*5.2. Quantitative Evaluation of Discharge of Surplus Soil*

In order to quantitatively evaluate the performance of the discharge of the surplus soil, the volume of the discharging surplus was estimated. The volume of the discharging surplus soil was estimated at the stage of static stirring at the bottom (40 s from 70 to 110 s) after the completion of the penetration and stirring.

The volume of the discharging surplus soil was calculated using the following equation, Equation (10), assuming the flow ratio of the particles that had passed through the cross section:

$$Q = A \cdot v \tag{10}$$

where *Q* is the unit volume, *A* is the cross-sectional area, and *v* is the moving velocity of the particles. Regarding the cross-sectional area, the cross-sectional area through which the particles pass was calculated by subtracting the cross-sectional area of the rod (φ = 440 mm) from the cross-sectional area around the rod (500 mm × 500 mm) and was set to 0.1 m2. For the moving velocity of the particles, the average moving velocity of the particles around the rod (the area surrounded by the black rectangle), shown in Figure 7, was adopted. The average moving velocity of the particles was calculated every 0.1 s, and the unit volume

was calculated every 0.1 s in the same way to estimate the volume of discharging surplus soil for 40 s.

**Figure 7.** Analysis cross section (velocity component in *Z*-axis direction) at stage of static stirring at bottom: (**a**) Stirring wing of NT; (**b**) Stirring wing of DRT.

Table 3 shows the results of calculating the volume of discharging surplus soil. When the stirring wing of the NT was used, the average moving velocity of the particles was very slow, namely, 0.007 m/s. As a result, the total volume of discharging surplus soil over 40 s was 0.026 m3. It can be confirmed that the discharge of surplus soil is rarely performed. On the other hand, when using the stirring wing of the DRT, the average moving velocity of the particles was 0.152 m/s. More particles continued to be discharged when using the stirring wing of the DRT than when using that of the NT, namely, the total volume of discharging surplus soil was 0.609 m3 over 40 s. With the stirring wing of the DRT, about 23 times more surplus soil was discharged than with that of the NT. In this study, the volume of discharging surplus soil was calculated within a limited range and time, so it is possible that the value was smaller than the actual volume of discharging surplus soil. However, because there was a large difference in the volumes of the discharging surplus soil, even under these measurement conditions, it can be said that the stirring wing of the DRT provides an excellent performance in discharging surplus soil.


**Table 3.** Calculation results of volume of discharging surplus soil.

#### *5.3. Comparison of Improved Body due to Different Stirring Wing*

The construction process and quality of the improved body constructed using the stirring wing of the NT and the improved body constructed using the stirring wing of the DRT are compared. Figures 8 and 9 show the analysis cross sections using the stirring wings of the NT and the DRT, respectively. The construction process is described every 20 s in order to compare the construction process of the improved body. It can be seen in these figures that there are no major differences in each construction process. In both cases, penetration and stirring are performed in a columnar shape while injecting the solidifying material at the beginning. After that, stirring is conducted so that the lower part swells from 60 to 100 s. This is thought to be due to the fact that static stirring is performed for 1 min at the bottom and that the surrounding ground is also stirred at the same time due to the viscosity of the ground. Then, from around 120 s, extraction and stirring are started while injecting the solidifying material again. As the solidifying material is injected from the lower part of the stirring wing, in accordance with the rotation of the stirring wing, there are some parts that do not exist in the cross-sectional display, but they are present in the columns as a whole. Therefore, it is unlikely that the quality will vary. In addition, the stirring wing is pulled out of the ground to the ground surface from 140 s to 160 s. At that time, the particles near the ground surface are stirred over a wider area than the particles per 1 m underground. Compared to the inside of the ground, the particles on the ground surface have a higher degree of freedom of movement, and it is thought that the range has expanded due to the large wavy effect.

From the above results, it is thought that the difference the in stirring wings does not affect the construction process of the improved body. However, construction using the stirring wing of the DRT can suppress the discharge of surplus soil and displacement while maintaining the quality of the improved body, but it exists near the ground surface due to the discharge of surplus soil. As the surplus soil contains solidifying material, it is necessary to dispose of it as industrial waste instead of disposing it as residual soil in the usual manner.

#### *5.4. Depth Distribution of Injected Cement Slurry*

In order to compare the distribution of injected cement slurry in the depth direction, the ground at the end of the analysis was divided into depths of 1 m, and the number of cement slurry particles existing in each range was measured. The results are shown in Figure 10. In both cases of the NT and DRT stirring wings, the number of particles present at a depth of 3 to 4 m was the largest, followed by 0 to 1 m, 2 to 3 m, 1 to 2 m, and 4 to 5 m. The reason why many cement slurry particles exist at the depths of 3 to 4 m and 0 to 1 m is considered to be that the operation of the stirring wing is changed (started/stopped). It is thought that this is because the cement slurry particles moved together with the soil particles pushed by the movement of the stirring wing, and the particles stayed due to the stoppage of the stirring wing. In addition, the number of cement slurry particles is extremely small at a depth of 4 to 5 m, but this result is inevitable because only the tip of the stirring wing can reach this region.

**Figure 8.** Analysis cross section of construction using stirring wing of NT.

**Figure 9.** Analysis cross section of construction using stirring wing of DRT.

**Figure 10.** Depth distribution of injected cement slurry particles.

The big difference between the two cases was at the depths of 0 to 1 m and 3 to 4 m. At 0 to 1 m, the number of cement slurry particles increased in the case of the stirring wing of the NT, but at 3 to 4 m, the number of cement slurry particles increased. The reason for this is thought to be an increase in the pressure inside the ground due to the injection of the solidifying material. The cause of the displacement is an increase in pressure inside the ground due to the injection of the solidifying material, and the discharge of surplus soil is performed to release this pressure. In the NT, without the discharge of surplus soil, it is considered that many soil particles and cement slurry particles adhered to the stirring wing due to the increase in pressure and were carried to the ground surface at the same time as the stirring wing was being pulled out. On the other hand, in the DRT, it is considered that the amount of soil particles and cement slurry particles adhering to the stirring wing decreased due to the release of pressure.

The effect of the improved body on the strength characteristics cannot be evaluated by the MPS-CAE analysis used in this study; thus, other treatments, such as curing, are also required. However, it was confirmed that the presence or absence of discharged surplus soil may affect the distribution of the solidifying material. In the future, it will be necessary to clarify this point by conducting strength tests.

#### *5.5. Applicability and Validity of Analysis in Real Fields*

As the subject of this study, the displacement reduction performance of just one improved body was evaluated in this analysis. Therefore, it will be necessary to increase the number of improved bodies and bring them closer to the site construction. The targeted soft ground was expressed here as an aggregate of the same particles, but grounds are originally non-uniform and contain impurities, such as stones and dust. By bringing the ground model settings closer to those of the site ground, it will be possible to perform more practical simulations. The targeted soft ground was set as a columnar region in this study, but site grounds originally exist semi-permanently, and it will be necessary to consider the effects of earth pressure and groundwater in the future. In addition, the validity of these analysis results must be evaluated by conducting an indoor model experiment. When conducting a model experiment, it will be necessary to carry out the experiment under conditions and an environment that imitate those of the targeted soft ground in situ.

Considering the above points, an analysis and model experiment must be carried out in the future that can more closely reflect the conditions of the construction site.

#### **6. Conclusions**

In this study, the performance of a visible and measurable evaluation of the relative stirred deep mixing method was conducted using an MPS-CAE analysis. By visualizing the case using the stirring wing of the NT and the case using the stirring wing of the DRT, the evaluation was performed by comparing the two cases. The results and findings obtained in this study are shown in the following.


**Author Contributions:** Conceptualization, S.I.; methodology, K.N., S.I. and T.T.; software, K.N. and S.I.; validation, S.T. and T.S.; formal analysis, K.N. and S.I.; investigation, T.T., S.T. and T.S.; resources, T.T., S.T. and T.S.; data curation, S.I. and T.S.; writing—original draft preparation, K.N. and S.I.; writing—review and editing, S.I.; visualization, S.I.; supervision, S.I.; project administration, S.I. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data sharing is applicable to this article.

**Conflicts of Interest:** The authors declare no conflict of interest.
