*3.2. Degradation Analysis of Semi-Permeable Boundary Conditions by the Improved Model*

Gray [20] pioneered the study of the semi-permeable boundary of the consolidation theory model, but the stratum studied was homogeneous. On this basis, Xie [23] studied the theoretical model of double-layer soil consolidation of the semi-permeable boundary. Therefore, we again use the example in Xie's study [23] for analysis. The parameters of example in paper [23] are shown in Table 3.

**Table 3.** Study data of semi-permeable boundary conditions.


Question 3: Under the conditions of an impervious bottom and semi-permeable top, how long will it take for the average consolidation degree of the foundation to reach 70%?

Answer to question 3: According to the data in Table 3, analysis of the double-layer soil consolidation degree is carried out by using the corresponding program compiled by this paper. *c* → 0 can simulate the bottom surface being impervious, but the semi-permeable boundary of top surface is a fuzzy concept. Through repeated debugging of *b* value, it is found that semi-permeable boundary of the top surface can be better simulated when *b* = 10. The obtained results are shown in Figure 4. Using the method provided, the growth rate of the first 50 days is faster than that in Xie's method, and then the consolidation degree gradually became consistent with Xie's, indicating that the method provided is suitable for double-layer soil and the prediction has high accuracy. The time required for

**Layer Layer Thickness** 

*h* **(m)** 

Table 3.

the proposed method and Xie's method to calculate the total average consolidation degree to 70% is 1115 and 1185 days, respectively, and the error is about 6%. The main reasons for the errors are as follows: (1) The proposed method is to control the permeability of the drainage boundary by adjusting parameters *b* and *c*. However, the parameter values do not easily fully correspond to those in Xie's method. (2) The Stehfest algorithm requires fewer parameters and has higher accuracy, but it also has some errors in the inversion process. the method provided is suitable for double-layer soil and the prediction has high accuracy. The time required for the proposed method and Xie's method to calculate the total average consolidation degree to 70% is 1115 and 1185 days, respectively, and the error is about 6%. The main reasons for the errors are as follows: (1) The proposed method is to control the permeability of the drainage boundary by adjusting parameters *b* and *c*. However, the parameter values do not easily fully correspond to those in Xie's method. (2) The Stehfest algorithm requires fewer parameters and has higher accuracy, but it also has some errors in the inversion process.

method, and then the consolidation degree gradually became consistent with Xie's, indicating that

*J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 9 of 18

**Table 3.** Study data of semi-permeable boundary conditions.

**Permeability Coefficient** *k* **(10<sup>−</sup><sup>9</sup>**

Question 3: Under the conditions of an impervious bottom and semi-permeable top, how long

Answer to question 3: According to the data in Table 3, analysis of the double-layer soil consolidation degree is carried out by using the corresponding program compiled by this paper. *c* → 0 can simulate the bottom surface being impervious, but the semi-permeable boundary of top surface is a fuzzy concept. Through repeated debugging of *b* value, it is found that semi-permeable boundary of the top surface can be better simulated when *b* = 10. The obtained results are shown in

Topsoil 3 1 8 Subsoil 3 5 1.6

will it take for the average consolidation degree of the foundation to reach 70%?

**m/s) Compression Modulus** *Es* **(MPa)**

Gray [20] pioneered the study of the semi-permeable boundary of the consolidation theory model, but the stratum studied was homogeneous. On this basis, Xie [23] studied the theoretical model of double-layer soil consolidation of the semi-permeable boundary. Therefore, we again use the example in Xie's study [23] for analysis. The parameters of example in paper [23] are shown in

*3.2. Degradation Analysis of Semi-Permeable Boundary Conditions by the Improved Model* 

**Figure 4.** Consolidation curve for the semi-permeable boundary. **Figure 4.** Consolidation curve for the semi-permeable boundary.

#### **4. Engineering Case Analysis 4. Engineering Case Analysis**

#### *4.1. Project Overview 4.1. Project Overview J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 10 of 18

The Guangxi Binhai Highway is located along the coastline of Beibu Gulf (Figure 5). According to the on-site investigation, the completed survey and design section, the soft land base section exceeds 200 km, accounting for 70% of the total length of the route. The Guangxi Binhai Highway is located along the coastline of Beibu Gulf (Figure 5). According to the on-site investigation, the completed survey and design section, the soft land base section exceeds 200 km, accounting for 70% of the total length of the route.

**Figure 5.** Location of the Guangxi Binhai Highway within China. **Figure 5.** Location of the Guangxi Binhai Highway within China.

on Xiniujiao town to Dafengjiang section of the Guangxi Binhai Highway, with a total length of 10.9 km. The road grade of the project is Grade I, and the width of the roadbed is 24.5 m (Figure 6). Geological research shows that the project section was originally a tidal zone between the high tide and low tide of the sea. After the construction of a flood control seawall, it was gradually reclaimed as paddy fields, shrimp ponds, or dry land. The surface is mostly distributed with typical coastal sedimentary soft soil or soft soil to saturate. Silt clay, silt, and fine sand are the main components, and the coarse sand and gravel sand are partially sandwiched between thin layers or lens bodies.

**Figure 6.** Relying on the engineering location map.

Figure 7 is a picture of the excavation site of marine soft soil.

The Guangxi Binhai Highway starts from Dongxing City, passes through Fangchenggang, Qinzhou, and Beihai, and ends in Shankou. The main line is 314.2 km in length. The project relies on Xiniujiao town to Dafengjiang section of the Guangxi Binhai Highway, with a total length of 10.9 km. The road grade of the project is Grade I, and the width of the roadbed is 24.5 m (Figure 6). Geological research shows that the project section was originally a tidal zone between the high tide and low tide of the sea. After the construction of a flood control seawall, it was gradually reclaimed as paddy fields, shrimp ponds, or dry land. The surface is mostly distributed with typical coastal sedimentary soft soil or soft soil to saturate. Silt clay, silt, and fine sand are the main components, and the coarse sand and gravel sand are partially sandwiched between thin layers or lens bodies. Figure 7 is a picture of the excavation site of marine soft soil. The Guangxi Binhai Highway starts from Dongxing City, passes through Fangchenggang, Qinzhou, and Beihai, and ends in Shankou. The main line is 314.2 km in length. The project relies on Xiniujiao town to Dafengjiang section of the Guangxi Binhai Highway, with a total length of 10.9 km. The road grade of the project is Grade I, and the width of the roadbed is 24.5 m (Figure 6). Geological research shows that the project section was originally a tidal zone between the high tide and low tide of the sea. After the construction of a flood control seawall, it was gradually reclaimed as paddy fields, shrimp ponds, or dry land. The surface is mostly distributed with typical coastal sedimentary soft soil or soft soil to saturate. Silt clay, silt, and fine sand are the main components, and the coarse sand and gravel sand are partially sandwiched between thin layers or lens bodies. Figure 7 is a picture of the excavation site of marine soft soil.

**Figure 5.** Location of the Guangxi Binhai Highway within China.

*J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 10 of 18

exceeds 200 km, accounting for 70% of the total length of the route.

The Guangxi Binhai Highway is located along the coastline of Beibu Gulf (Figure 5). According to the on-site investigation, the completed survey and design section, the soft land base section

**Figure 6.** Relying on the engineering location map. *J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 11 of 18 **Figure 6.** Relying on the engineering location map.

**Figure 7.** Site excavation of marine soft soil. **Figure 7.** Site excavation of marine soft soil.

The consolidation settlement calculation is carried out selecting a section from K8+000 to K9+000. The water table level is 1 m below the original ground line. The upper layer of the section is a crust layer with a thickness of 2–3 m, the high liquid limit soft plastic sand-containing clay has a high compression modulus of 15–20 MPa, and the permeability coefficient is only 3 × 10−6 to 4 × 10−<sup>6</sup> cm/s. The lower layer is a soft soil layer with a thickness of 5–10 m. The compression modulus of the soft soil containing sand is low, only 4.5–8.0 MPa, and the permeability coefficient is only 2 × 10−6 to 3.5 × 10−6 cm/s. The underlying bedrock in the soft soil layer is Indosinian granite. After discussion, it was decided to replace the crust layer with the middle-decomposed granite (*Es* = 1200 The consolidation settlement calculation is carried out selecting a section from K8+000 to K9+000. The water table level is 1 m below the original ground line. The upper layer of the section is a crust layer with a thickness of 2–3 m, the high liquid limit soft plastic sand-containing clay has a high compression modulus of 15–20 MPa, and the permeability coefficient is only 3 <sup>×</sup> <sup>10</sup>−<sup>6</sup> to 4 <sup>×</sup> <sup>10</sup>−<sup>6</sup> cm/s. The lower layer is a soft soil layer with a thickness of 5–10 m. The compression modulus of the soft soil containing sand is low, only 4.5–8.0 MPa, and the permeability coefficient is only <sup>2</sup> <sup>×</sup> <sup>10</sup>−<sup>6</sup> to 3.5 <sup>×</sup> <sup>10</sup>−<sup>6</sup> cm/s. The underlying bedrock in the soft soil layer is Indosinian granite. After discussion, it was decided to replace the crust layer with the middle-decomposed granite (*E<sup>s</sup>* <sup>=</sup> 1200 MPa, *<sup>k</sup>* <sup>=</sup> <sup>5</sup> <sup>×</sup> <sup>10</sup>−<sup>2</sup> cm/s). Figure 8

data and the laboratory soil test data sampled, the data obtained are shown in Table 4. The preloading was then carried out and monitored continuously for 205 days. The upper layer's drainage boundary is neither perfectly permeable nor perfectly impervious (actually, it is a semi-permeable boundary). Due to the strong dispersion of rock and soil, the consolidation settlement of this kind of soft soil foundation can be effectively predicted by adjusting the boundary

**Figure 8.** Schematic diagram of disposal of soft soil foundation by the replacement method.

**Table 4.** Soil parameters of subgrade settlement monitoring section.

layer 3 18.8 20.6 35.7 25.2 18.7 15 3.8 7

layer 7 16.7 45.2 36.7 4.5 8.6 7.0 3.0 6

in - 26 - - 150 45 1200 5 × 104 >50

**Cohesion (kPa)** 

**Friction Angle (°)** 

**Compression Modulus (MPa)**  **Permeability Coefficient (10-8m/s)** 

**SPT** 

**Liquid Limit (%)** 

parameters *b* and *c* in the proposed method.

**Layer** 

Crust

Soft soil

Filling

**Layer Thickness (m)** 

**Bulk Unit Weight (kN/m3)** 

**Water Content (%)** 

MPa, *k* = 5 × 10−2 cm/s). Figure 8 is a schematic diagram of the soft soil foundation treated by the

is a schematic diagram of the soft soil foundation treated by the replacement method. According to the data provided in the geotechnical engineering investigation report of the Soft Soil Foundation Treatment project of Guangxi Binhai Highway area (provided by Guangxi Communication Design Group Co., Ltd., Guangxi, China), in combination with in-situ test data and the laboratory soil test data sampled, the data obtained are shown in Table 4. The preloading was then carried out and monitored continuously for 205 days. The upper layer's drainage boundary is neither perfectly permeable nor perfectly impervious (actually, it is a semi-permeable boundary). Due to the strong dispersion of rock and soil, the consolidation settlement of this kind of soft soil foundation can be effectively predicted by adjusting the boundary parameters *b* and *c* in the proposed method. MPa, *k* = 5 × 10−2 cm/s). Figure 8 is a schematic diagram of the soft soil foundation treated by the replacement method. According to the data provided in the geotechnical engineering investigation report of the Soft Soil Foundation Treatment project of Guangxi Binhai Highway area (provided by Guangxi Communication Design Group Co., Ltd., Guangxi, China), in combination with in-situ test data and the laboratory soil test data sampled, the data obtained are shown in Table 4. The preloading was then carried out and monitored continuously for 205 days. The upper layer's drainage boundary is neither perfectly permeable nor perfectly impervious (actually, it is a semi-permeable boundary). Due to the strong dispersion of rock and soil, the consolidation settlement of this kind of soft soil foundation can be effectively predicted by adjusting the boundary parameters *b* and *c* in the proposed method.

discussion, it was decided to replace the crust layer with the middle-decomposed granite (*Es* = 1200

*J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 11 of 18

**Figure 7.** Site excavation of marine soft soil.

The consolidation settlement calculation is carried out selecting a section from K8+000 to K9+000. The water table level is 1 m below the original ground line. The upper layer of the section is a crust layer with a thickness of 2–3 m, the high liquid limit soft plastic sand-containing clay has a high compression modulus of 15–20 MPa, and the permeability coefficient is only 3 × 10−6 to 4 × 10−<sup>6</sup> cm/s. The lower layer is a soft soil layer with a thickness of 5–10 m. The compression modulus of the soft soil containing sand is low, only 4.5–8.0 MPa, and the permeability coefficient is only 2 ×

**Figure 8.** Schematic diagram of disposal of soft soil foundation by the replacement method. **Figure 8.** Schematic diagram of disposal of soft soil foundation by the replacement method.


**Table 4.** Soil parameters of subgrade settlement monitoring section. **Table 4.** Soil parameters of subgrade settlement monitoring section.
