height. It can be seen that the limiting fill height, H _max, decreases with the rise of dyke base width. As W increases, the failure surface extends accordingly. However, the increased bearing capacity of the foundation from enlarged failure surface is not proportional to the rise of associated dyke weight due to wider base. As a result, the limiting fill height of the dyke decreases accordingly. Similar conclusion was also reported by Borges and Cardoso (2002), who found that in terms of overall dyke stability, the embankment geometry, namely the B/H relation (the crest width of embankment), strongly influences the failure type, and the probability of occurring a global failure surface is greater when B/H has a small value. It is therefore concluded that increasing sandbag width at the base of the dyke will leads to adverse effect to the maximum filling height.

As demonstrated above, the failure of the dyke is always because of the failure of the soft clay underneath the stiff sand in the foundation, therefore the properties of the soft clay could strongly influence the performance of the dyke. In order to quantify the influence of the clay strength S _u on the failure mechanism and the limiting fill height of the dyke with non-uniform geotextile mats, a group of cases with the shear strength of clay layer varying from 5 kPa to 20 kPa are conducted, and the other parameters are kept constant as t _s = 5 m, t _c = 100 m, E = 20 Mpa, φ _s = 32°, C _s = 0.1 kPa, K = 1/2, W = 60 m, and J = 140 kN/m (Group V, Table 1 ). Figure 6A shows the soil flow mechanisms and failure surfaces for various S _u. It is clear that the soil failure zone reduces in both width and depth with the undrained shear strength S _u increases. Consequently, the limiting fill height of the dyke increases accordingly. In Figure 6B , it is clear that the failure modes of the large geotextile mat dyke with different shear strengths for the underlying clay are almost the same. Therefore, it can be concluded that with the increase of clay strength S _u, the failure surface gradually reduces, and the limiting fill height of dykes increases significantly under the same load. Similar finding was also reported by Rowe and Li (2005) who investigated the influence of the soil strength S _u on the stability of slopes or the traditional dyke (not geotextile mat) over soft clay.

To quantify the influence of the elastic modulus and friction angle of sand layer on the stability of dykes, the limiting fill height of the dykes and instability forms of large geotextile mat dykes, three different elastic modulus and four internal frictions of sand layer are applied. The detailed parameters are shown in Groups VI and VII, Table 1 , and the other parameters are set consistent as t _s = 5 m, t _c = 100 m, C _s = 0.1 kPa, S _u = 10 kPa, K = 1/2, W = 60 m, J = 140 kN/m. The results of the effects of sand properties are shown in Figure 7 . It can be found the sand properties (E and φ _s) have a minimal effect on the limiting fill height and failure mechanism of geotextile mat dykes on sand overlying clay.

The strength of the geotextiles could potentially influence the overall performance of the dyke. To derive an empirical formulae for engineering design, the effect of the tensile stiffness of geotextiles, J, onto the stability of large geotextile mat dykes, a group of cases with different geotextile tensile stiffness J = 50, 140, 200, 500, 1000, and 2000 kN/m, are modelled, and the other parameters are maintained the same as E = 20 Mpa, φ _s = 32°, C _s = 0.1 kPa, S _u = 10 kPa, W = 60 m, K = 1/2, t _s = 5 m, as shown Groups VIII, Table 1 . From Figure 8 , it can be seen that the tensile stiffness of geotextiles has a minimal effect on the limiting fill height. This is because the sand layer is much stiffer than the geotextiles. The geotextile only needs to bear the tensile force induced by the mat. Simply increase the stiffness of geotextiles is not beneficial to improve the bearing capacity of the foundation.

To evaluate the influence of the slope ratio of dykes K on the stability of the dyke, a group of cases with various K = 1/1, 1/2, 1/3 are modelled, while the other parameters are identical as t _s = 5 m, t _c = 100 m, E = 20 Mpa, φ _s = 32°, C _s = 0.1 kPa, S _u = 10 kPa, W = 60 m, J = 140 kN/m (Group IX, Table 1 ). From Figure 9 it can be seen that the slope ratio K has a minimal effect on the limiting fill height and failure modes of the geotextile mat dyke on sand-overlying-clay soil deposits.

The corresponding limiting fill height, H _max, can be analyzed using two non-dimensional parameters: (i) the normalized dyke base width, t _s/W, and (ii) the normalized soil strength γ _s H _max/S _u. Regression analysis is conducted, and Figure 10 shows the fitted result which can be expressed as Equation 1 with R ² = 0.95 for the range of W = 20 ~ 100 m.

For engineering design of the dyke with non-uniform geotextile mats on sand-overlying-soft clay, the safety factor is a key factor to evaluate the stability of dykes. Following the study of Zhang et al. (2015) where the finite element strength reduction method is used to obtain the safety factor F _s to evaluate the stability of the soil slope and the primary factors affecting the safety are the slope height H, slope angle β, cohesion c and friction angle φ that was consistent with the research of Dawson et al. (1999), the safety factors of the geotextile mat dyke with various fill heights from FE results are shown in Figure 11 . Based on the results, an equation can be approximated (with R² = 0.95) as

where the safety factor of the dyke can be design in the range of 0< H< H _max, and the filling height H varies from 2 m to 10 m within practical ranges.