3.4 Crack morphology distribution
It can be seen from Fig. 9 that the distribution of crack network is complex and interlaced. For different fiber content and layer thickness, geometric structure characteristics of cracks are different. Soil clods segmented by cracks are obvious without fiber, and the larger the layer thickness is, the larger the average clod area segmented becomes, such as S1, S5 and S9. With the addition of fiber content, due to the inhibition of fiber, the length of crack development is smaller in the process of crack propagation, and crack width is also significantly reduced. While the crack density is significantly increased, and the segmented soil clod is significantly reduced. It is indicated that fiber can inhibit the expansion of cracks to a certain extent, and reduce the length and width of crack propagation.
Figure 10 is the final frequency distribution of crack length. In Fig. 10, it can be seen that the relative frequency distribution range of crack length generally shows a gradually expanding trend with the increase of layer thickness for each fiber content. For example, when fiber content is 0, the relative frequency distribution ranges of crack length of S1, S5 and S9 are 0 ~ 22, 0 ~ 34 and 0 ~ 46 mm respectively. When fiber content is 0.10%, the relative frequency distribution ranges of crack length of S2, S6 and S10 are 0 ~ 38,0 ~ 38 and 0 ~ 70 mm respectively. When fiber content is 0.25%, the relative frequency distribution ranges of crack length of S3, S7 and S11 are 0 ~ 54 mm, 0 ~ 74 mm and 0 ~ 54 mm respectively. When fiber content is 0.50%, the relative frequency distribution ranges of crack length of S4, S8 and S12 are 0 ~ 38 mm, 0 ~ 46 mm and 0 ~ 46 mm respectively. Moreover, the maximum relative frequency of crack length decreases with the increase of layer thickness overall. For example, when fiber content is 0%, the maximum relative frequency of crack length of S1, S5 and S9 decreases, that is, the maximum relative frequency of crack length is 0.377,0.232 and 0.200 respectively. When fiber content is 0.10%, the maximum relative frequency of crack length of S2, S6 and S10 also shows a decreasing trend, that is, the maximum relative frequency of crack length is 0.381,0.324 and 0.300 respectively. When fiber content is 0.25%, the maximum relative frequency of crack length of S3, S7 and S11 decreases, that is, the maximum relative frequency of crack length is 0.399,0.363 and 0.341 respectively. When fiber content is 0.50%, the maximum relative frequency of crack length of S4, S8 and S12 decreases first and then increases slightly, that is, the maximum relative frequency of crack length is 0.502,0.387 and 0.435 respectively (Fig. 11a).
For each layer thickness, the relative frequency distribution range of crack length increases first and then decreases with the increase of fiber content. For example, when layer thickness is 5 mm, the relative frequency distribution ranges of crack length of S1, S2, S3 and S4 are 0 ~ 22, 0 ~ 38, 0 ~ 54, 0 ~ 38 mm respectively. When layer thickness is 10 mm, the relative distribution ranges of crack length of S5, S6, S7 and S8 are 0 ~ 34 mm, 0 ~ 38 mm, 0 ~ 74 mm and 0 ~ 46 mm respectively. When layer thickness is 20 mm, the relative distribution ranges of crack length of S9, S10, S11 and S12 are 0 ~ 46,0 ~ 70,0 ~ 54 and 0 ~ 46 mm respectively (Fig. 10). It is indicated that the increase of fiber content effectively inhibits the extension of cracks along the length direction. The crack resistance of fine-grained coral soil is further improved, thus reducing the relative frequency distribution range of crack length. Furthermore, the maximum relative frequency of crack length increases with the increase of fiber content. For example, when layer thickness is 5 mm, the maximum relative frequency of crack length of S1, S2, S3 and S4 is 0.377, 0.381, 0.399 and 0.502 respectively. When layer thickness is 10 mm, the maximum relative frequency of crack length of S5, S6, S7 and S8 is 0.232, 0.324, 0.363 and 0.387 respectively. When layer thickness is 20 mm, the maximum relative frequency of crack length of S9, S10, S11 and S12 is 0.200, 0.300, 0.341 and 0.435 respectively (Fig. 11b). In addition, through fitting analysis of frequency distribution of crack length, it can be concluded that frequency distribution of crack length of fine-grained coral soil conforms to the Lognormal function, namely
$$y={y_0}+\frac{A}{{\sqrt {2\pi } \omega x}}{e^{\frac{{ - {{\left( {\ln \frac{x}{{{x_c}}}} \right)}^2}}}{{2{\omega ^2}}}}}$$
1
Where y is relative frequency, is crack length, \({y_0}\), \(\omega\) and \({x_c}\)are the fitting parameters.
Figure 12 is the final frequency distribution of crack width. It can be seen from Fig. 12 that under the condition of each corresponding fiber content, the relative frequency distribution range of crack width gradually expands with the increase of layer thickness. For example, when fiber content is 0%, the relative frequency distribution ranges of crack width of S1, S5 and S9 are 0 ~ 0.75, 0 ~ 1.5 and 0 ~ 2.25 mm respectively. When fiber content is 0.10%, the relative frequency distribution ranges of crack width of S2, S6 and S10 are 0 ~ 0.5, 0 ~ 1, 0 ~ 1.75 mm respectively. When fiber content is 0.25%, the relative frequency distribution ranges of crack width of S3, S7 and S11 are 0 ~ 0.5 mm, 0 ~ 0.75 mm and 0 ~ 1.5 mm respectively. When fiber content is 0.5%, the relative frequency distribution ranges of crack width of S4, S8 and S12 are 0 ~ 0.5 mm, 0 ~ 0.5 mm and 0 ~ 1.5 mm respectively. The maximum relative frequency of crack width decreases with the increase of layer thickness. For example, when fiber content is 0%, the maximum relative frequency of crack width of S1, S5 and S9 decreases, that is, the maximum relative frequency of crack width is 0.739,0.341 and 0.294 respectively. When fiber content is 0.10%, the maximum relative frequency of crack width of S2, S6 and S10 decreases, that is, the maximum relative frequency of crack width is 0.990,0.679 and 0.493 respectively. When fiber content is 0.25%, the maximum relative frequency of crack width of S3, S7 and S11 decreases, that is, the maximum relative frequency of crack width is 0.996,0.829 and 0.734 respectively. When fiber content is 0.50%, the maximum relative frequency of crack width of S4, S8 and S12 also decreases, that is, the maximum relative frequency of crack width is 0.999,0.969 and 0.848 respectively (Fig. 13a).
The relative frequency distribution range of crack width decreases with the increase of fiber content for each layer thickness. For example, when layer thickness is 5 mm, the relative frequency distribution range of crack width of S1, S2, S3 and S4 is 0 ~ 0.75, 0 ~ 0.5, 0 ~ 0.5, 0 ~ 0.5 mm respectively. When layer thickness is 10 mm, the relative distribution range of crack width of S5, S6, S7 and S8 is 0 ~ 1.5, 0 ~ 1, 0 ~ 0.75, 0 ~ 0.5 mm respectively. When layer thickness is 20 mm, the relative distribution range of crack width of S9, S10, S11 and S12 is 0 ~ 2.25, 0 ~ 1.75, 0 ~ 1.5, 0 ~ 1.5mm respectively (Fig. 12). It shows that the crack resistance of fine-grained coral soil is improved with the increase of fiber content, which further effectively restrains the development of cracks along the width direction, thus reducing the relative frequency distribution range of crack width.
Moreover, the maximum relative frequency of crack width increases with the increase of fiber content. For example, when layer thickness is 5 mm, the maximum relative frequency of crack width of S1, S2, S3 and S4 is 0.739, 0.990, 0.996 and 0.999 respectively. When layer thickness is 10 mm, the maximum relative frequency of crack width of S5, S6, S7 and S8 is 0.341, 0.679, 0.829 and 0.969 respectively. When layer thickness is 20 mm, the maximum relative frequency of crack width of S9, S10, S11 and S12 is 0.294, 0.493, 0.734 and 0.848 respectively (Fig. 13b). In addition, it can be concluded that the frequency distribution of crack width of fine-grained coral soil also conforms to the Lognormal function relationship through fitting analysis, as shown in Eq. (1).
The direction of crack initiation and propagation affects the shape distribution of cracks. we can better describe the cracking phenomenon and understand the probability of crack development direction selection by studying the distribution law of crack direction. It can be seen from Fig. 14 that the crack direction frequency of S1 is mostly concentrated in 60°~100°, and the relative frequency is 0.377. The crack direction frequency of S2 is mostly concentrated in 0°~10° and 60°~110°, and the relative frequency is 0.075 and 0.348 respectively. The crack direction distributions of S3 and S4 are relatively uniform, and the crack direction frequencies of S4 are concentrated in 0°~20 ° and 150°~180°, with relative frequencies of 0.160 and 0.198, respectively. From the frequency distribution of crack direction of S1 ~ S4, it can be seen that the crack direction changes from relatively concentrated to uniform with the increase of fiber content when layer thickness is 5 mm. Crack directions of S5 are mostly concentrated in 80°~110° and 150°~180°, with relative frequencies of 0.216 and 0.195 respectively. Crack directions of S6 are mostly concentrated in 0°~10 °, 70°~100° and 160°~180°, with relative frequencies of 0.101, 0.244 and 0.166 respectively. Crack directions of S7 are mostly concentrated in 0°~10 ° and 50°~100°, with relative frequencies of 0.079 and 0.359 respectively. The crack direction distribution of S8 is relatively uniform, and it is more concentrated in 60°-100° and 170° -180°, with relative frequencies of 0.273 and 0.069 respectively. It can be seen from the frequency distribution in the crack direction of S5 ~ S8 that the crack direction is more concentrated when fiber content is less, and it gradually becomes uniform with the increase of fiber content at layer thickness is 10 mm. The relative frequencies of S9 are mostly concentrated in 20°~30°, 70°~80° and 140°~150°, and the relative frequencies are 0.081, 0.075 and 0.075 respectively. The relative frequencies of S10 are mostly concentrated in 0°~10°, 70°~120° and 170°~180°, and the relative frequencies are 0.092, 0.412 and 0.075 respectively. The relative frequencies of S11 are mainly concentrated in 0°~10°, 70°~100° and 160°~170°, and the relative frequencies are 0.075,0.271 and 0.080 respectively. The relative frequencies of S12 are mostly concentrated in 0°~10°, 80°~100° and 160°~180°, and the relative frequencies are 0.081,0.163 and 0.133 respectively. When layer thickness is 20 mm, the crack direction is more concentrated when fiber content is small, and it gradually becomes relatively uniform with the increase of the fiber content. The crack direction is random, but generally cracks tend to develop along the horizontal transverse direction and the horizontal longitudinal direction. The increase of fiber content can inhibit the propagation and expansion of cracks to a certain extent, thus affecting the frequency distribution characteristics of crack direction. The specific crack characteristics can be seen in Fig. 15.
It can be seen from Fig. 16 that the relative frequency distribution range of clod area gradually expands with the increase of layer thickness when the fiber content is 0, that is, the frequency distribution ranges of S1, S5 and S9 are 0 ~ 450, 0 ~ 1050 and 0 ~ 3750 mm2 respectively. The maximum relative frequency of clod area decreases with the increase of layer thickness, that is, the maximum relative frequencies of S1, S5 and S9 are 0.997, 0.693 and 0.500 respectively. When fiber content increases to 0.10%, the frequency distribution range of cold area decreases significantly first and then increases with the increase of layer thickness, that is, the frequency distribution ranges of S2, S6 and S10 are 0 ~ 3875, 0 ~ 875 and 0 ~ 1625 mm2 respectively. The maximum relative frequency of clod area decreases with the increase of layer thickness, that is, the maximum relative frequencies of S2, S6 and S10 are 0.920, 0.650 and 0.421 respectively. When fiber content increases to 0.25%, the frequency distribution range of clod area decreases significantly first and then increases with the increase of layer thickness, that is, the frequency distribution ranges of S3, S7 and S11 are 0 ~ 12000, 0 ~ 2000 and 0 ~ 6000 mm2 respectively. The maximum relative frequency of clod area increases significantly and then decreases slightly with the increase of layer thickness, that is, the maximum relative frequencies of S3, S7 and S11 are 0.333, 0.789 and 0.765 respectively. Because crack propagation is strongly inhibited by the fiber, the developed cracks cannot be effectively closed as fiber content continues to increase, resulting in a large difference in the size of clods (Fig. 17). When fiber content is low or no fiber is added, the frequency distribution of clod area conforms to the Lognormal function curve, as shown in Eq. (1).