Calibrating the Unit Cell Method for Jet-Grout Column Groups: A Field-Derived Mobilization Factor Approach

Abstract

Predicting the settlement behavior of jet-grout column groups in reclaimed coastal areas remains a significant geotechnical challenge, as conventional models do not capture the complex interaction between isolated stiff columns and the compliance of the composite system under wide-area loading. This study presents a field-calibrated analytical approach that reconciles single-column mechanics with full-scale group performance at a port terminal founded on highly compressible, liquefaction-prone marine backfill improved by 800 mm jet-grout columns. An extensive field-testing program—including cone penetration tests (CPTs), single-column load tests (SCLTs), and surface loading tests (SLTs)—was conducted. SCLT results revealed an elastic modulus exceeding 10 GPa, and CPT data confirmed up to a 250% increase in inter-column soil tip resistance. However, SLTs under an 85 kPa operational load yielded a back-calculated system stiffness of approximately 105 MPa, which is drastically lower than the theoretical unit cell prediction of 933 MPa. This empirical relation demonstrates that unit cell models fundamentally overestimate jet-grout group stiffness. Rather than proposing a site-specific static mobilization factor (β ≈ 0.11), this study introduces a novel, adaptive methodology. By systematically integrating single-column rigidity, group interaction, and stress transfer mechanics into untreated soil, this framework establishes a robust paradigm for accurately predicting composite stiffness and settlements across diverse geotechnical conditions.

1. Introduction

Soil improvement methods, such as compaction, grouting, soil mixing, dewatering, and jet grouting, play a critical role in modern geotechnical engineering [1]. Among these, jet grouting is widely applied due to its suitability for a wide range of soil types [2]. Jet grouting enhances subsoil properties by increasing shear strength and reducing permeability and is widely used in metro stations, tunnels, deep excavations, and coastal infrastructure projects [3]. Jet grouting is recognized for its low noise, low vibration, and high adaptability. It also provides environmental and economic advantages. In addition, it helps control construction-induced settlements [4].

Recent full-scale investigations indicate that system-scale stiffness and settlement response under wide-area loading may differ significantly from the behavior of isolated columns, emphasizing the need for field-calibrated parameters [5]. Field-based numerical studies have shown that the geometry of jet-grout columns and their spatial configuration can significantly influence settlement response and the overall stiffness characteristics of improved ground systems [6,7].

Settlement and bearing capacity evaluation of jet-grouted soils involves both analytical and numerical approaches. Phung and Thao [8] separated bearing capacity into shaft friction and tip resistance components using Plaxis 3D and proposed correction factors to align theoretical predictions with field load test results. Quality verification commonly relies on zone load tests (ZLTs), CPTs, and SPTs, with the deformation modulus back-calculated to assess long-term settlement behavior [9,10,11,12]. Cone penetration testing (CPT) has become a fundamental in situ investigation method for identifying soil behavior and stratigraphic variability in foundation soils. The CPT-based soil behavior type (SBT) framework enables interpretation of in situ soil response. It also provides key parameters for evaluating deformation characteristics and settlement behavior of improved ground systems [13,14].

Group-based field loading tests are particularly important because stiffness parameters derived from single-column tests may not represent the mobilized system stiffness under large-area operational loading [5].

Analytical settlement prediction is commonly based on the unit cell composite stiffness concept proposed by Balaam and Booker [15]. This approach idealizes the column–soil system as a homogeneous medium. However, such simplified approaches have limitations. They cannot fully represent the complex group interaction and load-sharing behavior of floating column groups in soft clay under wide-area loading conditions. Stress distribution with depth and load transfer beyond the column toe are not fully captured by rigid composite assumptions.

Priebe [16] introduced the concept of group efficiency to adjust analytically derived stiffness for better representation of field-scale behavior. While group efficiency is widely used for bearing capacity, recent studies indicate that it cannot be directly applied to settlement-based stiffness mobilization under serviceability loading conditions [6]. Recent studies have emphasized that design approaches primarily developed for bearing capacity evaluation may not fully represent the stiffness mobilization governing settlement behavior of column-reinforced ground. This discrepancy highlights the need to define settlement-oriented stiffness parameters for floating column systems [17,18]. Numerical analyses confirm that column spacing, interaction effects, and site conditions significantly influence settlement performance [19,20].

Despite these developments, there is insufficient research on site-specific calibration of jet-grout settlement predictions. Although group efficiency factors exist for bearing capacity evaluation, a unified stiffness mobilization factor for the settlement analysis of jet-grout columns under large-area loading is not provided in current design codes.

Accordingly, this study investigates a port terminal project where jet grouting was applied to reinforce cohesionless backfill, focusing on the discrepancy between analytically predicted and field-measured settlement behavior under operational loading.

Building upon the unit cell composite stiffness formulations of Balaam and Booker [15] and the group efficiency principles proposed by Priebe [16], this study extends beyond the conventional derivation of a modified design modulus. Rather than merely extracting an empirical reduction factor (β) to force-fit analytical discrepancies, this research introduces a fundamentally new analytical methodology. This advanced framework systematically quantifies scale effects, the deep penetration of stress bulbs into the underlying untreated soil, and the complex, partial mobilization of column stiffness under wide-area loading. This approach shifts the focus from static calibration to integrated analysis. It provides a framework for reconciling analytical predictions with the composite behavior observed in the field.

To validate this novel methodology, the research leverages a comprehensive, five-year evaluation of jet-grouting performance in a highly compressible port terminal backfill. The empirical framework combines theoretical analysis with extensive post-construction in situ testing. These include ZLTs, surface load tests (SLTs), CPTs, single-column load tests, and long-term geodetic monitoring. While the findings definitively elucidate settlement behavior, liquefaction mitigation, and load-bearing dynamics, the ultimate contribution of this study lies in its methodological evolution. Instead of proposing a site-specific, field-derived mobilization factor to merely patch the traditional unit cell method, this study establishes an adaptive, universal framework. This proposed methodology effectively bridges the critical gap between simplified analytical assumptions and complex, full-scale system mechanics, providing a robust, highly scalable tool for accurate settlement prediction across diverse and marginal geotechnical environments.

2. Materials and Methods

2.1. Site Description and Soil Conditions

The terminal reclamation area was divided into three zones. Zone III (landside) consisted of a former reclamation, whereas Zone I (seaside) was filled with rock fill ranging from 0.1 to 400 kg following dredging. Zone II, located between them, consisted of dredged sand from Zone I and imported granular fill below +1.00 m elevation. Existing levels ranged from −12 m to +2.0 m. The upper 0.93 m comprised paving base layers. Embankment and capping fill (from dredged or imported materials) were placed between +1.0 m and +2.47 m. The final terminal level was +3.40 m and was designed to support a container loading of 40 kPa.

Zone II was further divided into Zones II-A and II-B. This study focuses on Zone II-A (~16.000 m²), covering offshore and onshore sections. Boreholes (FMDBH-01 to -05) and CPT soundings (CPT1–5, CPT10–14, CPT22–37) were conducted in this area.

The subsurface layers comprise Quaternary alluvial deposits of varying ages. The younger alluvial deposits include loose to medium sands and low-plasticity silty clays, whereas the underlying older alluvial deposits contain very stiff clays, dense sands, and hard silty clays. Borehole logs and CPT cross-sections indicate significant stratigraphic variability. The younger alluvial deposits were most relevant for settlement analysis, as deeper layers were less affected by applied loading. Based on investigation data, soils were classified as Type A (loose–medium gravelly sand), Type B (stiff clay/silt with sand/gravel lenses), and Type C (medium-dense to very dense silty sand and gravel). Figure 1 presents the general characteristics of Reclamation Zone II-A.

Settlement was estimated using Serviceability Limit State (SLS) criteria. For sand fill and slurry layers, modulus of elasticity (Ed) or volume compressibility (mv) values were derived from SPT correlations and plasticity index according to Stroud [22]. In the absence of direct data, conservative values reported in geotechnical assessment reports [23,24] were used (

Table 1. Representative values for soil parameters [23].

Unit	Soil Type	γsat (kN/m3)	Ed (MPa)	Ca (-)	Cv (m2/year)	mv (m2/MN)
-	Granular fill	19	8	-	-	-
-	Sand fill from dredging	20	4	-	-	-
-	Slurry material	19	-	-	-	0.50
A	Sand	20	5	-	-	-
B	Clay/Silt	19	10–40	0.003	1.2	0.20–0.10
	Sand/Gravel	21	10–50	-	-	-
C	Sand	22.5	10–50	-	-	-
	Silt	19	10–40	0.003	1.2	0.033
	Clay	19	10–40	0.003	1.2	0.033

γ_sat: Saturated unit weight (kN/m³), E_d: Modulus of elasticity for soil (MPa), C_a: Creep coefficient (-), C_v: Coefficient of vertical consolidation (m²/year), m_v: Coefficient of volume compressibility (m²/MN).

).

The overall methodological framework adopted in this study is illustrated in Figure 2, showing the progression from site characterization and analytical assessment to field validation and β-based interpretation of jet-grout column group behavior.

2.2. Analytical Settlement and Liquefaction Analyses

Fill placement increased vertical stress, causing settlements in both the underlying strata and new reclamation fill. Immediate, primary, and secondary settlements under pavement, stacking, and reclamation loading were evaluated. Analyses conducted at each borehole in Zone II-A were used to estimate maximum and minimum deformations. Three loading cases were assessed: (1) fill self-weight, (2) 50 kN/m² from embankment and pavement loads, and (3) 40 kN/m² from container stacking (Figure 3).

Settlement calculations ensured compliance with the design limits. These were defined as 135 mm over 20 years and 50 mm over 2 years post provisional takeover. Reclamation used dredged sand (Unit A) and/or imported granular fill up to +1.0 m elevation, followed by ground improvement. Pavement layers were placed to reach the final ground level +3.40 m FGL. Embankment fill was compacted to 95% Standard Proctor density to prevent excessive settlement and ensure long-term pavement serviceability. As the exact fill type was unknown during initial design, geotechnical parameters were assumed using SPT correlations. The sand-dominant fill was placed by tipping into water. It was not compacted in layers. Settlement under self-weight was estimated using BRE 424 [25] (Equation (1)). Immediate settlement (Si) of shallow foundations was assessed using modulus values derived from SPT N-values and elastic theory [26]. Ishihara and Yoshimine [27] related settlement to maximum distortion and initial relative density.

$$S_{max}={\displaystyle \frac{0.3\gamma H^2}{E_d}}$$

(1)

• S_max: Maximum settlement of the sand fill.
• $\gamma$: The bulk density (kN/m³).
• H: The height of fill (m).
• $E_d$: The constrained modulus (MPa).

The primary settlement of the sand fill and/or imported granular fill material due to surcharge loads (embankment and pavement loads) and container loads was calculated using the elastic method with Equation (2).

$$S_p={\displaystyle \frac{∆\sigma }{E_d}}H$$

(2)

• $S_p$: Total primary settlement (m).
• Δσ: Stress increase (MPa).
• E_d: The constrained modulus (MPa).
• H: The total average thickness of sand/gravels layers (m).

The secondary settlement of the sand fill and/or imported granular fill material due to a post-construction container stacking load of 40 kPa was presumed to be of the creep type. The S_creep has been calculated with Equation (3).

$$S_{creep}={\displaystyle \frac{\alpha H({\log t}_2-{\log t}_1)}{100}}$$

(3)

• S_creep: The secondary settlement due to creep (m).
• α: The creep coefficient and was assumed to be 0.5%.
• H: The layer thickness (m).
• t₁: The construction period.
• t₂: The design period.

The creep compression rate (α) was conservatively taken as 0.5%, according to BRE 427 [28]. Due to erratic stratification, each borehole was analyzed separately. Settlement due to self-weight, immediate effects, and creep was calculated for all boreholes. Settlement of the sand fill due to its own weight, as well as the immediate and creep settlements for borehole FMDBH03, are presented in

Table 2. Self-weight, immediate, and creep settlements (FMDBH03, before improvement).

Description		Top Layer	Thickness (m)	∆σ + 50 (kPa)	Ed (kPa)	mv	Stotal (1) (mm)	Stotal (2) (mm)	Stotal (3) (mm)
New surface level		3.40	1.31
Embankment fill		2.09	1.09
0–63 mm fill > GWL		1.00	0.91	53.65	8000		7.2	12.9	16.5
0–63 mm fill < GWL		0.09	5.00	89.79	8000		64.2	90.3	110.0
Dredged sand		−4.91	1.00	117.29	<1000		30.5	41.2	45.1
Unit A	SAND	−5.91	2.50	134.79	5000		67.4	87.4	87.4
Unit B	SAND	−6.91	2.50	161.04	14,000		28.8	35.9	35.9
	CLAY	−8.41	1.00	179.29		0.0001	21.5	23.0	25.4
	CLAY	−9.41	2.00	192.79		0.0001	45.8	48.8	53.5
	CLAY	−11.41	2.50	213.04		0.0001	62.3	66.0	71.9
	CLAY	−13.91	2.00	233.29		0.0001	53.9	56.9	61.6
Unit C	SAND	−15.91	0.95	248.23	30,000		8.0	9.0	9.0
End of profile		−16.86             Total (mm)					389.5	471.4	516.3

(1) Construction period (1.5 years): Settlement induced by the self-weight of the reclamation fill and an additional 50 kPa surcharge from embankment fill and pavement. (2) Post-construction period (2 years): Settlement under a 40 kPa container load applied at the terminal stacking area. (3) Post-construction period (20 years): Settlement under sustained 40 kPa container load at the terminal stacking area, including creep (secondary compression) effects.

(before improvement) and

Table 3. Self-weight, immediate, and creep settlements (FMDBH03, after improvement).

Description		Top Layer	Thickness (m)	Stotal (1) (mm)	Stotal (2) (mm)	Stotal (3) (mm)
New surface level		3.40	1.31	0.00	0.00	0.00
Embankment fill		2.09	1.09	0.00	0.00	0.00
0–63 mm fill > GWL		1.00	0.91	1.12	1.61	3.04
0–63 mm fill < GWL		0.09	5.00	12.77	10.51	18.39
Dredged sand		−4.91	1.00	2.38	2.40	3.97
Unit A	SAND	−5.91	2.50	3.55	4.60	4.60
Unit B	SAND	−6.91	2.50	4.24	5.29	5.29
	CLAY	−8.41	1.00	4.71	2.20	4.57
	CLAY	−9.41	2.00	9.55	4.54	9.27
	CLAY	−11.41	2.50	12.19	5.92	11.83
	CLAY	−13.91	2.00	9.95	4.94	9.67
Unit C	SAND	−15.91	0.95	2.00	3.00	3.00
End of profile		−16.86	Total (mm)	62.46	45.01	73.63

(1) Construction period (1.5 years): Settlement induced by the self-weight of the reclamation fill and an additional 50 kPa surcharge from embankment fill and pavement. (2) Post-construction period (2 years): Settlement under a 40 kPa container load applied at the terminal stacking area. (3) Post-construction period (20 years): Settlement under sustained 40 kPa container load at the terminal stacking area, including creep (secondary compression) effects.

(after improvement).

The consolidation settlements are calculated using the coefficient of volume compressibility m_v with Equation (4).

$$S_c={\sum }_{i=1}^n{m}_v∆\sigma H_i$$

(4)

• S_c: The consolidation settlement (m).
• m_v: Coefficient of volume compressibility of the layer (1/MPa).
• Δσ: Stress increase (MPa).
• H_i: Thickness of the layer (m).

The clay layers (Units B and C) were considered over-consolidated in this study. Therefore, settlement was calculated using the total layer thickness. The layer was not divided into sub-layers. For the granular soil layers, the immediate settlements were calculated using Equation (5).

$$S_i={\displaystyle \frac{∆\sigma }{E_d}}H$$

(5)

• S_i Total immediate settlement (m).
• Δσ: Stress increase (MPa).
• E_d: Constrained modulus (MPa).
• H: Total average thickness of sand/gravel layers (m).

The settlement resulting from a 40 kPa container loading was determined. Primary settlement was calculated using Equation (4). Secondary settlement for the clay layers (Units B and C) was calculated using Equation (6). The time required for 100% consolidation (hydrodynamic period) was calculated assuming two-way drainage in the clay/silt layers.

$$S_{creep}=C_{\alpha }H({\log t}_2-{\log t}_1)$$

(6)

• S_creep: Secondary settlement (m).
• C_α: Creep coefficient and has been assumed to be 0.003 [29].
• H: Layer thickness (m).
• Log t₁: Time required for 100% primary consolidation settlement.
• Log t₂: Time for creep settlement estimation, for present case it has been taken as 20 years.

In the present analysis t₁ = 1.5 years and t₂ = 21.5 years are considered.

Settlement calculations assumed a 1.5-year duration for filling and construction. Secondary settlement was evaluated for the periods of 1.5–3.5 and 1.5–21.5 years from the start of construction. A uniform 40 kPa container load and a groundwater level at +0.402 m (mean sea level) were used. The results indicated the need for ground improvement (

Table 4. Settlement calculation results based on borehole data.

No.	Description	Borehole No.
		FDMHB01	FDMHB02	FDMHB03	FDMHB04	FDMHB05	Aver.
1	Immediate settlement during construction period (mm)	259	202	206	291	113	214
2	Consolidation and creep settlement during construction period (1.5 years) (mm)	-	50	184	347	385	242
1	Post-construction immediate settlement (mm)	320	251	263	363	152	270
2	Post-construction consolidation and creep settlement (2 years) (mm)	17	70	208	398	413	221
3	If soil improvement is not done total settlement in 2 years (mm)	337	321	471	761	565	491
1	Post-construction immediate settlement (mm)	320	251	263	363	152	270
2	Post-construction consolidation and creep settlement (20 years) (mm)	52	108	253	444	456	263
3	If soil improvement is not done total settlement in 20 years (mm)	372	359	516	807	608	533

).

Table 3 presents various scenarios. The main contributor to settlement is the fill’s self-weight. Without soil improvement, total settlement—including post-construction creep after 2 and 20 years—is presented in lines two and three.

2.3. Liquefaction Assessment Based on SPT and CPT Data

The site is located very close (around 3.5 km) to the North Anatolian Fault Zone and is therefore situated in a highly seismic region. Therefore, soil improvement of the reclamation fill was required to mitigate this risk. The liquefaction risk for clean sand was evaluated using Cliq v.1.7.6.34-liquefaction assessment software [30] considering cyclic stress ratio (CSR) as a function of SPT blow count proposed by Seed et al. [31] (Equation (7)).

$$CSR={\displaystyle \frac{{\tau }_{seismic}}{{\sigma }_{vo}^{\prime }}}=0.65{\displaystyle \frac{a_{max}}{g}}{\displaystyle \frac{{\sigma }_{vo}}{{\sigma }_{vo}^{\prime }}}{r}_d$$

(7)

a_max is the maximum ground surface acceleration in gals; g is the acceleration due to gravity; σ_vo is the total overburden pressure at the depth under consideration. Seed and Idriss [32] developed a simplified procedure for estimating τ seismic for depths less than 15 m. The relationship between S_u/σ’_vo, (i.e., cyclic yield strength) and standard penetration blow count is given by Equation (8) as

$$CRR=⌊{\displaystyle \frac{S_u}{{\sigma }_{vo}^{\prime }}}⌋=0.011({N_1)}_{ 60}$$

(8)

CRR curves in Cliq v.1.7.6.34 assume clean sand conditions. For soils containing fines, SPT blow counts must be corrected. The clean sand correction was applied to adjust (N₁)₆₀ for fines by using Equation (9) developed by Idriss and Boulanger (2008) [33].

(N₁)_60cs = (N₁)₆₀+ Δ(N₁)₆₀

(9)

The factor of safety against liquefaction (F_s) for each soil layer was calculated using Equation (10) to obtain values consistent with the safety requirements of the relevant structure type.

$$F_s=⌈{\displaystyle \frac{CRR}{CSR}}⌉$$

(10)

• CRR: Resistance ratio for liquefaction.
• CSR: Stress ratio from design earthquake.

Liquefaction risk was assessed for Units A, B, and the fill material. The results for borehole FMDBH01 are presented in

Table 5. Summary of liquefaction analysis of Zone II-A.

No	Depth (m)	Fines %	u0 (kPa)	σv (kPa)	σ’v (kPa)	N SPT	rd	CN	CR	CB	Cs	CE	N1(60)	N1(60)cs	CRR	CSR	F.S.	Layer
FMDBH01	0.5	1	0	10	10	20	1	1.7	0.75	1	1	0.75	19	19	4	2	2	Imported Fill Granular Fill
	1.5	0	0	30	30	7	1	1.7	0.8	1	1	0.75	7	7	0.1	0.24	0.42
	3	0	14.72	60	45.28	6	0.98	1.61	0.85	1	1	0.75	6	6	0.09	0.32	0.29
	4.5	2	29.43	90	60.57	3	0.97	1.4	0.95	1	1	0.75	3	3	0.08	0.36	0.21
	6	1	44.15	120	75.85	4	0.95	1.2	0.95	1	1	0.75	3	3	0.08	0.38	0.2
	7.5	0	58.86	150	91.14	7	0.93	1.06	0.95	1	1	0.75	5	5	0.09	0.4	0.22
	9	11	73.57	180	106.43	2	0.91	0.96	1	1	1	0.75	1	3	0.08	0.4	0.19	Dredged
	10.5	7	88.29	210	121.71	13	0.89	0.9	1	1	1	0.75	9	9	0.11	0.41	0.27	Unit A
	12	45	103	241.5	138.49	6	0.87	0.82	1	1	1	0.75	4	10	0.12	0.4	0.29	Unit B
	13.5	22	117.72	273	155.28	9	0.84	0.77	1	1	1	0.75	5	10	0.12	0.4	0.30
	15	37	132.43	306.75	174.32	50	0.82	0.82	1	1	1	0.75	31	37	1.75	0.43	2.00	Unit C

. Both SPT and CPT data were utilized, and correlations between the two datasets were established. Liquefaction assessments based on SPT N-values and CPT data obtained from FMDBH01 and CPT-1 are presented in Figure 4.

Settlement and liquefaction analyses showed that soil improvement was necessary due to excessive settlement.

2.4. Jet-Grouting Method Selection, Column Bearing Capacity, Application Parameters, Column Layout

The terminal yard was designed for container storage and movement, with additional areas for service buildings, equipment, and truck parking. Interlocking block pavement was planned for the stacking zone. Estimated settlements exceeded allowable limits, and liquefaction risk was present. Therefore, soil improvement was deemed necessary. Due to high groundwater levels and variable soil conditions, a flexible improvement method was needed. Jet grouting was recommended as the optimal method, as it can be adapted to varying soil thicknesses on site. High-pressure grout injection creates soilcrete columns with significantly higher undrained shear strength than the natural soil. These stiff columns enhance vertical resistance. Embankment fill and pavement layers distribute loads over the jet-grouted ground.

The ultimate bearing capacity of jet-grouted columns is derived from a combination of shaft friction and end bearing. For the preliminary static design in Zone II-A, column lengths were determined based on stratigraphy, and the ultimate shaft friction (fs) was calculated using Equation (11).

$$f_s={\sigma }_{vo}^{\prime }{K}_{s}tan\delta$$

(11)

• f_s: Frictional resistance of the jet-grout columns.
• K_s: Effective soil pressure coefficient (equal to Ks to 1.8Ks where Ks = (1 − sin ϕ*).
• σ’_vo: Effective vertical stress at the depth under consideration.
• δ: Soil steel friction angle (approximately 0.5 to 0.8 ϕ′).

Total shaft friction is calculated with Equation (12).

$$Q_s=D\pi L{f}_s$$

(12)

Considering a column with length (L) and diameter (D), its theoretical ultimate capacity parameters are summarized in Table 5. The ultimate end-bearing capacity (Qa) of jet-grout columns can be calculated using Equation (13):

$$Q_a={\sigma }_V^{\prime }{N}_q{A}_p$$

(13)

• Qa: Total end-bearing capacity.
• Nq: Bearing capacity factor (function of shear resistance angle is given 81.3 for ϕ = 40-Unit C).
• σ’_v: Effective vertical stress at the jet-grout column toe.
• Ap: Area of jet-grout base.

Down drag (negative surface friction) from consolidation in compressible layers increases pile load and is calculated using Equation (14).

$$f_{neg}=\beta p_0$$

(14)

where p₀ is the effective overburden pressure and β is a reduction factor shown by Meyerhof [34] to be equal to 0.3 for piles up to 26 m length. The total negative friction at various depths is calculated using Equation (15).

$$Q_{neg}=D\pi L{f}_{neg}$$

(15)

The preliminary calculations for theoretical capacity and negative friction are summarized in

Table 6. The bearing capacity of jet-grout columns.

Zone No	JG Column Length (m)	Proposed JG Column Diameter (m)	Shaft Friction of the Column (fs) (kPa)	Total Shaft Friction (σs) (kN)	Total End Bearing (Qa)/Factor of Safety (Fs) (kN)	Negative Skin Friction of the Column (fneg)	Total Negative Friction (σneg) (kN)
Section 1	16	0.80	15.20	611	1734	19	760
Section 2	18	0.80	17.10	773	1951	22	990
Section 3	20	0.80	19.00	955	2168	24	1200
Section 4	22	0.80	20.09	1110	2385	26	1430
Section 5	24	0.80	22.80	1375	2602	29	1740
Section 6	26	0.80	24.70	1613	2818	31	2015

.

The design aimed to transfer embankment, pavement, and container loads to sound layers beneath soft fill via jet-grout columns. Column configuration is based on bearing capacity, calculated from unconfined compressive strength tests of trial columns, with a minimum strength of 4 MPa [35]. Equations (16) and (17) are used for the bearing capacity calculations.

$$Q_{net}=q_{u}A=4\times 0.5=2 \mathrm{M}\mathrm{N}=2000 \mathrm{k}\mathrm{N}$$

(16)

$$Q_{allowable}={\displaystyle \frac{Q_{net}}{FS}}={\displaystyle \frac{2000}{3}}=667$$

(17)

• Q_net: Net ultimate capacity (kN).
• q_u: Ultimate unit bearing capacity.
• FS: Factor of safety.
• Q_allow: Allowable column capacity (kN).
• A: Tributary area supported by one column (m²).

Hence, the proposed grid system for jet-grout columns is calculated using Equation (18), which represents the ratio of the allowable bearing capacity of a jet-grout column to the total load transferred to that column.

$$The grid system s=\sqrt{A}=\sqrt{{\displaystyle \frac{Qallow}{q}}}=\sqrt{{\displaystyle \frac{667}{90}}}=2.7 \mathrm{m}$$

(18)

• s: Column spacing (m).
• q: Applied pressure (kPa).

Although the theoretical shaft friction and end bearing provide vast ultimate reserves (Table 5), the operational structural capacity of the 800 mm jet-grout column is conservatively limited to 667 kN. The 90 kPa maximum service load is safely supported within this limit. Columns were spaced on a 2.4 m × 2.4 m grid, ensuring that the distributed stresses are adequately supported while remaining strictly within the elastic, serviceability-controlled range governed by stiffness mobilization rather than ultimate bearing failure.

Jet grouting in Zone II began at the existing ground level (+2.09 m CD) prior to embankment fill construction. No grouting was performed between +2.09 m and +1.0 m CD (embankment fill level). Column lengths varied but were generally extended and socketed into the very dense clayey sand beneath dredged sand, imported fill, slurry, and soft clay layers. Settlement and liquefaction analyses were performed for both the new and existing reclamation areas. Based on these results, jet grouting was implemented in accordance with established standards. These include the Geo-Institute of the ASCE Grouting Committee guidelines [36] (2009), BS EN 12716:2001 [37] and ASTM D1143 [38], for load testing.

Jet grouting involves drilling a vertical bore using a high-pressure water jet. Cement grout is then injected through nozzles while the monitor is rotated and withdrawn. Nozzle pressure reaches 350–400 bar, with withdrawal speed around 50 cm/min depending on soil conditions. Cement fineness (Blaine) should exceed 2800 cm²/g and a 1:1 cement-to-water ratio is commonly used and monitored during construction. Ground improvement by jet grouting was planned for Zone II-A after trial works finalized the grout type. Zone II-A slopes to a water depth of approximately 12.5 m. The sea bottom is covered by 1–4.5 m of loose/medium sand (Unit A), overlain by 2–20.5 m of soft to medium soil (Unit B). After land filling to +1.00 m, jet-grout columns were extended into the very dense clayey sand (Unit C). Based on boreholes (FMDBH1–FMDBH5) and CPTs, Zone II-A was divided into six sections according to the depth of very dense clayey sand (SPT N > 30). Maximum jet-grout column lengths ranged from 16 m in Section 1 to 26 m in Section 6. The general layout and typical cross-section of the jet-grouting design in Zone II-A are given in Figure 5.

2.5. Post-Improvement Settlement and Liquefaction Assessment of Treated Soils

Settlement analysis for Zone II-A was updated using principles presented in Table 2. After ground improvement, the deformation modulus of the reclaimed layer was assumed to be 95 MPa, based on trial column strengths [39]. Geotechnical tests confirmed the effectiveness of the soil improvement.

Table 7. Probable settlement values after soil improvement.

No	Description	Borehole No
		FDM BH01	FDMBH02	FDMBH03	FDMBH04	FDMBH05	Average
1	Post-construction immediate settlement (mm)	14	12	12	18	11	13
2	Post-construction consolidation and creep settlement (2 years)	7	11	17	20	25	16
3	If soil improvement is done total settlement in 2 years (mm)	21	23	29	38	36	26
1	Post-construction immediate (mm)	14	12	12	18	11	13
2	Post-construction consolidation and creep settlement (20 years)	21	30	45	54	65	43
3	If soil improvement is done total settlement in 20 years (mm)	35	42	57	72	76	56

shows that post-improvement settlements remain within the design limits.

Soil properties were analyzed for liquefaction risk, focusing on uniform fine sands prone to seismic effects. Jet-grout columns were installed in a grid pattern to improve ground strength, increase SPT blow counts, limit shear strain and pore pressure, and contain liquefiable zones. The columns also restrain horizontal shear stresses. Post-grouting quality control involved field inspections and laboratory tests to ensure compliance with design standards.

3. Results

3.1. Validation of Jet-Grouting Performance Through Visual Inspection and Core Strength Tests

A total of 2666 jet-grout columns were installed at the terminal site within Zone II-A. The distribution of columns was as follows: 1051 in Section 1, 174 in Section 2, 414 in Section 3, 351 in Section 4, 286 in Section 5, and 390 in Section 6. The properties and performance of the jet-grouted columns were monitored and evaluated using a range of inspection and testing methods. The test location plan is shown in Figure 6. Explanations of these tests and control procedures are provided below.

Sonic Logging for Integrity Assessment of Jet-Grout Columns: Sonic Integrity Tests (SITs) were performed on 87 jet-grout columns across Sections 1–6: 27 columns (16–18 m), 15 columns (20 m), and 45 columns (20–24 m). SITs detect defects using velocity–time graphs from reflected waves. The results showed no inclusions, cracks, joints, or cross-section reductions, and the column lengths were within acceptable tolerances.

Quality Control Considerations During the Installation Process: During installation, grout volume, injection pressure, and monitor speeds were controlled to ensure column quality. Data were recorded automatically to ensure precise monitoring. All parameters met the required standards for successful continuation of the works.

Visual Quality Inspections: As part of visual inspections, diameters of 87 jet-grout columns were measured, averaging 930 mm. In Section 1, some columns (e.g., Nos. 64, 207, 212, 234) had diameters of approximately 800 mm and lengths of 16 m. The diameter report includes examples such as the measurement of column 64 shown in Figure 7.

Quality Control via Core Sampling and UCS Testing: Coring of eight jet-grout columns verified column verticality and length, although the risk of core loss exists in heterogeneous soils. Column No. 476 confirmed a length of 16.0 m. The adjacent Column No. 485 showed a length of 17.73 m based on SIT results. Columns 75 and 1781 measured 18.0 m and 20.0 m, respectively, with suspected core loss. SIT results for columns Nos. 1727 and 1809 indicated lengths of 19.75 m and 20.78 m, respectively. Figure 7 shows the core sample box for No. JG-476.

Uniaxial compression strength tests were performed on jet-grout core specimens with a length-to-diameter ratio of approximately two. The jet-grouting operational parameters, visual inspection results, and the laboratory test data obtained from core specimens of columns JG-75 and JG-476 are presented in

Table 8. Jet-grouting operational parameters and visual inspection results for columns JG-75 and JG-476.

Jet-Grout Parameter		Jet-Grout Visual Check Results
Jet-Grouting Type	JET 1	Height (cm)	120
Cement Type	CEM II A 42.5	First (Long) Diameter (cm)	113
Nozzle Diameter	2.2	Second (Short) Diameter (cm)	109
Number of Nozzles	2	Upper Perimeter (cm)	381
Column Diameter (cm)		Lower Perimeter (cm)	388
Grout Pump Pressure (bar)	400
Pull-Out Rate for Grouting (cm/min)	50
Rotation Rate for Grouting (rpm)	25
Water/Cement Ratio	1/1

and

Table 9. Laboratory test results of core specimens from jet-grout columns JG-75 and JG-476.

Zone No	Column No.	Depth (m)	Specimen Length (cm)	Specimen Diameter (cm)	Unit Weight (kN/m3)	Compressive Strength (MPa)	Modulus of Elasticity (GPa)
		1.00	16.82	8.30	21.2	10.20	2353.60
		5.80	16.90	8.30	21.9	7.26	1667.13
	75	8.50	16.73	8.30	19.2	20.10	3530.39
		11.25	16.85	8.30	17.7	2.65	588.40
		14.60	16.75	8.30	17.8	13.24	2255.53
2-A		0.60	16.85	8.30	21.8	10.89	1667.13
		4.10	16,80	8.20	21.2	6.08	1569.06
	476	6.80	16.88	8.30	23.2	8.53	1912.30
		9.20	14.55	8.05	17.8	10.98	2059.40
		13.65	16.80	8.20	17.1	14.51	1372.93
		15.50	12.50	8.30	21.3	25.50	5491.72

.

3.2. Load Performance of Single Jet-Grout Columns

A pile load test was conducted on a jet-grout column (800 mm diameter, 16 m length). The column had been installed at least 28 days prior to testing. A rigid beam and reaction supports were used. A 1.8 m × 1.8 m concrete plate equipped with four dial gauges was installed. Ultimate loads were 1291 kN and 1625 kN in two trials. Maximum settlements were 3.93 mm (1.83 mm permanent) and 5.11 mm (3.45 mm permanent), respectively. The ultimate load (QF) occurs when the column fails by plunging without further increase in load. If this condition is not reached, the maximum test load (QL) is taken as the failure load. The test verifies whether the column settlement is within acceptable limits. The allowable gross settlement is 80 mm (10% of the column diameter). This value is significantly higher than the observed settlement under 1625 kN. Test setup and results are shown in Figure 8. The secant modulus (E_sec) was calculated using Equation (19), and the computed result is presented below.

$$E_{sec}={\displaystyle \frac{\sigma }{\epsilon }}={\displaystyle \frac{Q/A}{s/L}}$$

(19)

$$E_{sec}={\displaystyle \frac{1.291 \mathrm{M}\mathrm{N}/0.503{\mathrm{m}}^2}{0.00393 \mathrm{m}/16 \mathrm{m}}}={\displaystyle \frac{2.566 \mathrm{M}\mathrm{P}\mathrm{a}}{0.000245}}\cong 10.473 \mathrm{M}\mathrm{P}\mathrm{a}$$

where

• E_sec/(Col): Secant modulus of elasticity (kPa or MPa).
• σ: Axial stress (kPa = kN/m²)/
• ε: Axial strain (dimensionless).
• Q: Applied axial load (kN).
• A: Cross-sectional area (m²).
• L: Original length of the element (m).

3.3. Zone Load Test Evaluation of Jet-Grout Column Groups

Two-zone pile tests were performed on four jet-grout columns (800 mm diameter, 16 m length) installed 28 days prior. Loads were distributed over a 4.8 m × 4.8 m area using a sand fill layer and a 0.5 m reinforced concrete slab. Column heads at +1.00 m elevation extended 0.4 m above the structural fill, with sand fill extending at least 0.2 m above them.

Table 10. Multi-column static test columns and load details.

Jet-Grout Test Columns	755, 754, 801, 802	Recommended Test Load (kN)	4057
Outer Diameter (mm)	800	Effective Area of Hydraulic Jacks (cm2)	1998.7
Length (m)	16	1 bar/1 kN/cm2	0.010
Test Loading
Working Load (kN)	2029
Factor of Safety	2

presents the multi-column static load test arrangement and loading details.

The jet-grout columns were designed to carry the working load corresponding to a 4.80 m × 4.80 m area of the stocking ground. The average stress acting on this area, including both the weight of the embankment and the container load, was calculated to be 90 kPa. The working load applied to the four-column test area was estimated as follows.

Q = (4.80 × 4.80) × 90 = 2073.6 kN

A rigid beam spanned the test columns and was secured to supports. Three large jacks applied loads between the beam and a 0.5 m concrete base. A 1.5 × 2.25 m steel plate equipped with four dial gauges measured settlement. Ultimate loads of 2049 kN (Trial 1) and 4055 kN (Trial 2) were recorded. The corresponding test durations were 4 h 24 min and 15 h 48 min. Under 2049 kN (Trial 1), the maximum settlement was 0.63 mm, with a permanent settlement of 0.56 mm. Under 4055 kN (Trial 2), the maximum settlement was 3.44 mm, with a permanent settlement of 2.56 mm. The load per column was 1014 kN (maximum) and 507 kN (working load). Single-column tests gave a working load of 647 kN. End-bearing capacity is estimated to range between 1014 kPa and 1294 kPa. Figure 9 shows the zone load test on multiple jet-grout columns of JG-237, including the setup plan, test photograph, and settlement–load graph.

3.4. Surface Load Test Evaluation of Treated Ground

A surface loading test was carried out at the site. The test area was approximately 12 m × 12 m and was loaded using fill material. Heads of jet-grout columns were buried under 1.00 m thick sand and 4.70 m thickness of fill. The total pressure applied to the loading area was approximately 85 kPa (4.70 m × 18 kN/m³). Settlement was monitored at 16 locations (SP1–SP16). The surface loading test setup and the corresponding settlement response with values are shown in Figure 10. Immediate settlements (Si) were lower than predicted. The average settlement was 0.013 m after 30 days, indicating effective ground improvement. Settlement behavior reflected non-cohesive soils, showing no time-dependent deformation, as confirmed by the surface load tests.

The settlement–time relationship obtained from the monitoring data during the surface loading test is presented in Figure 11. The monitoring points show a generally consistent settlement trend, with an initial adjustment phase followed by a gradual increase in settlement. The maximum settlement observed in the monitoring points is approximately 13 mm, after which the rate of settlement decreases, indicating the gradual stabilization of the backfill material under the applied load.

3.5. Evaluation of Soil Improvement Effectiveness via Pre- and Post-CPT Data

Following completion of the marine reclamation works but prior to the implementation of jet-grout (JG) improvement, subsurface investigations were carried out in Section 1 of the project area as part of the site characterization program. These investigations included borehole drilling and cone penetration tests. CPT-1 and CPT-2, CPT-22 and CPT-23, and CPT-30 to CPT-32 were selected as representative CPT soundings conducted before jet-grout application and are used in this study to describe the pre-improvement ground conditions in Section 1. In addition, surface loading CPTs (SCP-1 to SCP-12), performed after jet-grout installation, were incorporated to represent the post-improvement soil response for the same section. The pre-improvement CPT dataset consisted of six soundings (n = 6), with an average cone resistance of 3.46 MPa (SD = 0.80 MPa; range = 2.47–4.35 MPa). After jet grouting, twelve CPT soundings were evaluated, and representative post-improvement qc values show an average cone resistance of 6.64 MPa (SD = 2.14 MPa; range = 3.55–8.65 MPa). The observed variability reflects the natural heterogeneity of the granular backfill and the interaction between the jet-grout columns and the surrounding soil. A comparison of the pre- and post-improvement CPT tip resistance values is summarized in

Table 11. Comparison of pre- and post-jet-grout CPT tip resistance values for Section 1.

Depth (m)	FMDBH01-Soil Description		Pre-qc (MPa)	Post-qc (MPa)
0.00			0.00	0.00
−6.41	0–63 mm Material -Imported Backfill		3.30	3.55
−7.96	Dragged Sand		2.47	8.65
−10.01	Unit A	Sand	4.31	8.45
−12.91	Unit B	Sand	3.03	6.57
−13.76	Unit C	Sand	4.35	6.00

, while their graphical representation is presented in Figure 12.

Pre-construction CPTs (pre-CPTs) and post-construction CPTs were performed to assess the modifications in the mechanical properties of the backfill. The results of CPT 1 and CPT 2 represent the soil resistance conditions prior to improvement, whereas CPT 1A and CPT 2A illustrate the resistance values obtained after the ground improvement works.

The comparison of CPT results before (CPT1) and after (CPT1A) ground improvement shows significant improvements. Cone resistance increased from 1 to 6 MPa to over 10 MPa, while sleeve friction increased from <0.2 MPa to >0.4 MPa. Corrected SPT N60 values also improved, increasing from 5 to 15 to over 25 blows/30 cm. This indicates denser and stronger soil and confirms the effectiveness of ground improvement.

3.6. Long-Term Settlement Assessment Based on Geodetic Elevation Monitoring in Zone II-A

After completion of the terminal and quay construction in 2015, geodetic survey points were established for vertical settlement monitoring through 2023. Nine points in Zone II-A were monitored to assess long-term performance of the ground improvement. The results, shown in

Table 12. Distribution of geodetic measurement data by year, maximum settlement and rate of settlement values.

Measurement Point		SP107	SP108	SP111	SP112	SP113	SP120	SP121
First measurement date		04/08/15	04/08/15	04/08/15	04/08/15	04/08/15	30/11/15	30/11/15
Last measurement date		23/06/23	23/06/23	23/06/23	23/06/23	23/06/23	23/06/23	23/06/23
Measurement count		37	37	36	36	36	32	32
Maximum settlement	mm	30.1	32.2	30	18.0	26.0	43.7	22.3
Measurement period	Day	1785	1785	1785	1785	1785	1667	1667
	Month	59.5	59.5	59.5	59.5	59.5	55.6	55.6
The rate of cumulative settlement	mm/day	0.017	0.018	0.017	0.010	0.015	0.026	0.013
	mm/month	0.51	0.54	0.50	0.30	0.44	0.79	0.40
The maximum rate of settlement	mm/day	0.222	0.222	0.111	0.222	0.333	0.171	0.080

and Figure 13, reveal maximum settlements between 40 and 60 mm, well within allowable limits, confirming the success of the ground improvement.

Surface loading tests verified the earlier settlement calculations. Analyses from boreholes FMDBH01–FMDBH05 predicted an average settlement of about 270 mm. Settlements accounting for jet-grout columns were calculated at 13 mm. Settlements stabilized after 17 days, allowing the test to be concluded. Calculated and recorded settlements from borehole data and surface load tests are shown in

Table 13. Calculated settlements from borehole soil data and recorded settlements from the surface loading test.

Description	Borehole No.
	FMDBH 01	FMDBH 02	FMDBH 03	FMDBH 04	FMDBH 05	Mean
Post-construction predicted immediate settlement (mm)	320	251	263	363	152	270
Post-construction measured immediate settlement (mm)	14	12	12	18	11	13

.

3.7. Bridging Single-Column Test Results and Large-Area Loading Through a β-Reduction Framework

Based on this theoretical background, a comprehensive analysis is presented. The analysis integrates available CPT data with the field-measured settlement of 13 mm. The analysis is formulated using an Enhanced Unit Cell Method, in which the improvement of the inter-column soil—quantified through CPT data—is explicitly incorporated into the analytical model.

The results of the pre- and post-installation CPT investigations show that cone resistance (q_c) values increased markedly following jet-grout installation, indicating substantial densification of the surrounding soil. The corresponding increases in q_c at selected depths are summarized below.

Dredged Sand, 7.96 m: qc increased from 2.47 MPa to 8.65 MPa (250% increase).

Unit A, 10.01 m: qc increased from 4.31 MPa to 8.45 MPa (96% increase).

Unit B, 12.91 m: qc increased from 3.03 MPa to 6.57 MPa (117% increase).

For sandy soils, the elastic modulus was derived using the correlation Es = 3qc [41], and the resulting values were employed as input parameters in the analytical unit cell model.

Average untreated soil modulus (Es, pre): ≈2.5 × 3.3 MPa = 10 MPa.

Average improved soil modulus (Es, post): ≈3 × 7.9 MPa = 23.7 MPa.

The interaction between the jet-grout columns and the surrounding soil was modeled using the unit cell approach. Two analytical models were evaluated and compared:

Area replacement ratio (as): 0.087.

Column modulus (E_col): 10,473 MPa, derived from single-column static load test results.

Model A: Conventional Approach (Inter-Column Soil Improvement Neglected).

In this model, the elastic modulus of the untreated soil (E_{s, pre}) is adopted as the representative soil modulus. The composite modulus, E_comp, was calculated using Equation (20). Substitution of the relevant parameters into the equation yields the following result:

E _{comp, A} = E_col as + E_s,pre (1 − as)

(20)

E_comp,A = 10,473 × (0.087) + 10 × (0.913) ≈ 920 MPa

where

• E_comp: Composite modulus of the improved soil (MPa).
• E_col: Modulus of the column material (MPa).
• E_s,pre: Modulus of the surrounding soil before improvement (MPa).
• as: Area replacement ratio (dimensionless).

Model B: CPT-Supported Approach (Inter-Column Soil Improvement Considered).

In this model, the increased soil modulus resulting from jet-grout-induced densification and arching effects (E_{s, post}) is adopted. Using the unit cell formulation (Equation (20)), the composite modulus of the improved ground is determined. Substituting the relevant parameter values yields

E _{comp, B} = 10,473 × (0.087) + 23.7 × (0.913) ≈ 933 MPa

The analytical predictions were compared with the measured field settlement of 13 mm under large-area surface loading.

Field Performance Modulus (E_meas): The system stiffness was back-calculated from the measured field settlement of 13 mm (S = 0.013 m) under an applied surface pressure of 85 kPa. Assuming a representative influence depth of 16 m, the measured modulus (E_meas) was determined using Equation (21), after which the field performance modulus was calculated as follows. A comparison between the analytical predictions and the field performance results is summarized in

Table 14. Comparison of analytical predictions and field performance.

Parameter	Model A (Conventional)	Model B (CPT-Supported)	Field Measurement
Soil Modulus Used	10 MPa (untreated)	23.7 MPa (improved)	–
Composite Modulus (Ecomp)	920 MPa	933 MPa	105 MPa
Predicted/Measured Settlement	1.48 mm	1.45 mm	13 mm

.

E_meas = q L/S

(21)

E_meas = q L/S = 0.085 MPa × 16 m/0.013 m = 104.6 MPa ≈ 105 MPa

where

• E_meas: Measured deformation modulus (MPa).
• q: Applied vertical stress (MPa).
• L: Length of the improved column (m).
• S: Measured settlement under the applied load (m).

The comparison shows that both analytical models overestimate the composite ground stiffness relative to the field-measured response. The predicted settlements (≈1.45–1.48 mm) are nearly nine times smaller than the measured settlement of 13 mm, indicating that the mobilized system stiffness under large-area loading is substantially lower than that predicted by the conventional unit cell approach.

Field observations indicate that stiffness values derived from single-column load tests cannot be directly applied to large-area surface loading conditions. Analytical predictions based on such values significantly overestimate the system stiffness relative to actual field performance. To address this discrepancy, a field reduction factor(β) is introduced to calibrate analytical formulations, ensuring they realistically represent the behavior of jet-grout-improved ground under massive operational loading.

The reduction factor β is defined as the ratio between the field-measured system modulus (E_field) and the theoretically predicted composite modulus (E_theoretical) obtained from classical unit cell analysis:

β = E_field/E_theoretical

(22)

where (E_field) is the modulus back-calculated from the measured surface settlement (S_field approx. = 13 mm), and E_theoretical is derived using the high stiffness values obtained from single-column load tests. The analytical models initially predicted an excessively high system stiffness of approximately 933 MPa. In contrast, field measurements indicated that the actual mobilized system stiffness was approximately 105 MPa. This discrepancy yields a calibration factor of β = 0.11.

The back-calculated composite system stiffness is approximately 105 MPa, which is significantly lower than the theoretical unit cell prediction of 933 MPa. Based on this difference, a field-calibrated stiffness mobilization factor (β) of approximately 0.11 is derived. To ensure the physical validity of this linear reduction approach, the bearing capacity analysis was used primarily as a critical verification step. By confirming an adequate factor of safety against ultimate failure under the applied operational loading levels (e.g., 85 kPa), it is ensured that the composite system’s behavior remains strictly within the elastic, serviceability-controlled range. This confirms that the observed settlements are governed purely by complex stiffness mobilization rather than plastic yielding. Consequently, this verification serves as a fundamental prerequisite that robustly validates the applicability of the linear, β-based stiffness calibration framework proposed in this study.

4. Discussion

4.1. General Field Performance and Structural Integrity

Multiple soil investigations conducted before and during construction revealed complex and highly variable soil conditions. The design allowable settlement tolerances were strictly defined as 50 mm within the first two years and 135 mm over a 20-year operational period. The initial fill and underlying strata (Units A and B) exhibited non-uniform settlement potential and high liquefaction susceptibility. Therefore, jet grouting was implemented to support the 90 kPa wide-area surface load. Although the preliminary structural capacity per isolated column was extremely high, the allowable load was conservatively limited at 667 kN. The adopted 2.4 m × 2.4 m grid spacing limited the applied load per column to an average of 415.2 kN. This provided a robust structural margin.

The structural integrity and dimensional quality of the 2666 jet-grout columns constructed in Zone II-A were verified through multi-tier testing. Visual measurements from the Jet-Grout Visual Check Report indicated that the as-built column diameters consistently exceeded the nominal 800 mm design, frequently reaching 1.18–1.38 m. This geometric expansion significantly reduces the untreated soil spacing between adjacent columns, thereby enhancing lateral confinement and global composite stiffness. Furthermore, Pile Integrity Test (PIT) results indicated nearly constant wave velocities (approximately 3800–4100 m/s) and reflection ratios generally below 15%. These low-amplitude reflections confirm structural continuity along the column shafts. They also indicate limited impedance contrast and relatively uniform soil stiffness.

4.2. Kinematics of the Composite Ground and Liquefaction Mitigation

The cone penetration test (CPT) results demonstrated a clear depth-dependent response to jet-grout improvement, governed by the contrast between the reclaimed fill and the underlying natural soils. The coarse-grained upper reclaimed layers (down to approximately −8 m) showed only marginal increases due to their inherent permeability. In contrast, the natural sand layers below −8 m exhibited significant increases in qc, reaching up to three times the initial values.

The marked increase in cone resistance following soil improvement (as demonstrated in Figure 12) reflects a substantial gain in soil matrix stiffness within the previously liquefaction-prone layers. This densification is not only a seismic safety measure, but also a critical kinematic requirement for the static settlement framework. By eliminating liquefaction potential, the densified soil matrix provides the essential lateral confinement for the jet-grout columns and strictly enforces the equal-strain boundary condition under wide-area loading. Consequently, the combined structural and matrix stiffness reduces settlement potential under service loading. This provides the physical and mechanical basis for validating the calibration of the system-wide β factor.

Table 6 presents a preliminary static assessment based on isolated column assumptions. However, the actual kinematic behavior under wide-area surface loading differs. The preliminary design aimed to transfer embankment and container loads strictly to the competent layers beneath the soft fill. However, under the distributed operational load (e.g., 85–90 kPa), a deep stress bulb develops. This stress bulb penetrates the underlying competent strata and induces elastic compression beneath the column toe. Furthermore, the equal-strain condition imposed by the wide-area load forces the soil matrix and columns to settle concurrently, fundamentally altering the development of the calculated drag load. Consequently, under actual service conditions, the system does not act as a purely rigid end-bearing structure. Instead, it behaves as a composite, friction-dominated semi-floating group. Load transfer is governed by both shaft resistance mobilized in the upper strata and the clayey sand toe layer.

Preliminary calculations (e.g., Table 6) provide a static baseline for evaluating ultimate structural capacity. However, the kinematic boundary conditions of a semi-floating column group under wide-area surface loading differ significantly from those of an isolated element. The equal-strain condition imposed by the stiff surface fill causes the compressible soil matrix and the rigid jet-grout columns to settle concurrently. This collective downward movement essentially eliminates the relative shear displacement between the column shaft and the surrounding soil in the upper strata. Consequently, the classical development of negative skin friction (drag load) is altered. The neutral plane shifts deeper into the soil profile.

Explicitly tracking the time-dependent migration of this neutral plane and the dynamic evolution of drag load would require advanced fully coupled transient numerical modeling. However, within the proposed semi-analytical framework, the macroscopic impact of these complex soil–structure interactions on the final settlement is intrinsically captured by the full-scale field measurements (S_field). Therefore, the proposed mobilization factor (β) functions as a lumped parameter. It compensates for deep stress bulb penetration. It also accounts for kinematic stiffness losses and group interaction inefficiencies associated with the evolution of the neutral plane.

4.3. The Necessity for β Calibration Framework and Limitations of the Unit Cell Method

The necessity for this β factor is rooted in the fundamental applicability limits of the classical unit cell model, which is strictly governed by boundary conditions at the column toe. The jet-grout columns in this study are nominally socketed 1–2 m into the underlying very dense clayey sand. However, they do not rest on a perfectly incompressible bedrock. The deep three-dimensional stress bulb generated by the 85 kPa wide-area surface load penetrates deeply into this untreated competent layer, inducing finite elastic sub-toe compression. As a result, the entire improved composite block undergoes slight downward displacement as a coherent unit.

From a load-transfer perspective, this kinematic behavior is critical. Shaft resistance is mobilized at very small relative displacements (e.g., 5–10 mm). In contrast, significant end-bearing capacity requires much larger toe movements. The system reached an operational settlement of only 13 mm. Therefore, load transfer is primarily governed by shaft friction mobilized along the upper marine fill. This minor sub-toe elastic yield prevents the mobilization of a perfectly rigid end-bearing resistance, causing the system to fundamentally behave as a friction-dominated semi-floating group.

Under these specific constraints, the direct and uncalibrated application of the unit cell model fails to capture sub-toe elasticity and complex group load-transfer mechanisms. As a result, the composite stiffness is overestimated. Therefore, the applicability of the unit cell model in marine soils under wide-area loading is strictly conditional upon the integration of the field-calibrated β factor.

In particular, the full-scale field investigation by Wang et al. (2023) [5] demonstrates that settlement behavior and mobilized stiffness of jet-grout-improved soils under realistic large-area loading conditions differ significantly from predictions based on conventional or element-scale approaches. Their results highlight the importance of a system-level response and confirm that simplified analytical assumptions tend to overestimate stiffness.

Similarly, the numerical study by Düzen et al. (2024) [6] shows that settlement performance of jet-grout column groups is highly dependent on column–soil interaction, spacing, and stress distribution, with results indicating that group effects and deformation mechanisms lead to reduced effective stiffness compared to idealized models.

These findings are consistent with the results of the present study, where the analytically predicted composite stiffness significantly exceeds the field-mobilized stiffness obtained from surface loading tests. The inclusion of these references reinforces that the observed discrepancy is not site-specific, but rather reflects a broader, well-established limitation of conventional analytical approaches in capturing the true composite behavior of jet-grout-improved ground under serviceability loading conditions.

When considering the influence of deeper stress distribution extending beyond the column length, it is observed that adopting a greater influence depth (e.g., 18–22 m) leads to a moderate increase in the back-calculated modulus. However, even with such adjustments, these values remain substantially lower than the analytically predicted composite stiffness derived from the rigid unit cell method. This approach demonstrates that the observed stiffness gap cannot be attributed solely to the selection of influence depth. Instead, it reflects the combined physical effects of sub-toe elastic compression, stress redistribution into underlying untreated layers, and the inherent limits of column stiffness mobilization under wide-area service loading. Consequently, the back-calculated modulus functions as an effective system stiffness that inherently incorporates these deeper deformation mechanisms, reinforcing the robustness of the proposed β-based calibration framework.

5. Conclusions

Jet grouting was selected as a flexible ground improvement method for a coastal terminal site. It was used to address high groundwater levels, variable soil conditions, and liquefaction risk. Long-term monitoring (2015–2023) recorded a maximum settlement of 44 mm. This value is well within allowable limits and confirms stable ground behavior. Based on the integrated use of design analysis, advanced testing, and long-term monitoring, the following principal conclusions are drawn:

• Field Execution and Structural Integrity: Visual inspection reports confirmed that the constructed jet-grout column diameters exceeded the planned 800 mm. In some cases, diameters reached 1.3–1.4 m. This increase enhanced the composite ground stiffness. Furthermore, Pile Integrity Test (PIT) results showed a nearly constant wave velocity of approximately 4.0 km/s. Reflection ratios were generally below 0.15. The absence of significant impedance discontinuities indicates continuous structural stiffness and high-quality execution along the treated depth.
• Kinematic Role of Inter-Column Soil Improvement: Although the substantial structural rigidity of the columns mathematically dominates the analytical composite modulus, the densification of the inter-column soil remains physically indispensable. Matrix stiffness increases significantly, with post-improvement CPT tip resistance rising by up to 250%. This improvement mitigates the severe liquefaction risk inherent in the marine backfill. More importantly, it provides lateral confinement that prevents column buckling. It also enforces equal-strain compatibility, which is required for uniform settlement under wide-area loading.
• Deep Stress Bulb Effects and Semi-Floating Kinematics: According to Boussinesq’s stress distribution theory, the massive 85 kPa wide-area surface load generates a deep three-dimensional stress bulb that penetrates beyond the 16 m column length into the underlying competent strata. This induces finite elastic sub-toe compression, causing the entire composite block to displace slightly downward. Consequently, the system does not behave as a perfectly rigid end-bearing structure, but rather fundamentally reflects the kinematics of a friction-dominated semi-floating group.
• Limitations of the Classical Unit Cell Method: Because the classical unit cell method mathematically assumes a fixed, incompressible boundary at the column toe, it is theoretically blind to this sub-toe elasticity and complex group load transfer. This study demonstrates that relying solely on single-column stiffness parameters leads to an overestimation of composite system performance. Consequently, settlement predictions under large-area loading are unrealistically small.
• The Calibrated Unit Cell Method and β Factor: To mathematically compensate for these deep stress bulb effects, sub-toe elastic yielding, and group interaction inefficiencies, a field-calibrated mobilization factor is required. A corrected composite modulus for wide-area loading conditions is strongly recommended in the form E_design = β [E_single as + E_soil (1 − as)]. For this specific project, the lumped parameter was derived as β = 0.11.
• Methodological Framework for Future Research: Current geotechnical design codes lack a unified coefficient for calibrating the rigid unit cell method applied to jet-grout column groups. While the specific numerical value (β = 0.11) is uniquely bound to the investigated marine backfill conditions and is not proposed as a universal constant, the underlying Dual-Testing Protocol (SCLT + SLT) establishes a robust and highly scalable methodological framework. This novel approach—integrating isolated column testing with full-scale surface loading measurements—serves as a foundational benchmark, guiding future researchers in systematically deriving and compiling site-specific mobilization factors across diverse geological profiles.

In this study, β is explicitly defined as a system-level stiffness mobilization factor under wide-area loading conditions, representing the ratio between the field-mobilized composite stiffness and the analytically predicted stiffness derived from idealized unit cell assumptions. Rather than being interpreted as a generalized empirical coefficient, β should be understood as a physically meaningful, site-specific parameter that quantifies the extent to which the theoretically available stiffness is effectively mobilized at the field scale. Although it inherently reflects the combined influence of mechanisms such as stress bulb penetration, group interaction, sub-toe elastic compression, and partial stiffness mobilization, its primary role is to provide a clear and consistent link between analytical predictions and the actual system response observed under serviceability conditions.

While the proposed framework is substantiated by an extensive field dataset, its applicability must be carefully interpreted within the specific geotechnical and loading context from which it is derived. The methodology is fundamentally developed for jet-grout column systems embedded in compressible soils and subjected to wide-area surface loading, where settlement behavior is governed by system-level stiffness mobilization rather than ultimate capacity. Its direct application to alternative conditions may be limited. In particular, for stiff or rock-supported soil profiles, where sub-toe deformation is negligible, or for fully end-bearing column systems, where load transfer is predominantly controlled by rigid base resistance, the underlying assumptions of the framework may not hold. Furthermore, different loading configurations—such as isolated or highly non-uniform loading—can significantly alter stress distribution patterns and mobilization mechanisms, thereby affecting the validity of the proposed approach. Accordingly, the framework should be applied with due consideration of boundary conditions, soil profile, and load characteristics, and, where necessary, complemented by site-specific calibration to ensure reliable interpretation.