3.1. Calculation Model
The software used in this study is Plaxis (Delft University, Netherlands) and the version is 7.1. The basic characteristics of the creep model of soft foil are as follows: stress-related stiffness; the difference between main loading and unload-reload; secondary compression; memory of pre-consolidation stress; disruptive behavior based on the Mohr-Coulomb criterion; and shallow clay. The parameters of the creep model of soil include dry severe γd, saturation severe γsat, horizontal permeability Kh, vertical permeability Kv, the corrected compression index γ*, modified swelling index k*, correction creep index μ*, cohesion c, friction angle φ, and expansion angle Ψ. The parameter calculation formulas of some individual parameters are as follows:
- (1)
Fixed compression index:
where
is the compression index.
- (2)
Modified swelling index:
where
Cr is the swelling index, and
υur is the unload-reload poison ratio.
- (3)
Fixed creep index:
where
Cα is the creep index.
3.2. Initial Condition
Because this problem relates to plane strain, the construction conditions of the roadbed model are: (1) Considering the settlement after filling, the height of filling plus the settlement are taken as the filling height of the section. (2) The surface of the ground is of free deformation, the left and right horizontal boundaries are subject to constraints, the end of the horizontal and vertical to the boundary are constrained, and the horizontal and vertical displacements are zero. (3) Considering the seepage boundary, the two vertical boundaries are impervious, the bottom layer of the model is sand that is permeable, and the upper boundary is permeable. (4) One metre below the surface of the original ground, the height is 6 m. (5) The creep deformation of soft soil is considered. (6) The models are Mohr Coulomb and Soft Soil Creep.
3.3. Simplified Calculation of the Plastic Drainage Plate
Since the subgrade is considered as a plane strain problem, so the sand is transformed into the sand wall; the sand drain space and permeability coefficient of sand are in equivalent adjustment. After sand-drained ground is adjusted equally to sand wall subgrade, the degrees of consolidation in same depth or average degree of consolidation in any depth should be as equal as possible at any time. Plastic drainage plate uses the equivalent sand-wall method and equals 3D sand-drained ground to 2D sand wall subgrade. As vertical consolidation effects little on the consolidation degree of the sand wall, so the vertical permeability of the sand wall is equal with vertical permeability of undisturbed soil. To reflect the real situation of foundation reinforcement where possible, the principle of equal is used to calculate the half width of equivalent sand wall Bw, and then calculate the half width of sand wall B and horizontal penetration parameter of sand wall khp.
where
rw is the sand well radius (plastic drainage plate equals sand well radius), and
d is the sand drain space (plastic drainage plate equals impacted diameter).
When the plane strain problem of the vertical wall ground is equal with the ax symmetric problem of the sand-drained ground, the principle that the average consolidation degree is equal at the depth of z is used, and then it shows:
To make sure that the plane strain problem of vertical wall ground is equal with the ax symmetric problem of sand-drained ground, then
Brp =
Bra is needed, so:
where
n is the hole diameter ratio;
S is the smear factor;
kh is the horizontal soil permeability;
ks is the horizontal permeability coefficient of the smear zone soil;
rw is the radius of the vertical drain;
rs is the smear zone radius;
re is the valid radius of the effected zone; and
kw is the permeability coefficient of the vertical drain.
The diameter and spacing of the sand well mainly depends on the characteristics of soft soil consolidation and the time requirement. Narrowing the spacing has a better effect than the lagging diameter, in terms of it being good for the sand drain to be both thin and dense in principle. However, the diameter of the sand drain has a certain relationship with the construction method. The hole diameter of the plastic drainage plate is width × thickness (
b ×
δ); the translation diameter is:
where
α is the reduction factor of the drain’s permeable ability under the pressure of the surrounding soil, and would generally be 0.75;
b and
δ are the plastic drainage plate’s width and thickness; and
dw is the equivalent impact diameter.
The plastic drainage plate can be used as a vertical drain, and it can be arranged according to a square, plum shape, or equilateral triangle configuration, among others. An arrangement of squares and triangles are most commonly used. In design calculations, the vertical drain is usually replaced by a cylinder whose effective drainage diameter is
de, and the relationship between
de with vertical drain spacing d is as follows:
where
de is the effective drainage diameter of the drainage body, and
d is the spacing between the drainage.
3.6. Analysis of Numerical Results
According to the finite element simulation, the stress strain diagram is obtained from different stages of the model.
Figure 10 and
Figure 11 show the vertical and horizontal displacement of the cloud 1 year after the preloading of the drainage line model and equivalent sand-wall model.
According to the practical positions of CJ1-1 and CJ1-2 in field, feature points C and H were chosen and the outputs of their vertical displacements are shown in
Figure 12.
As is shown in
Table 7, at 1 year after preloading, as calculated by the drainage line model, the vertical displacement of C is −1465.97 mm, and that of H is −1433.42 mm. If calculated by the equivalent sand-wall model, the vertical displacement of C is −1460.87 mm, and that of H is −1427.22 mm. After 1 year of operation, at the time when construction is completed, as calculated by the drainage line model, the vertical displacement of C is −1502.21 mm, and that of H is −1468.37 mm. If calculated by the equivalent sand-wall model, the vertical displacement of C is −1497.00 mm, and that of H is −1462.17 mm. After operating for 30 years as calculated by the drainage line model, the vertical displacement of C is −1618.49 mm, and that of H is −1581.07 mm. If calculated by the equivalent sand-wall model, the vertical displacement of C is −1612.77 mm, and that of H is −1573.11 mm. According to the project experience, the settlement after operating for 30 years to the time that the road damages are small, the settlement from the time that the operation begins to the time of operating for 30 years is nearly called the settlement after construction. As calculated by the drainage plate model, the settlement after construction of C is 146.18 mm, and the vertical displacement of H is 142.08 mm. If calculated by the equivalent sand-wall model, the settlement after construction of C is 146.64 mm, and the vertical displacement of H is 141.31 mm.
Therefore, using the drainage consolidation method to settle the soft soil embankment can achieve a good reinforcement effect and can effectively reduce the settlement after construction. Meanwhile, it can be seen that, as calculated by the drainage plate model, the settlement of the middle of the embankment is larger than that calculated by the equivalent sand-wall model, but the settlement curves of both models are highly similar. According to
Figure 12, at a height of 7 m, comparing the settlements by the drainage plate model and equivalent sand-wall model at the finish of preloading, 1 year after preloading, and 30 years after operation, shows a high degree of fitting.
The calculation of the soft consolidation of the creep model of soft is taken from the equivalent sand-wall model and drainage line model, and it is feasible to use just the equivalent sand-wall model. According to the analysis in
Figure 12, it can be seen that the maximum settlement of the embankment section happens at abscissa 40~45 m of the model, which is near feature point C. Combined with
Figure 13, this shows that the largest settlement of the section is near the middle of the new embankment. The settlement of the lateral toe of the slope of the new embankment is very small; the lateral toe of the slope of the old flood embankment is slightly uplifted, which means the settlement at the new filled embankment is very large and that makes the settlement at the joint of the old and new embankment very large. Because the old embankment has existed for a long time and has good integrity, the settlement happens at the joint part and the lateral toe of the slope of the old embankment achieves a slight uplift.
According to the positions of the side pile and inclinometer tube that are at locale disposal, feature point A was chosen to output the horizontal displacement and to draw a graph, as shown in
Figure 13. From
Figure 13, we can see that in the beginning stages of setting the drainage plate, the horizontal displacement of A offsets to a positive direction of the model, which is medial of the embankment, while if calculated by the drainage plate model, during the first 35 days—which is after the beginning of the first layer of barged-in fill sand—the horizontal displacement of A offsets to a negative direction of the model, which is lateral of the embankment. The analysis shows that at the stage of setting the drainage plate, because there is suddenly a more vertical drainage channel in the soil, the water in the soft soil is excluded quickly in a short period of time under the pressure of the surrounding soil, which makes the soil in the treatment area compress, and the peripheral soil contract to the center of the embankment. After the beginning of filling, because of the settlement of the upper filled soil, the soft soil under the filling area starts to be squeezed and is extruded to the periphery, and the peripheral soil starts to laterally offset to the embankment. Then, according to
Figure 13, the lateral toe of the old flood embankment G offsets to the direction that deviates from the embankment after the beginning of the construction. As calculated by the drainage line model, the horizontal offset of the toe of the embankment is smaller than that calculated by the equivalent sand-wall model. Meanwhile, because it is affected by construction, the lateral horizontal offset of the new filled embankment offsets to the medial embankment first at the stage of setting the drainage plate, and this is the main reason for the final horizontal offset to be smaller than that of the old lateral embankment.
Figure 14 shows the deep horizontal displacement curves of the toe of the new filled embankment (A) and that of the old embankment (F). The ordinate is the same as that of the calculation model, and is called the WuSong height, which is an elevation system established with the sea level determined by the lowest tide level measured at Wusongkou tide gauge station in Shanghai from 1871 to 1900. From
Figure 14, we can see that the deep horizontal displacement shows an obvious transition and mutant near the interface of all soils, meaning that different prosperities of soil cause different horizontal displacements of different soils. The deep horizontal displacement of the soil under the new filled embankment reaches the maximum at a height of 0 m (nearly 7.5 m from the surface), but the maximal transition and mutant occur at nearly a height of 4 m of the interface, which means the maximal lateral displacement happens in a certain depth of soft soil under the surface. Meanwhile, it can be seen that the change laws of the deep horizontal displacement of the drainage line model and equivalent sand-wall model are very similar, but the horizontal displacement calculated by the drainage line model is relatively small.
3.7. Analysis and Comparison of Field Monitoring Data and Numerical Calculations
Figure 15 shows the contrasting pattern of the field monitoring data and numerical calculation. According to
Figure 15, the settlement dates of the field monitoring data and numerical calculation are similar, which means that using the drainage consolidation method to treat the soft soil foundation achieves a good outcome in practical engineering. The settlement date of the measurement is a little smaller than that of the numerical calculation, and the gap between them increases with time. The reason for the gap is because after a long time of working, the plastic drainage plates plug, fracture and so forth, impacting the normal operation of the drainage plates and causing lower drainage efficiency. However, the reduction of the drainage system efficiency was not considered in the numerical calculation, so the posterior settlement of the measured data is very small.
According to the calculation results, the deep horizontal displacement law obtained from the field monitoring is consistent with the numerical calculation results. Horizontal displacement occurs mainly in silty soft soil. Due to the poor mechanical properties of silty clay, this soil layer also has a certain horizontal displacement. Deep horizontal displacement mainly occurs in the soft soil layer at a certain depth from the surface, which is most likely to be damaged. Therefore, attention should be paid to it, and certain treatment measures should be taken to ensure the safety and stability of the embankment. At the same time, the field monitoring data and the numerical calculation data rule is similar. The pore pressure increases during the loading period and decreases gradually during the interval. After the completion of the construction, the excess pore water pressure gradually dissipates completely with the pre-loading of the reactor, and the pore water pressure remains at a low value and tends to be stable. In summary, the monitoring data of the embankment are consistent with the settlement deformation law of numerical calculation. The numerical simulation calculation is close to engineering practice and has high reliability.
3.8. Settlement Prediction
Generally, primary consolidation is the main part of total settlement. After primary consolidation settlement, when the excess pore water pressure dissipates, and on the condition that effective stress remains still, some soft clay under load will keep settling over time, and this settlement is called secondary consolidation settlement. The reason for secondary consolidation settlement is the rheology of soil, which includes creep deformation, stress relaxation, long-term strength, and the strain rate effect, and creep deformation is the most frequent factor so that deformation of the soil mass increases with time under the action of a constant load. Therefore, secondary consolidation settlement is treated as volume creep of soil.
Figure 16 shows the displacement diagram of the vertical increment of the model of the equivalent sand-wall in the first year of the operation. According to
Figure 16, in the field test, the vertical displacement of soil layers except for the silt layer under the embankment is small. This means that by preloading for a while after construction of the road crust, settlement happens mainly in the silt clay. By analysis of the numerical calculation, the excess pore water pressure is −0.79 kPa after the pavement construction and dissipates to about 0 after that, as the settlement of the silt layer is creep settlement. Because the settlement later happens mainly in silt clay, after operating for 30 years the creep settlement is the same as the settlement after construction, as shown in
Table 8.