Soil Strength Improvement Ability of Spartina alterniflora Established on Dredged Soils in Louisiana Coastal Area

Abstract

This research focused on studying the soil improvement ability provided by the roots of smooth cordgrass, Spartina alterniflora, flourishing in the dredged soil of the Sabine Refuge Marsh Creation Project in the coastal area of Louisiana, USA. Vane shear tests were conducted in the created marshland to obtain the in situ undrained shear strength of the soil vegetated with Spartina alterniflora. Direct shear tests were performed on undisturbed rooted soil samples to investigate the overall effect of the roots on soil shear strength. Laboratory tensile tests were conducted on the roots of Spartina alterniflora to estimate their tensile strength. In this research, the W&W model and the fiber bundle model (FBM), were adopted, and modified ones were proposed to study the correlation between root-enhanced soil cohesion and the nominal tensile strength of the roots. The model outcomes were compared with field and laboratory measurements. The research results showed that the roots of Spartina alterniflora significantly increased soil shear strength, with an increase in cohesion of up to 130% at one location. The increases varied at different locations depending on the root area ratio (RAR), soil sample depth, and root tensile strength.

1. Introduction

Louisiana’s coastal wetlands are vital for protecting coastal communities from storm surges and floods. They absorb wave energy, reduce the area of open water where winds can form, trap sediments, and act as natural sponges, helping to maintain shallow water depths [1,2,3,4,5]. It is estimated that one hectare of wetland in Louisiana provides an annual net benefit of about USD 1749 [6], which translates to roughly USD 450,000 per square mile (1 mi² = 2.58999 km²). These advantages make coastal wetlands a cost-effective and sustainable alternative to constructing barrier islands.

However, these wetlands are vanishing at an alarming rate, with an average loss of 16.57 ± 3.26 square miles per year, equivalent to the area of an American football field (360 ft × 160 ft; 1 ft = 0.3048 m), every hour [7]. From 1932 to 2010, Louisiana lost 1883 square miles of its coastal wetlands, representing a 25% reduction in its 1932 land area [7]. Projections estimate an additional loss of 513 square miles of Louisiana wetlands between 2000 and 2050 [8]. A more recent study by Couvillion et al. [9] indicated a slower rate of wetland loss, equivalent to one American football field of coastal wetland disappearing every 100 min. A study by NASA compared images of Barataria Bay [10], one of Louisiana’s major bays, from 1985 to 2020, and noted a loss of a football field of land every 90 min, as reported by the USGS in 2011. According to Brasuell [11], Louisiana has already lost 2000 square miles of coastal land since 1932.

This significant loss of wetlands is driven by both human activities and natural processes. Human-induced factors include the construction of levees and floodways on the Mississippi [12,13,14] dredging canals for drainage, logging, and activities related to the oil industry [13,14]. Other contributing factors are land reclamation projects, rapid urbanization, and oil spill disasters [15,16,17]. Natural factors involve rapid subsidence, which is further worsened by oil and gas exploration [18,19], rising sea levels [20], saltwater intrusion, and the annual hurricanes that impact the coast [21]. The 2017 Coastal Master Plan of Louisiana, developed by the Coastal Protection and Restoration Authority (CPRA), allocated USD 17.1 billion for marsh creation projects. These initiatives, together with other sediment diversion projects, are projected to sustain or generate around 800 square miles of land over the next 50 years [22]. Marsh creation involves dredging and transporting sediments to designated areas, where they are deposited, allowed to settle, and gradually stabilize. However, managing millions of cubic feet of sediment and the absence of older projects as benchmarks make it difficult to assess the success of these efforts. The resilience of these newly formed marshlands relies on both the inherent shear strength of the dredged soil and the stabilizing effects of native vegetation that establishes itself. To ensure sustainable and resilient marshlands, it is essential to understand the strength contributions from both the soil and the vegetation. Therefore, the investigation of the soil-binding properties of native vegetation—especially Spartina alterniflora—on established dredged land along the Louisiana coast is both essential and timely.

Vegetation is essential for stabilizing slopes and preventing erosion [23,24,25,26,27,28]. As the need to reduce carbon footprints and the reliance on man-made materials grow, bio-inspired anchors and deep foundations will likely receive greater attention in the future [29]. The strength of below-ground biomass, especially vegetation roots, directly enhances soil cohesion and boosts the overall shear strength of the soil [24,25,28,30]. Vegetation roots also act as a physical barrier between the soil and water, aiding in the stabilization of tidal creeks [31]. Above-ground stems help slow water flow, reduce turbulence, and decrease bed shear stress, promoting the settling and trapping of sediments carried by the water [2,32,33]. Additionally, decaying plant matter contributes to peat formation, thereby increasing the vertical accretion rate of wetlands [34]. Research has quantified the impact of Johnson grass roots on increasing resistance to surface erosion [35,36]. They found that Johnson grass roots enhanced soil cohesion by approximately 102%, although their effect on the friction angle was minimal.

In this research, the soil reinforcement provided by the roots of the grass species Spartina alterniflora was studied. Vane shear tests were conducted to estimate the in situ shear strength of the dredged soil. Direct shear tests were performed on both rooted and plain soil samples to estimate the root reinforcement coefficient (c_R) for the soils. Soil samples were taken from three different layers, and for each layer, the values of cohesion and friction angle were estimated from the tests. The nominal tensile strength of various root samples was determined through laboratory tensile tests, and these values were utilized to calculate c_R in the analytical models.

Two different root reinforcement models were employed to examine the relationship between root-induced cohesion (c_R) and nominal root tensile strength. The first developed model is a perpendicular root reinforcement model that assumes all roots intersecting the shear plane mobilize their tensile strength simultaneously and fail at the same time [28]. This model is referred to as the “W&W model” [37], where the first “W” refers to “Tien Wu [28]” and the second “W” refers to “Waldron L. J. [30]”, two independent researchers.

The second model, known as the Rip-Root model, accounts for progressive root failure and varying root orientations within the soil matrix [26]. The model is equivalent to the fiber bundle model (FBM) and is referred to as the FBM hereafter. It assumes that due to the varying tensile strength values of roots, they break at different points as a load is applied to the rooted soil.

2. A Brief Description of the Shear Strength Models for Rooted Soils

Waldron [30] applied the Mohr–Coulomb failure criterion to estimate the shear strength of rooted soils. He assumed that root reinforcement serves as an additional factor contributing to the shear strength of the soil. Then, the criterion was extended as follows:

$$s=c+c_R+{\sigma }_N^{\prime }\tan \varphi$$

(1)

Here, c_R represents the additional cohesion due to the presence of roots, while c is the cohesion of plain soil. Waldron’s study [30] modeled roots as cylindrical, flexible structures oriented perpendicular to the slip surface. It was assumed that as the soil–root matrix starts to shear, the tensile strength of all roots is fully mobilized. This tensile strength is then decomposed into a tangential component that resists the shear force and a normal component that enhances the confining pressure on the plane. The additional cohesion c_R can be expressed as follows:

$$c_R=t_R\left(sin\theta +cos\theta tan\varphi \right)$$

(2)

where t_R is the tensile strength of the roots, and θ is the angle between the root and the direction of the shear plane. The term within the parentheses in Equation (2) ranges between 1.0 kPa and 1.3 kPa due to the typical values of θ and ϕ, varying from 40° to 90° and 25° to 40°, respectively [28]. To simplify and make it more practical, Wu et al. [28] substituted the term in the parentheses with a constant of 1.2.

$$c_R=1.2\sum _{i=1}^n{T}_{ri}\left({\displaystyle \frac{A_{ri}}{A}}\right)$$

(3)

where T_ri is the tensile strength (tensile resistance per unit area) of the individual root (i), and A_ri is the total area occupied by the root (i) in the considered area A of the soil cross-section shear plane. The term A_ri/A represents the fraction of the cross-sectional area occupied by a single root (i), also known as the root area ratio (RAR) of the single root (i). The variable n represents the total number of roots within the analyzed soil cross-section. Equation (3) is used in this research to quantify the root reinforcement of Spartina alterniflora. The tensile strength T_r can be correlated with the root diameter d using the power law equation given by Gray and Sotir [24]:

$$T_r\left(d\right)=\alpha d^{-\beta }$$

(4)

where α and β are empirical constants that vary depending on the plant species.

The research by Coppin and Richards [23] revealed that the W&W model’s assumption of tensile failure as the sole failure mechanism for roots, without considering slip failure, significantly overestimates root reinforcement. Similarly, Pollen and Simon [26] found that the tensile strength of all the plant roots is not fully developed to its peak value during soil shearing, further suggesting that the W&W model’s assumption of simultaneous tensile failure for all roots may substantially overestimate actual root reinforcement.

In response, Pollen and Simon [26] proposed a new root reinforcement model called the Rip-Root model, based on the traditional fiber bundle model (FBM). This model assumes that the load is evenly distributed among all the roots in a bundle, and due to variations in tensile strength, the roots fail at different times. When the applied load surpasses the strength of an individual root, the weakest root fails first, and the load is redistributed among the remaining intact roots. Complete failure occurs once all the roots in the bundle have been broken by the acting force. Cohen et al. [38] derived analytical expressions for the FBM, linking the pullout force to displacement.

Building on this, Karimi et al. [39] investigated the role of white mangrove roots in coastal stabilization using three models: W&W, the FBM, and Root Bundle Weibull (RBMw). Their findings indicated that the Root Volume Ratio (RVR) and the number of roots (NoR) decreased with distance from the tree stem, while root tensile forces increased with root diameter. Moreover, recent years have seen a surge in experimental, analytical, and numerical studies on the strength of vegetated/rooted soils based on these three models, leading to significant advancements in the field [40,41,42,43,44,45,46,47,48].

3. Materials and Methodology

3.1. Subsurface Soils and Site Classification

Spartina alterniflora, also known as smooth cordgrass or saltmarsh cordgrass, is a leading emergent grass species native to the Atlantic and Gulf coastlines. It typically flourishes in the low marsh zones of intertidal wetlands, where frequent flooding occurs. Spartina alterniflora tends to grow taller along the outer edges of marshes and shorter toward the interior, featuring hollow stems, long, tapered leaves, and dense networks of rhizoidal roots. This resilient plant exhibits a high tolerance for salinity and readily reproduces by seed or through its rhizoidal roots. Its aerial roots enhance oxygen uptake, enabling its survival in highly hypoxic environments [49]. The use of Spartina alterniflora in marsh creation and restoration is well documented in numerous studies [50,51,52].

The Sabine Refuge Marsh Creation project (CS-28) was selected to investigate the soil-binding ability of Spartina alterniflora. This project is located northeast of the Sabine National Wildlife Refuge, which is on the south side of Black Lake, and west of LA 27 in Cameron Parish, Louisiana. The CS-28 project consists of five cycles, with only Cycle 1 (the oldest man-made marsh zone) and Cycle 3 selected for field testing and soil sampling as part of the Coastal Science Assistantship Program (CSAP)-funded project. Three cores were taken from Cycle 1 and three from Cycle 3.

Cycle 1 was completed in February 2002, resulting in the creation of 214 acres of marshland, while Cycle 3 was completed in March 2007, creating 232 acres. Both cycles involved dredging sediments from the Calcasieu River Ship Channel into the shallow open water area within retention dikes [53]. Spartina alterniflora was planted along the perimeters of both projects. The primary objectives were to prevent saltwater intrusion into the marshes, create a new marsh ecosystem, and protect the existing marshes from erosion. A site visit was conducted in March 2017, during which in situ tests were performed and undisturbed soil samples were collected from three different locations within each cycle.

Hydraulically dredged soils were used to create artificial marshlands. These marsh soils are a complex mixture of sand, silt, and clay, which makes it challenging to categorize them into stable combinations. The marsh creation sites are underlain primarily by soft clays, with varying thicknesses of organic material beneath the mud line. Additionally, many of the clay layers contain silt, sand, and shell deposits, while sand and silty sand layers are encountered at various depths.

The surface layer typically consists of soft fat clay (CH) extending to depths in a range between 8 and 15 feet. This layer generally overlies a stratum of sandy clay (CL), clayey sand (SC), or lean clay (CL) [54]. Along the coastline, the thickness of the very soft to soft fat clay (CH) can reach up to 60 feet. Below approximately 12 feet, the soil becomes slightly more competent and may show signs of weathering (oxidation).

Table 1. Properties of marshland creation soils along Louisiana coastal line [55].

Soil Properties	${\mathit{\omega }}_{\mathit{n}}$ (%)	${\mathit{ɤ}}_{\mathit{d}}$ (Pcf)	${\mathit{\omega }}_{\mathit{l}}$ (%)	PI (%)	${\mathit{G}}_{\mathit{s}}$	${\mathit{C}}_{\mathit{c}}$	${\mathit{e}}_{\mathit{o}}$
Range	24.4–418	18.5–100	37–394	17–268	2.35–2.72	0.16–2.86	0.669–12.74
Average	110.52	55.08	116.93	79.52	2.60	0.96	2.96
SD	83.86	23.18	105.37	73.98	0.11	0.73	2.48

Note: $c_c$ = compression index; $e_o$ = initial void ratio; ${\omega }_l$ = liquid limit; ${\omega }_n$ = moisture content; ${\mathit{ɤ}}_d$ = dry unit weight; PI = plasticity index; $G_s$ = specific gravity; SD = standard deviation.

summarizes the physical properties of coastal marsh clay based on laboratory data from several CPRA projects [55].

3.2. The Direct Shear Tests

Direct shear tests were conducted on the soil samples from the site using an ELE International direct shear test apparatus, in accordance with ASTM D3080 [56] standards. As root reinforcement varies with depth, the soil samples were classified into three layers: Layer 1 from 0 to 8 cm, Layer 2 from 8 to 16 cm, and Layer 3 from 16 to 24 cm. Below a depth of 24 cm, there were very few live roots in the soil samples. Laboratory observations revealed that most of the few dead roots had nearly decomposed and had a minimal impact on the soil’s shear strength. Therefore, soil samples collected below a depth of 24 cm were classified as belonging to the “plain soil layer”.

Twenty-four soil samples were prepared and tested as part of the direct shear investigation, with twelve samples collected from Cycle 1 and twelve from Cycle 3. For each layer, at least three specimens from the same core were tested to determine their shear strength parameters: cohesion (c) and angle of friction (ϕ). During the consolidation stage preceding direct shear testing, three normal pressures—5 kPa, 11 kPa, and 19 kPa—were selected to represent the range of overburden pressures experienced by the soil samples in the marsh ground. To maintain drained conditions, a fully controlled horizontal load, corresponding to a strain rate as low as 0.1 mm/min, was applied to the shear box using a motor and gear system. A minimum of three valid tests were performed for each soil layer. The peak shear stress and corresponding normal stress were used to plot a graph of shear strength versus normal stress (τ vs. σ) for each layer.

3.3. The Tensile Strength Tests of the Roots

The root system of Spartina alterniflora consists of thicker underground stems (rhizomes) and finer fibrous roots. Rhizomes were found at shallow depths, with their diameters gradually decreasing as they extended deeper into the soil. Shoots and adventitious roots emerged from nodes along the rhizomes. Although the plants appeared as separate individuals above ground, they remained interconnected through these underground rhizomes. The adventitious roots grew nearly perpendicular to the rhizomes, creating a dense mesh near the surface. Unlike the rhizomes, these roots featured fine root hairs and were capable of penetrating deeper into the soil. The root system was divided into three primary categories based on diameter—R₁, R₂, and R₃—with average diameters of 4.57 mm, 2.54 mm, and 0.76 mm, respectively. Root diameters were measured at the midpoint and at both ends of each segment using an electronic slide caliper with a precision of 0.01 mm.

Because tensile strength is influenced by moisture content, all roots were soaked in water for 24 h prior to testing to ensure consistency. A major challenge during tensile testing was securing the clamping ends of each root specimen, as roots often slipped out or broke at the clamps, resulting in inaccurate data and the loss of valuable samples. After evaluating several methods, two approaches were finalized, both shown in Figure 1: the grip arrangement (GA) and the hook arrangement (HA). In the GA method, pneumatic grips were used to secure and pull the roots at both ends. To prevent slipping and protect the roots from being crushed by the pneumatic grips, the root ends were coated with hot glue. The HA used hooks to pull the roots, with the ends also secured by hot glue.

All tensile strength tests for the roots of Spartina alterniflora were conducted using the ADMET eXpert 2611 universal tensile testing equipment (ADMET, Inc. Norwood, MA 02062, USA) at Louisiana Tech University. The root samples were tested at a pulling rate of 0.10 in/min (2.54 mm/min) using a servo-controlled tensile testing machine equipped with a load cell (50 lbf or 222 N) sensitive to two decimal places. Each root specimen was trimmed to a uniform length of 50.8 mm, maintaining a consistent spacing of 25.4 mm between the two pneumatic grips or hooks.

For both arrangements, a test was deemed invalid if failure occurred at either of the clamping ends to eliminate the influence of the hot glue on the root tensile strength. After several tests, a total of thirteen valid results were obtained. The grip arrangement (GA) was used to test root type R₁, which had larger diameters, while the hook arrangement (HA) was applied to root types R₂ and R₃, which had smaller diameters.

3.4. The Vane Shear Tests in the Field

Field tests to determine the undrained shear strength of rooted soils were conducted using the Vane Tester VT12 by Pagani Geotechnical Equipment (Pagani Geotechnical Equipment S.r.l., Località Campogrande, 26, 29010 Calendasco, PC, Italy). A vane with a diameter of 30 mm and a height of 60 mm was selected for the tests. The vane shear tests were performed at three different locations in both Cycle 1 and Cycle 3, in accordance with ASTM D2573 (2011) [59] standards. The tests were conducted to a depth of 40 cm, assuming that this represents the maximum depth that the roots of Spartina alterniflora can reach. Vertical profiles of vane shear strength distribution were generated in 10 cm increments at each testing location. To account for factors such as anisotropy, strain effects, and disturbance, the measured undrained shear strength was corrected as recommended by Bjerrum [60].

4. Results and Discussion

4.1. The Direct Shear Test Results

For the marsh creation zone of Cycle 1, Figure 2a–c illustrate the stress–strain curves under normal stresses of 5 kPa, 11 kPa, and 19 kPa, respectively. The plot of normal stress versus shear strength is presented in Figure 3a. As shown in

Table 2. Cohesion (c) and friction angles (ϕ) for rooted soils in Cycles 1 and 3 [57].

Normal Stress (kPa)	Peak Shear Strength (kPa)
	Layer 1 (0–8 cm)		Layer 2 (8–16 cm)		Layer 3 (16–24 cm)		Plain Soil Layer
	Cycle 1	Cycle 3	Cycle 1	Cycle 3	Cycle 1	Cycle 3	Cycle 1	Cycle 3
5	9.00	9.04	7.24	6.35	5.43	3.55	3.62	3.20
11	14.54	12.00	9.04	10.85	6.03	7.01	5.43	5.43
19	19.80	19.00	14.54	12.70	10.90	9.00	7.15	6.90
Cohesion c (kPa)	5.51	4.94	4.08	4.81	2.75	2.07	2.48	2.14
Friction Angle (ϕ)	37.40	35.76	27.80	23.83	21.93	20.89	14.04	14.56

[57], the cohesion ranged from 5.51 kPa for ‘Layer 1’ to 2.48 kPa for the plain soil layer, representing the highest and lowest values, respectively. The results revealed that peak shear strength increased in all rooted soil samples compared to the plain soil. Additionally, the cohesion was observed to decrease with depth. Roots enhanced the cohesion of the reinforced soils by approximately 130% in Layer 1, 70% in Layer 2, and 12.5% in Layer 3.

The data in Table 2 show a significant effect of root reinforcement up to a depth of 24 cm, beyond which there was little to no increase in the cohesion or friction angle. These findings differ slightly from the conclusions of Wu et al. [28], who suggested that roots had no influence on a soil’s friction angle. Figure 3a and Table 2 summarize the results from the direct shear tests for Cycle 1, showing that both cohesion and friction angles decrease with soil depth. Comparing the three selected shear stress–strain curves presented in Figure 2, it is evident that plain soil is the most ductile, and root reinforcement enhances the shear modulus of the soils. As shown in Table 2, the friction angles (ϕ) of the three soil layers increased significantly due to root reinforcement.

Similarly, Figure 4a–c present the results from the direct shear tests conducted on soil samples from Cycle 3. These figures present three selected stress–strain curves for normal stresses of 5 kPa, 11 kPa, and 19 kPa, respectively. According to Table 2, the highest cohesion value of 4.94 kPa was recorded in Layer 1, while the lowest value, 2.14 kPa, was found in the plain soil layer. Interestingly, the cohesion of the plain soil layer in Cycle 3 was similar to that in Cycle 1. As expected, the shear strength was higher in all rooted soil layers. Figure 3b shows that the Mohr–Coulomb failure criterion gradually flattened from Layer 1 to the plain soil layer. The cohesion in the rooted soil increased by about 127% in Layer 1 and 124% in Layer 2, and showed a minimal increase in Layer 3 [57,58].

The results revealed that root reinforcement significantly impacted cohesion up to a depth of 16 cm, with little to no further increase beyond that depth. This contrasts with the findings from Cycle 1, where the influence on cohesion extended through all three layers. This suggests that root reinforcement penetrated deeper in Cycle 1 than in Cycle 3, likely due to the earlier establishment of the marshland in Cycle 1. Additionally, shear stiffness increased due to vegetation roots, following the same pattern observed in the Cycle 1 soil samples.

4.2. The Vane Shear Test Results

Vane shear tests were conducted on the created marshland in both Cycles 1 and 3. The land was frequently flooded by tides and the soils were classified as clay with high plasticity (CH) based on the United Soil Classification system, as described in Section 3.1. Figure 5 displays the corrected undrained shear strength profiles of the soils from different locations [58].

The undrained shear strength (S_u) of the soils was greatest at the ground surface and progressively decreased with depth. In general, Cycle 1 exhibited the highest S_u values, while Cycle 3 showed the lowest. At the top layer, S_u ranged from 6.82 to 10.45 kPa, attributed to the significant root reinforcement provided by the dense concentration of rhizomes and adventitious roots near the surface. As the depth increased to 10 cm, S_u decreased notably to a range of 5.50 to 7.50 kPa, reflecting the reduction in root density with depth. Between 10 and 20 cm, the S_u values continued to decline slightly across most testing stations, ranging from 5.45 to 6.36 kPa.

At depths between 30 and 40 cm, the S_u values were relatively consistent, largely due to the minimal presence of roots in this zone. The lowest S_u values were observed at a depth of 40 cm, ranging from 3.18 to 4.54 kPa.

4.3. The Tensile Test Results

The original tension test data for root types ‘R₁’, ‘R₂’, and ‘R₃’ are presented in Figure 6, Figure 7 and Figure 8, where tensile load is plotted against percentage deformation (tensile strain). Given that a single root exhibits different diameters at its ends and midpoint, plotting load against percentage deformation provides a more meaningful analysis. The root type ‘R₁’, having the largest average diameter of 4.741 mm, withstood the highest peak load at failure, ranging from 28.169 N to 42.658 N. Root type ‘R₂’, with an average diameter of 2.54 mm, supported peak loads ranging from 9.520 N to 16.590 N. Root type ‘R₃’, the smallest, with an average diameter of 0.767 mm, bore the lowest peak load, ranging from 5.429 N to 8.767 N. The peak loads at root failure varied significantly.

One of the research objectives was to identify the pattern of root tensile strength relative to different root diameters. To accomplish this, the tensile strength for each root was calculated based on its original cross-sectional area, and the results were averaged to determine the nominal tensile strength for each root type, as shown in

Table 3. Nominal tensile strength of Spartina alterniflora with different root types [58].

Root Type	Root Samples	Peak Load (N)	Diameter (mm)	Tensile Strength (kPa)	Average Tensile Strength (kPa)
R1	R11	42.66	4.32	2913.062	2198.05
	R12	39.74	4.57	2420.523
	R13	28.17	5.33	1260.572
R2	R21	16.59	3.30	1937.54	2652.37
	R22	9.52	2.03	2935.37
	R23	8.50	1.78	3421.89
	R24	15.75	3.05	2158.09
	R25	14.68	2.79	2394.18
	R26	12.59	2.29	3067.12
R3	R31	8.18	0.86	13,972.98	15,617.63
	R32	7.92	0.76	17,362.27
	R33	7.07	0.74	16,597.02
	R34	5.65	0.69	15,293.44
	R35	5.43	0.64	17,135.97
	R36	8.76	0.91	13,344.13

Note: Three samples of root type R₁, six of R₂, and six of R₃ were selected from the tensile tests to illustrate the load–strain curves. The average diameters of root types R₁, R₂, and R₃ were 4.57 mm, 2.54 mm, and 0.76 mm, respectively.

. The data clearly indicate an inverse relationship between root diameter and tensile strength: smaller-diameter roots exhibited higher tensile strength, aligning with the findings of Shahrier et al. [36]. The nominal tensile strengths were 2.20 MPa for root type R₁, 2.65 MPa for root type R₂, and 15.62 MPa for root type R₃, as shown in Table 3.

To maintain consistency with the tensile strength values, the root area ratio (RAR) was calculated based on the average diameter of each root type, as expressed in Equation (3) [57]. Figure 9 illustrates an exponential increase in nominal root tensile strength as root diameter decreases. Notably, the tensile strength of smaller-diameter roots exhibited greater variability compared to that of larger-diameter roots. The parameters α and β were calculated as 10.102 and 1.22, respectively, using the data from Figure 9 and Equation (4). These values offer a starting point for the preliminary calculation of the tensile strength of Spartina alterniflora considering root type and diameter [58].

4.4. Calculations of the Root Area Ratio (RAR)

Representative soil samples for measuring the root area ratio (RAR) were taken from three separate cores, each 63.5 mm in diameter, and air-dried. Once dried, the samples were extracted from the cores and split in two, and the roots of each type were counted. The RAR was calculated as the ratio of the total root area to the total cross-sectional area of the soil core, using the average diameter of each root type.

Consistent with previous studies [25,27], the RAR values for the Spartina alterniflora samples decreased with depth at all sampling locations. The number of roots, as well as their average diameter, also decreased with depth, as shown in

Table 4. Root-reinforced soil cohesion from the direct shear tests and the W&W model and FBM.

Layer	Soil Shear Plane Area (mm2)	Root Type	Root Dia. (mm)	No. of Roots	Root Area (mm2)	RAR for Each Root Type	Tensile Strength (kPa)	Root Cohesion Cr (kPa) (Wu et al. Perpendicular Model) [37]	Root Cohesion Cr (kPa) (FBM) [26]	Cr from Direct Shear Test (kPa)	Cr from Tensile Test (Excluding 1.2 of Wu et al. Model) [37]	Correlation Coefficient	Average of Correlation Coefficient
CYCLE 1													0.058
0–8 cm	3166.92	R1	5.33	1	22.346	0.0071	1260.57	54.97	49.65	3.10	45.81	0.07
		R1	4.32	1	14.644	0.0046	2913.06
		R2	3.30	1	8.5530	0.0027	1937.54
		R2	2.79	1	6.1136	0.0019	2394.18
		R3	0.86	1	0.5809	0.0002	13,972.98
		R3	0.76	1	0.4536	0.0001	17,362.27
		R3	0.74	1	0.4301	0.0001	16,597.02
		R3	0.69	1	0.3739	0.0001	15,293.44
		R3	0.64	1	0.3217	0.0001	17,135.97
		R3	0.91	1	0.6504	0.0002	13,344.13
8–16 cm	3166.92	R1	4.57	1	16.417	0.0052	2420.52	36.32	19.02	1.70	30.27	0.06
		R2	2.79	1	6.1136	0.0019	2394.18
		R2	2.29	1	4.1187	0.0013	3067.12
		R3	0.86	1	0.5809	0.0002	13,972.98
		R3	0.76	1	0.4536	0.0001	17,362.27
		R3	0.74	1	0.4301	0.0001	16,597.02
		R3	0.69	1	0.3739	0.0001	15,293.44
16–24 cm	3166.92	R1	4.57	No roots found in category R1				13.79	13.58	0.30	11.49	0.03
		R2	1.78	1	2.4885	0.0008	3421.89
		R2	2.03	1	3.2365	0.001	2935.37
		R3	0.74	1	0.4301	0.0001	16,597.02
		R3	0.69	1	0.3739	0.0001	15,293.44
		R3	0.64	1	0.3217	0.0001	17,135.97
CYCLE 3
0–8 cm	3166.92	R1	4.57	1	16.417	0.0052	2244.34	48.07	27.16	2.76	40.06	0.07
		R2	3.30	1	8.553	0.0027	1937.54
		R2	3.05	1	7.3062	0.0023	2158.09
		R2	2.79	1	6.1136	0.0019	2394.18
		R3	0.86	1	0.5809	0.0002	13,972.98
		R3	0.76	1	0.4536	0.0001	17,362.27
		R3	0.74	1	0.4301	0.0001	16,597.02
		R3	0.69	1	0.3739	0.0001	15,293.44
		R3	0.64	1	0.3217	0.0001	17,135.97
		R3	0.91	1	0.6504	0.0002	13,344.13
8–16 cm	3166.92	R1	4.57	No roots found in category R1				24.70	24.45	2.66	20.58	0.13
		R2	2.79	1	6.1136	0.0019	2394.18
		R2	2.29	1	4.1187	0.0013	3067.12
		R2	2.03	1	3.2365	0.001	2935.37
		R3	0.86	1	0.5809	0.0002	13,972.98
		R3	0.76	1	0.4536	0.0001	17,362.27
		R3	0.74	1	0.4301	0.0001	16,597.02
		R3	0.69	1	0.3739	0.0001	15,293.44
		R3	0.64	1	0.3217	0.0001	17,135.97
		R3	0.91	1	0.6504	0.0002	13,344.13
16–24 cm	3166.92	R1	4.57	No roots found in category R1				10.19	10.87	0.00	8.49	0.00
		R2	1.78	1	2.4885	0.0008	3421.89
		R3	0.74	1	0.4301	0.0001	16,597.02
		R3	0.69	1	0.3739	0.0001	15,293.44
		R3	0.64	1	0.3217	0.0001	17,135.97

. In Cycle 1, the RAR value ranged from 0.07 (7.0%) in Layer 1 (0–8 cm) to 0.03 (3.0%) in Layer 3 (16–24 cm). In contrast, Cycle 3 exhibited slightly lower RAR values, ranging from 0.07 (7.0%) in Layer 1 to 0.0 (0.0%) in Layer 3. This difference is likely due to the younger age of the marshland in Cycle 3 compared to Cycle 1.

4.5. The W&W Model and FBM

For the CS-28 project, a modified W&W model for rooted soils was developed by calculating the root-induced cohesion (c_R) for each layer. This was achieved by subtracting the cohesion of the plain soil layer from that of the rooted soil at the corresponding depth, using the data from the direct shear tests. The resulting values of c_R for different layers are presented in the fourth column from the right in Table 4. The root-induced cohesion (c_R) for each layer was also determined using the W&W model, as presented in Equation (3) (column six), and the FBM, according to the flowchart from Pollen and Simon [26] (column five).

A decreasing trend in root-induced cohesion (c_R) was observed from Layer 1 to Layer 3. In Cycle 1, c_R values ranged from 54.97 kPa to 13.79 kPa using the W&W model and from 49.65 kPa to 13.58 kPa using the FBM. In Cycle 3, c_R values ranged from 48.07 kPa to 10.19 kPa with the W&W model and from 27.16 kPa to 10.87 kPa with the FBM. Both models significantly overestimated the root reinforcement coefficient compared to the c_R values obtained from the direct shear tests. It was assumed that the direct shear tests provided accurate values for root-induced cohesion (c_R). The ratio of the actual root-reinforced cohesion (c_R) obtained from these tests to the term ${\sum }_{i=1}^n{T}_{ri}\left({\displaystyle \frac{A_{ri}}{A}}\right)$ in Equation (3) was computed for each rooted soil layer at every sampling station. The average of these ratios across different sampling locations at the CS-28 project site was found to be 0.058. Consequently, Equation (3) can be re-written as Equation (5), referred to as the modified W&W model for the CS-28 marsh creation project. The coefficient 0.058 in Equation (5) adjusts the root reinforcement coefficient of 1.2 proposed by Wu et al. [28] to better fit the conditions of Spartina alterniflora growing in the dredged soils of the CS-28 project. This modified equation provides a valuable tool for the preliminary estimation of vegetated soil shear strength in coastal marshes:

$$c_R=0.058\sum _{i=1}^n{T}_{ri}({\displaystyle \frac{A_{ri}}{A}})$$

(5)

where $({\displaystyle \frac{A_{ri}}{A}})$ is the root area ratio (RAR) for an individual root (i).

The analysis of Table 4 reveals that while the FBM provides root-induced cohesion (c_R) values more closely aligned with the direct shear test results than the W&W model, both approaches markedly overestimated root reinforcement. The ratio of c_R between the FBM and W&W model fell between 0.52 and 1.07 [58].

Various factors play a role in the inaccuracies seen in these models. Although the two models incorporate root tensile strength and consider root diameter as a factor in soil reinforcement, they do not account for the slipping effect between the soil and roots, leading to the incomplete mobilization of root tensile strength. Challenges in accurately representing root orientation relative to the failure surface and the distortion of roots during shearing also contribute to errors in the models. The variability in root diameter measurements, particularly for smaller roots, increases errors in estimating the root area ratio (RAR) and the corresponding tensile strength from peak loads.

Furthermore, the models primarily consider roots as stretched cables, neglecting their bending and compression strengths [61]. Additionally, coastal soils experience various forces, including torques during hurricanes, such as twisting, which current models do not adequately address.

5. Conclusions

For the first time, the vegetation of Spartina alterniflora was experimentally studied for its root-strengthening ability in marsh soils in coastal Louisiana. The tests conducted both in the laboratory and in the field on rooted soil samples from CPRA’s CS-28 marsh creation project emphasize the important contribution of Spartina alterniflora roots to improving the shear strength of dredged soils. The direct shear test results indicated a progressive decline in root reinforcement with increasing depth across all stations. The vane shear test results showed a consistent decline in both undrained shear strength (S_u) and root area ratio (RAR) with increasing depth across all six sampling locations in Cycles 1 and 3.

The influence of Spartina alterniflora roots on soil cohesion was pronounced in Cycle 1, with increases of roughly 130% in Layer 1 at a depth from 0 to 8 cm, 70% in Layer 2 at a depth from 8 to 16 cm, and 12.5% in Layer 3 at a depth from 17 to 24 cm. In Cycle 3, root reinforcement yielded similar improvements in Layers 1 and 2—approximately 127% and 124%, respectively—while the effect in Layer 3 remained minimal.

The vane shear test results revealed a consistent decline in both undrained shear strength (S_u) and root area ratio (RAR) with increasing depth across all six sampling locations in Cycles 1 and 3. The highest undrained shear strength was observed in the top layer, ranging from 6.82 kPa to 10.45 kPa, while the lowest values were recorded at a depth of 40 cm, ranging from 3.18 kPa to 4.54 kPa.

These findings underscore the significant impact of roots on the undrained shear strength of rooted soils. Although larger-diameter roots supported higher peak loads in the tensile tests, smaller-diameter roots demonstrated a relatively greater tensile strength, consistent with the findings of Shahrier et al. [36]. This research led to the development of a modified W&W model with a root-induced cohesion coefficient of 0.058, significantly lower than the previously proposed value of 1.2 [28]. This modified model provides a useful tool for estimating the root-induced soil cohesion of Spartina alterniflora at the site of project CS-28. The findings from the in situ vane shear tests, laboratory direct shear tests, and analytical models consistently demonstrated that Spartina alterniflora roots contribute significantly to soil reinforcement, enhancing the shear strength of coastal soils. These findings underscore the effectiveness of Spartina alterniflora as a soil reinforcement agent for the recently created dredged lands in coastal Louisiana. This study further suggests that root reinforcement should be more accurately assessed using in situ direct shear tests or large-scale direct shear apparatuses in the laboratory, as these methods are better suited for testing samples with large roots. Additionally, collecting soil and root specimens across different seasons is recommended to provide a more comprehensive evaluation of the reinforcement effect contributed by vegetation.