Introduction
Experimental Study
Materials
Properties | Test method | Value |
---|---|---|
Grain size distribution | ||
Gravel (%) | ASTM D6913 (2017) | 1.6 |
Sand (%) | ASTM D6913 (2017) | 10.8 |
Silt (%) | ASTM D7928-17 (2017) | 37.7 |
Clay (%) | ASTM D7928-17 (2017) | 49.9 |
Consistency limits | ||
Liquid limit, LL (%) | ASTM D4318 (2017) | 52.1 |
Plastic limit, PL (%) | ASTM D4318 (2017) | 22.7 |
Plasticity index, PI (%) | ASTM D4318 (2017) | 29.4 |
Soil class (USCS) | ASTM D2487 (2017) | CH |
Moisture contenta, w (%) | ASTM D2216-19 (2019) | 29.4 |
Liquidity indexa, LI | ASTM D4318 (2017) | 0.23 |
Specific gravity, GS | ASTM C128-15 (2015) | 2.67 |
Unit weighta, γn (kN/m3) | ASTM D7263-21 (2021) | 18.9 |
Activity, A | Skempton (1953) | 0.59 |
Initial void ratioa, e0 | ASTM D2435 (2020) | 0.805 |
Deep mixing equipment
Procedures of DM column installation
Liquidity index, LI | Compression stress (kPa) | Moisture content, w (%) | Unit weight, γn (kN/m3) | Void ratio, e |
---|---|---|---|---|
0.4 | 38.0 | 35 | 18.25 | 0.941 |
0.6 | 18.0 | 40 | 17.65 | 1.087 |
0.8 | 6.0 | 45 | 17.05 | 1.258 |
1.0 | 2.5 | 52 | 16.85 | 1.321 |
Symbol | Definition | Notation | Unit |
---|---|---|---|
BD | binder dosage |
\(\text{BD}=\frac{{M}_{b}}{{V}_{column}}=\frac{{M}_{C}+{M}_{FA}}{{V}_{column}}\)
| kg/m3 |
FA | fly ash replacement ratio |
\(\text{FA}=\frac{{M}_{FA}}{{M}_{b}}\cdot 100=\frac{{M}_{FA}}{{M}_{C}+{M}_{FA}}\cdot 100\)
| % |
SP | super plasticizer ratio |
\(\text{SP}=\frac{{M}_{SP}}{{M}_{b}}\cdot 100=\frac{{M}_{SP}}{{M}_{C}+{M}_{FA}}\cdot 100\)
| % |
W/B | water/binder ratio |
\(\text{W}/\text{B}=\frac{{M}_{W,slurry}}{{M}_{b}}=\frac{{M}_{W,slurry}}{{M}_{C}+{M}_{FA}}\)
| dimensionless |
LI | liquidity index of soil |
\(LI=\frac{w-LL}{\text{PI}}\)
| dimensionless |
aw | binder content |
\({a}_{w}=\frac{{M}_{b}}{{M}_{soil}}\cdot 100=\frac{{M}_{C}+{M}_{FA}}{{M}_{soil}}\cdot 100\)
| % |
VR | volume ratio of slurry |
\(\text{VR}=\frac{{V}_{slurry}}{{V}_{column}}\cdot 100=\frac{{V}_{C}+{V}_{FA}+{V}_{SP}+{V}_{W,slurry}}{{V}_{column}}\cdot 100\)
| % |
WT:WB | total water to binder ratio |
\({\text{W}}_{T}/{W}_{B}=\frac{{M}_{W,mix}}{{M}_{b}}\cdot 100=\frac{{M}_{W,slurry}+{M}_{W,soil}}{{M}_{C}+{M}_{FA}}\cdot 100\)
| % |
LImix | liquidity index of mixture |
\({LI}_{mix}=\frac{{w}_{mix}-PL}{\text{PI}}\)
| dimensionless |
Design of experiments
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Specifying parameters and their limits: The soil consistency and slurry parameters have a decisive effect on DM column performance. The DM machine is forced when the LI of clay is smaller than 0.4. The excess water leaks away from the soil when the LI of clay is greater than 1. Therefore, the LI of untreated clay is between 0.4 (plastic consistency) and 1.0 (liquid state). Slurry parameters are BD, FA replacement ratio, SP content, and W/B ratio. In soil stabilization with the DM technique, Topolnicki (2013) proposed that BD can be between 100 and 500 kg/m3. BD was between 200 and 425 kg/m3. The optimum FA amount in soil stabilization changes between 10% (Sengul et al. 2023) and 40% (Oner et al. 2005; Mir and Sridharan 2013). When the FA content is more than 60%, it causes an early strength problem (Gunasekera et al. 2019; Li et al. 2022). Therefore, FA content was between 0 and 60% to observe the optimum FA replacement ratio. The supplier recommends using 0–5% SP in slurry for economical and effective usage (CHRYSO 2023). The upper limit of W/B is 1.4 (Kitazume and Terashi 2013; Topolnicki 2013). The lower limit of the W/B parameter was determined as 0.8 by Marsh funnel tests (ASTM D6910 2019) because the slurry must have a certain viscosity in order to be injected easily (see Fig. 4).
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Orthogonal array (OA) selection: OA is a mathematical tool used in the Taguchi method to practice numerous parameters minimizing the number of analyses or experiments (Taguchi and Konishi 1987; Taguchi 1988). Taguchi developed many OA tables (L4, L8, L9, L12, L16, L18…L81) depending on the number of parameters and levels in order to minimize the number of experiments and analyses. 1024 (45) designs are required to investigate the effect of all parameters and levels (5 parameters and 4 levels) if an experimental program is created with a full factorial design, which needs all possible combinations of parameters and levels. However, 16 designs are enough in the Taguchi method. DOE was constituted with the L16 (45) OA table comprising 5 controllable parameters (BD, FA, SP, W/B, LI) and 4 levels for each parameter (Tables 4 and 5).Table 4Installation parameters and their levelsParametersLevel 1Level 2Level 3Level 4BD (kg/m3)200275350425FA (%)0204060SP (%)0135W/B0.81.01.21.4LI0.40.60.81.0Table 5DOE with Taguchi’s L16 OADesign NoParameters and their levelsBD (kg/m3)FA(%)SP (%)W/BLI1200000.80.422002011.00.632004031.20.842006051.41.05275011.21.062752001.40.872754050.80.682756031.00.49350031.40.6103502051.20.4113504001.01.0123506010.80.813425051.00.8144252030.81.0154254011.40.4164256001.20.6
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Testing and analyzing: After the installation of DM columns, response characteristics (qu and RI) were determined at different curing periods. Before the statistical analysis, the evaluation of response characteristics to fit any distribution is performed by multiple probability graphs with the help of Anderson-Darling statistics (Anderson and Darling 1952). It is hard to compare design parameters and results because the parameter levels are different in each design in the L16 OA table. Therefore, in the Taguchi method, the effects of parameters and their levels on the results are determined by signal-to-noise (S/N) analysis. The main effect graph obtained from the S/N analysis allows the evaluation of all parameters independently of each other. Taguchi (1988) defined the S/N ratio as the ratio of mean and standard deviation. The value of the S/N ratio is the quality characteristic of the Taguchi method. The S/N ratio is categorized as smaller-the-better, larger-the-better, and nominal-the-better if the response value is minimized, maximized, or nominalized in the optimization process. S/N analysis was performed to maximize the DM column performance (qu and RI) by the larger-the-better case (Eq. 2).where Yi is the response (output) of the i-th experiment and n is the repetition number of response characteristics.$$\text{S}/\text{N}=-10{\text{log}}_{10}\left(\frac{1}{\text{n}}{\sum }_{\text{i}=1}^{\text{n}}\frac{1}{{\text{Y}}_{\text{i}}^{2}}\right)$$(2)
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Optimization and verification: Response characteristics (qu and RI) are statistically evaluated by variance (ANOVA) analysis. Optimum parameter levels were determined by performing multiple-response optimization technique by the desirability function method to maximize qu and RI values for the highest performance of the DM column. Then, the DM column was installed using optimum installation parameters to verify the optimization results.
Testing procedures
Results and Discussions
Slurry properties
Design No | Mix proportions of slurries | Properties of slurries | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Mass of materials (kg) | Volume of materials (× 10-3 m3) | Marsh funnel viscosity (s) | Bleeding (%) | Density (× 103 kg/m3) | |||||||||
C | FA | SP | W | C | FA | SP | W | 15 min | 30 min | 120 min | |||
1 | 11.31 | 0.00 | 0.00 | 9.05 | 3.54 | 0.00 | 0.00 | 9.05 | 34.32 | 2.1 | 3.7 | 16.2 | 1.618 |
2 | 9.05 | 2.26 | 0.11 | 11.31 | 2.83 | 1.06 | 0.11 | 11.31 | 29.68 | 3.7 | 4.9 | 19.5 | 1.485 |
3 | 6.79 | 4.53 | 0.34 | 13.58 | 2.12 | 2.12 | 0.32 | 13.58 | 29.07 | 3.0 | 5.9 | 20.9 | 1.391 |
4 | 4.53 | 6.79 | 0.57 | 15.84 | 1.41 | 3.19 | 0.53 | 15.84 | 29.90 | 3.8 | 8.0 | 30.0 | 1.322 |
5 | 15.56 | 0.00 | 0.16 | 18.67 | 4.86 | 0.00 | 0.15 | 18.67 | 27.19 | 4.0 | 7.4 | 33.0 | 1.452 |
6 | 12.45 | 3.11 | 0.00 | 21.78 | 3.89 | 1.46 | 0.00 | 21.78 | 28.25 | 3.4 | 8.0 | 31.8 | 1.376 |
7 | 9.33 | 6.22 | 0.78 | 12.45 | 2.92 | 2.92 | 0.73 | 12.45 | 39.35 | 1.1 | 2.5 | 8.6 | 1.513 |
8 | 6.22 | 9.33 | 0.47 | 15.56 | 1.94 | 4.38 | 0.44 | 15.56 | 36.31 | 1.6 | 2.8 | 12.8 | 1.415 |
9 | 19.80 | 0.00 | 0.59 | 27.72 | 6.19 | 0.00 | 0.56 | 27.72 | 26.99 | 4.3 | 9.5 | 35.0 | 1.396 |
10 | 15.84 | 3.96 | 0.99 | 23.76 | 4.95 | 1.86 | 0.93 | 23.76 | 28.45 | 3.2 | 6.0 | 22.2 | 1.414 |
11 | 11.88 | 7.92 | 0.00 | 19.80 | 3.71 | 3.72 | 0.00 | 19.80 | 34.65 | 2.8 | 4.0 | 12.8 | 1.454 |
12 | 7.92 | 11.88 | 0.20 | 15.84 | 2.48 | 5.58 | 0.19 | 15.84 | 69.24 | 1.0 | 1.5 | 4.0 | 1.488 |
13 | 24.04 | 0.00 | 1.20 | 24.04 | 7.51 | 0.00 | 1.13 | 24.04 | 28.51 | 2.9 | 4.8 | 16.4 | 1.508 |
14 | 19.23 | 4.81 | 0.72 | 19.23 | 6.01 | 2.26 | 0.68 | 19.23 | 32.98 | 1.3 | 2.4 | 9.2 | 1.561 |
15 | 14.43 | 9.62 | 0.24 | 33.66 | 4.51 | 4.52 | 0.23 | 33.66 | 28.57 | 3.2 | 7.0 | 26.1 | 1.350 |
16 | 9.62 | 14.43 | 0.00 | 28.85 | 3.01 | 6.77 | 0.00 | 28.85 | 31.62 | 2.0 | 3.9 | 15.0 | 1.369 |
Physical properties of DM column
No | aw (%) | VR (%) | WT:WB | LImix | BRN (rev/m) |
---|---|---|---|---|---|
1 | 14.6 | 22.3 | 3.20 | 0.61 | 252 |
2 | 15.6 | 27.1 | 3.56 | 0.87 | 306 |
3 | 16.7 | 32.1 | 3.90 | 1.13 | 363 |
4 | 17.8 | 37.1 | 4.32 | 1.45 | 419 |
5 | 24.5 | 41.9 | 3.32 | 1.46 | 473 |
6 | 22.9 | 48.0 | 3.36 | 1.37 | 542 |
7 | 21.5 | 33.6 | 2.66 | 0.83 | 380 |
8 | 20.0 | 39.5 | 2.75 | 0.79 | 446 |
9 | 27.3 | 60.9 | 2.86 | 1.32 | 689 |
10 | 25.5 | 55.7 | 2.57 | 1.01 | 630 |
11 | 31.2 | 48.1 | 2.67 | 1.39 | 544 |
12 | 29.1 | 42.6 | 2.34 | 1.03 | 481 |
13 | 35.4 | 57.8 | 2.27 | 1.25 | 654 |
14 | 37.9 | 49.8 | 2.17 | 1.26 | 563 |
15 | 30.9 | 75.9 | 2.53 | 1.27 | 858 |
16 | 33.2 | 68.3 | 2.41 | 1.27 | 772 |
Mixing efficiency of DM column
Mechanical properties of DM column
No | qu,s (kPa) | 28 days of curing time | 56 days of curing time | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Na | qu,max/qu,min | COV | qu (kPa) | RI (%) | Na | qu,max/qu,min | COV | qu (kPa) | RI (%) | ||
1 | 74.8 | 10 | 2.5 | 0.28 | 1058.5 | 1415 | 17 | 2.3 | 0.26 | 1625.3 | 2173 |
2 | 45.9 | 11 | 2.1 | 0.17 | 1119.8 | 2440 | 16 | 1.9 | 0.21 | 2065.0 | 4499 |
3 | 25.0 | 15 | 1.8 | 0.38 | 729.2 | 2917 | 14 | 1.9 | 0.25 | 1533.6 | 6134 |
4 | 6.9 | 15 | 1.3 | 0.33 | 491.2 | 7119 | 13 | 1.3 | 0.21 | 641.2 | 9293 |
5 | 6.9 | 17 | 1.2 | 0.14 | 1223.0 | 17,725 | 12 | 1.6 | 0.11 | 1708.1 | 24,755 |
6 | 25.0 | 16 | 1.2 | 0.21 | 1316.1 | 5264 | 14 | 1.2 | 0.22 | 2048.5 | 8194 |
7 | 45.9 | 15 | 2.0 | 0.37 | 1598.8 | 3483 | 17 | 1.8 | 0.24 | 2953.5 | 6435 |
8 | 74.8 | 12 | 2.2 | 0.21 | 1519.5 | 2031 | 16 | 2.1 | 0.21 | 2463.0 | 3293 |
9 | 45.9 | 17 | 1.5 | 0.20 | 1817.3 | 3959 | 18 | 1.6 | 0.17 | 2207.3 | 4809 |
10 | 74.8 | 15 | 1.9 | 0.18 | 2075.0 | 2774 | 19 | 1.7 | 0.20 | 2366.8 | 3164 |
11 | 6.9 | 14 | 1.4 | 0.28 | 1806.7 | 26,184 | 12 | 1.2 | 0.21 | 2813.8 | 40,780 |
12 | 25.0 | 11 | 1.6 | 0.35 | 1765.0 | 7060 | 16 | 1.4 | 0.38 | 2536.0 | 10,144 |
13 | 25.0 | 16 | 2.1 | 0.30 | 2792.1 | 11,168 | 20 | 1.8 | 0.25 | 3041.0 | 12,164 |
14 | 6.9 | 17 | 1.2 | 0.27 | 3269.8 | 47,388 | 19 | 1.2 | 0.19 | 3837.1 | 55,610 |
15 | 74.8 | 14 | 1.7 | 0.34 | 2266.2 | 3030 | 18 | 1.5 | 0.31 | 3456.0 | 4620 |
16 | 45.9 | 13 | 1.3 | 0.15 | 2168.2 | 4724 | 19 | 1.4 | 0.22 | 2429.6 | 5293 |
Statistical evaluations
S/N analysis
ANOVA results
Response | Source | Df | Contribution | F value | P value | Regression Equation | R2 |
---|---|---|---|---|---|---|---|
qu (28 days) | BD | 3 | 84.98% | 498.4 | 0.000 | qu = 1688.5 + 935.6∙BD-88.3∙FA + 145.4∙SP + 234.5∙W/B | 0.998 |
FA | 3 | 5.84% | 34.3 | 0.008 | |||
SP | 3 | 2.17% | 12.7 | 0.033 | |||
W/B | 3 | 6.84% | 40.1 | 0.006 | |||
Error | 3 | 0.17% | |||||
Total | 15 | 100.00% | |||||
RI (28 days) | BD | 3 | 21.50% | 1069.6 | 0.000 | RI−0.14 = 0.31–0.02∙BD + 0.0013∙FA -0.004∙W/B-0.051∙LI | 0.994 |
FA | 3 | 0.97% | 48.5 | 0.005 | |||
W/B | 3 | 1.17% | 58.0 | 0.004 | |||
LI | 3 | 76.33% | 3796.7 | 0.000 | |||
Error | 3 | 0.02% | |||||
Total | 15 | 100.00% | |||||
qu (56 days) | BD | 3 | 65.21% | 72.7 | 0.003 | qu1.57 = 92,073 + 47,613∙BD + 18,294∙FA + 8899∙SP + 21,727∙w/b | 0.991 |
FA | 3 | 13.92% | 15.5 | 0.025 | |||
SP | 3 | 2.78% | 3.1 | 0.189 | |||
W/B | 3 | 17.20% | 19.2 | 0.018 | |||
Error | 3 | 0.90% | |||||
Total | 15 | 100.00% | |||||
RI (56 days) | BD | 3 | 12.42% | 16.6 | 0.023 | RI−0.23 = 0.125–0.01∙BD- 0.005∙FA -0.003∙W/B-0.032∙LI | 0.993 |
FA | 3 | 2.37% | 3.2 | 0.185 | |||
W/B | 3 | 2.11% | 2.8 | 0.209 | |||
LI | 3 | 82.36% | 109.9 | 0.001 | |||
Error | 3 | 0.75% | |||||
Total | 15 | 100.00% |
Optimization and verification
Permeability characteristics
Material | k (m/s) | |
---|---|---|
28 days | 56 days | |
Untreated soil (LI = 1) | 0.529∙10–8 | 0.529∙10–8 |
DM column of design 4 | 2.854∙10–9 | 1.854∙10–9 |
DM column of design 14 | 2.382∙10–11 | 1.182∙10–11 |
DM column of opt. design | 1.612∙10–11 | 0.849∙10–11 |
Consolidation characteristics
SEM characterization
Slurry cost
Method | Mass of materials (kg) | Unit cost ($/kg) | Total cost ($) | Slurry cost ($) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
C | FA | SP | W | C | FA | SP | W | C | FA | SP | W | ||
Cement DM | 425 | - | 12.75 | 340 | 0.1 | - | 0.6 | 0.003 | 42.5 | - | 7.65 | 1.02 | 51.17 |
FA-replaced cement DM | 255 | 170 | 12.75 | 340 | 0.1 | 0.017 | 0.6 | 0.003 | 25.5 | 2.89 | 7.65 | 1.02 | 37.06 |
Conclusion
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Experience in the laboratory has shown that the slurry viscosity should not exceed 70 s for operational tooling safety purposes.
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Super plasticizer does not affect the slurry density substantially, but it reduces the viscosity significantly if water/binder ratio is smaller than 1.2.
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During the installation of the FA-replaced cement DM column, the minimum quantity of mixing process to reach a homogeneously mixed fresh soilcrete depends on the liquidity index (LI) of untreated soil and the volume ratio (VR) of slurry. A key parameter (LI∙VR) is defined to decide a minimum number of mixing processes. The drilling shaft of the DM machine should be penetrated and withdrawn 6, 4, and 2 times in cases where LI∙VR ≤ 0.2, 0.2 < LI∙VR ≤ 0.35, and LI∙VR > 0.35, respectively to obtain a homogeneous mixture. These results lead to a shortening of the installation time of FA-replaced cement DM column in the field. However, the authors recommend testing these findings for different types of soils.
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In the cement DM column installation, the minimum blade rotation number (BRN) should be 252 rev/m. The minimum BRN number of 306 rev/m is sufficient to reach a homogeneous soil-slurry mixture in the FA-replaced cement DM column installation. BRN and VR are in a linear relationship as BRN = 11.3VR.
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The highest performance of the FA-replaced cement DM column was obtained with LImix = 1.25∙LI.
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Optimum installation parameters were determined as binder dosage of 425 kg/m3, FA replacement ratio is 40%, SP content is 3%, water/binder ratio is 0.8, and LI of the untreated soil is 1. In the optimum design, column strength (qu = 4088.5 kPa) and soil improvement ratio (RI = 59,254%) were maximum, permeability coefficient (k = 0.849∙10–11 m/s) and compression index (Cc = 0.048) were minimum. The local site conditions may have a significant role in DM column installation. Therefore, the authors note that the optimal levels of installation parameters may change according to the geological conditions of the field. Additional studies may be required to reveal this problem.
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SEM images prove the increase in column performance due to the cementation products (CSH and CAH gels) formed in the microstructure of the FA-replaced cement DM column depending on the curing time and installation parameters.