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Soil Physics

Shrinkage and Subsidence in a Marsh Soil

Measurements and Preliminary Model

^a UMR HYDRASA 6532 du CNRS, Ecole Supérieure d'Ingénieurs de Poitiers, 40, Av. du Recteur Pineau, 86022 Poitiers Cedex, France
^b INRA Domaine Expérimental de St Laurent de la Prée, 17450 St Laurent de la Prée, France

^* Corresponding author (patrick.dudoignon{at}univ-poitiers.fr)

	ABSTRACT

TOP ABSTRACT INTRODUCTION SITE DESCRIPTION THEORY RESULTS DISCUSSION CONCLUSIONS APPENDIX 1 REFERENCES

 
Modeling the shrinkage and subsidence of soils is generally based on the laboratory shrinkage curves established from liquid state to shrinkage limit, rarely exhibited in situ. We studied the vertical behavior of clay-dominant soils from the Marais de l'Ouest (France) in the 20 to 100% water content range. The consolidation states were quantified by recording profiles of wet density (_b) and gravimetric water content (W) down to the depth of 2.50 and 2.00 m in a sunflower (Helianthus annuus L.) field and a grassland, respectively. Under the evident surface consolidation, a paleosol was observed at 1.3-m depth in the sunflower field. The W profiles show two superimposed layers: in the upper layer, W increased from the shrinkage limit (W_s) to the plasticity limit (W_p), the W profiles bounded by the wet and dry season profiles; in the subjacent layer (100% > W > W_p), the W profiles were quite constant. The depth of W_p marks the end of the downward progression of the shrinkage cracks. The properties of shrinkage were established through drying stages on intact samples. In the W_s to W_p domain, the linearity of the volume–water content relation allows the modeling of the interseasonal volumetric distribution of the macroporosity due to the shrinkage cracks. The preliminary model of porosity behavior proposed agrees with the two superimposed layers: the W_s to W_p domain characterized by isotropic shrinkage (shrinkage geometry factor r = 3), and the W > W_p domain characterized by subsidence only (r = 1).

	INTRODUCTION

TOP ABSTRACT INTRODUCTION SITE DESCRIPTION THEORY RESULTS DISCUSSION CONCLUSIONS APPENDIX 1 REFERENCES

 
MARSH SOILS mainly result from the reclaiming of lands from the sea by polders. They are clay-dominant soils generally formed by the "maturation" of the initial fluviomarine sediments. The downward progression of the desiccation front from the air–soil interface to depth causes a shrinkage mechanism that operates in three dimensions. On the horizontal plane (x, y), it is the development of the fracture network. Along the vertical axis (z), the volume decrease induces subsidence (Hallaire, 1988a, 1988b; Camuzard, 2000; Pons et al., 2000; Bruand et al., 2001). This mechanism of soil consolidation from the surface may be due to (i) the shrinkage induced by air desiccation, (ii) the shrinkage caused by water consumption by plants, and (iii) possibly farm machinery compaction.

The clay-dominant soil undergoes shrinkage and swelling that induce drastic evolution of its microstructure and, consequently, hydraulic properties (Tessier and Pedro, 1984; Biarez et al., 1987; Tessier et al., 1992; Bruand and Tessier, 2000; Chertkov and Ravina, 2000; Dudoignon et al., 2004). That is why the calculation of hydraulic mass balances in such complex media needs the modeling of the porosity behavior on two scales: the fracture network progressing from surface to depth and the associated micro- to mesoporosity within the prisms.

The shrinkage curves measured on intact peds show a typical sigmoid shape with linear and curvilinear parts associated with W domains (Tariq and Durnford, 1993; Braudeau et al., 1999). In the unsaturated domain, the shrinkage curves differ following the scale of investigation and the associated size of porosity taken into account (Hallaire, 1988a, 1988b; Cabidoche and Ozier-Lafontaine, 1995; Voltz and Cabidoche, 1995; Chertkov et al., 2004; Chertkov, 2005).

We present a preliminary model of the shrinkage fracture behavior and subsidence due to the seasonal drying cycles. This model is based on in situ recording of the gravimetric water content (W) and wet density (_b) profiles in a grassland and a sunflower field of the INRA experimental site of St Laurent de la Prée (Atlantic coast of France). The profiles exhibit W values ranging from the W_s on the surface to the liquid limit (W_l) at depth. The shrinkage curves of the clay-rich material were determined on intact samples whose small sizes avoided the shrinkage cracks. The preliminary model of shrinkage cracking and subsidence was also supported by the in situ location of the depths of W_s, W_p, and W_l.

	SITE DESCRIPTION

TOP ABSTRACT INTRODUCTION SITE DESCRIPTION THEORY RESULTS DISCUSSION CONCLUSIONS APPENDIX 1 REFERENCES

 
In the Marais de Rochefort (French Atlantic Coast, Charente Maritime), the marshes and associated soils are formed on the clay-rich formations named Bri that result from the silting of an erosion basin in Jurassic limestones during the Flandrian transgression. The soil studied is located at the experimental site of St Laurent de la Prée (INRA) in the Marais de Rochefort. These recent soils (10 000 yr BPE) have developed from the maturation and compaction of salt-marsh mud. Two series of profiles, P1 and P2, were studied and investigated through the successive seasons of 2003 and 2004. The profiles P1 (45°58'35'' N, 01°00'05'' W) developed under sunflower crops drained by polyvinyl chloride pipes. The profiles P2 (45°59'16'' N, 01°01'04'' W) have developed under grassland since at least 1964.

The samples represent a range of properties consistent with the pelosol characteristics of the INRA pedologic referential: heavy clay everywhere and rich in carbonates (Morizet et al., 1970; Baize and Girard, 1995; Pons and Gerbaud, 2005; Table 1). Illite, kaolinite, smectite, illite–smectite mixed layers, and minor chlorite are the dominant clay minerals (Morizet et al., 1970; Ducloux, 1989).

The vertical prismatic structure, which developed into pillar structure, occurs in both fields (Fig. 1a and 1b; Table 3). The downward progression of the vertical cracks stops at the depth of W_p: 0.70 m under the grassland and 1.50 m under the sunflower field.

View larger version (114K): [in this window] [in a new window]   Fig. 1. (a) Prismatic structure of the consolidated Bri induced by the shrinkage cracks; the ancient cracks are filled with recent clay-rich material deposit (depth of 0.50 m); (b) contact between the beige Bri and the black and organic paleosol. The vertical cracks crosscut the paleosol level (depth of 1.30 m).

	THEORY

TOP ABSTRACT INTRODUCTION SITE DESCRIPTION THEORY RESULTS DISCUSSION CONCLUSIONS APPENDIX 1 REFERENCES

[1]

[2]

[3]

where V_wet is the volume of the initial prism in wet state, V_dry is the volume of the prism in the dry state, and V, a, and h are the volumetric shrinkage, side shrinkage, and height shrinkage of the prism, respectively. Finally, a expressed as a function of the volumetric shrinkage, is:

[4]

Moreover, the variation of the crack aperture is a.

View larger version (30K): [in this window] [in a new window]   Fig. 2. Schematic representation of (a) the volumetric shrinkage of the unitary prism (a = prism side dimension, h = prism height dimension, a and h = decrease of prism dimensions), and (b) crack opening (horizontal shrinkage) and subsidence (vertical shrinkage) phenomenon in the grassland field. Layer 1 = solid state (W [gravimetric water content] < Wp [plasticity limit]), crack opening and subsidence operate simultaneously. Layer 2 = plastic to "pseudo liquid" state (W > Wp), only subsidence operates (b = wet density of the clayey matrix, = microporosity of the clayey matrix, fracture area = horizontal shrinkage (cracks) at the soil surface, a1/3 = calculated aperture of crack, WSTS = wet season topographic surface, DSTS = dry season topographic surface).

View larger version (20K): [in this window] [in a new window]   Fig. 3. Scheme of the shrinkage lines of the fraction <400 µm (Circle 1 to Circle 2) and shrinkage lines including the volume of cracks (Vc): hatched area = Vc; dry and wet black points = state of the soil at surface (depth = 0) for the dry and wet seasons, respectively; r = shrinkage geometry factor; Circle 1 = initial high water content sample; Circle 2 = zero water content sample.

View larger version (17K): [in this window] [in a new window]   Fig. 4. Representation of (a) the shrinkage curves, in the void ratio–water content (e–W) diagram, of 1.65- (), 1.80- () and 1.96-m-deep (•)intact samples (lozenges = fraction <400 µm, full straight line = e linear regression calculated in the 20 to 40% W domain, ZS = zero shrinkage, RS = residual shrinkage, PS = proportional shrinkage, SS = structural shrinkage); and (b) height–water content of the intact samples (full curved line = polynomial height calculation according to the isotropic shrinkage, Ws = shrinkage limit, Wp = plasticity limit).

[5]

where z is the vertical dimension of the volume and z, the variation of z, is equal to 3 (Chertkov et al., 2004; Chertkov, 2005). In the plastic state, W > W_p, the shrinkage curve represents the shrinkage of the saturated clay-rich matrix without any crack opening. Only the vertical shrinkage (subsidence) operates (r = 1).

Model Development
In the void ratio (e)–W diagram (Fig. 4), the shrinkage curves of the clay-dominant soils show four domains in agreement with the zero shrinkage, residual shrinkage, proportional shrinkage, and structural shrinkage zones distinguished by Tariq and Durnford (1993) and Braudeau et al. (1999). In the proportional shrinkage domain, the equation of the shrinkage line of intact samples is

[6]

where A is the _s/_w ratio, where _s is the real density of grains (g cm^–3) and _w is the water density (1 g cm^–3), and W is the gravimetric water content (%).

Consequently, in a V–W diagram, the volumetric shrinkage line is

[7]

where V_s is the volume of grains, V_v is the volume of voids, = AV_s, and ß = V_s.

In the case of isotropic shrinkage of saturated material, the relations between the volumetric (V) and linear (h) shrinkages are simple. In the case of cylindrical samples, with h equal to diameter, the variation of h can be calculated from the V/W relation Eq. [7] as follows:

[8]

Thus, a preliminary model of crack apertures may be calculated from the differences between the value of W of an in situ W profile and a reference of W₁₀₀ (W = 100%). According to the relation prevailing between the volumetric and linear shrinkage lines (Eq. [8]), the vertical variations of volume V of the clayey soil can be easily calculated with W profiles simplified in linear segments (Appendix 1). So, for each linear segment, the V of one unitary volume located between the z₁ and z₂ depths, can be calculated as follows:

[9]

where the segment equation is W = (z – d)/c, z [z₁; z₂], c is the slope of the segment and d is the value of the intersection between the segment and the ordinate axis. More generally, for n successive segments between z₁ and z_n:

[10]

Considering the differences between the wet and dry season W profiles (Fig. 5 and 6) or referring to an initial W_p state (Fig. 7 ), the calculation indicates the macroporosity profiles of cracks during the dry season and the possible residual macroporosity during the wet season (Fig. 6 and 7).

View larger version (34K): [in this window] [in a new window]   Fig. 5. Vertical profiles of (a) wet density and (b) gravimetric water content in the sunflower field (P1) recorded in July 2003, January 2004, and March 2004, and (c) wet density and gravimetric water content in the grassland field (P2) recorded in February 2003, July 2003, March 2004, and May 2004 (straight line = simplified dry water content profile, dashed line = simplified wet water content profile).

View larger version (18K): [in this window] [in a new window]   Fig. 6. Vertical profiles of (a) the volumetric shrinkage (% v/v) between the wet and the dry water content profiles, and (b) the half crack width (cm) calculated by difference between the wet and dry water content profiles of grassland (prism side a = 7 cm) and sunflower (prism side a = 13 cm).

View larger version (16K): [in this window] [in a new window]   Fig. 7. Vertical profiles of (a) the volumetric shrinkage (% v/v) for the wet and dry water content profiles referring to the plasticity limit (Wp) in the grassland field, and (b) the half crack width (cm) calculated for the wet and the dry water content profiles referring to the plasticity limit (Wp) in the grassland field (prism side a = 7 cm).

[11]

where and are the coefficients of the straight line h = W/100 + .

The generalization with n successive W segments allows the calculation of the vertical shrinkage:

[12]

	RESULTS

TOP ABSTRACT INTRODUCTION SITE DESCRIPTION THEORY RESULTS DISCUSSION CONCLUSIONS APPENDIX 1 REFERENCES

 
Shrinkage Characteristics of Small Samples
In the Casagrande diagram, the liquid limit (W_l) and the plasticity index (I_p) values, measured on the fraction <400 µm (International Organization for Standardization, 2004), classify the soil surface (depth to 0.05 m, P1) as organic clay minerals and others (0.5 m in P2, 1.85 m in P2, and 2.00 m in P1) as very plastic clay minerals (Table 4). Following these measurements, which are independent of the in situ microstructure of the soils, the different samples present the same linear evolution of volume vs. water content (the volumetric shrinkage line) and an equivalent shrinkage limit (W_s) in the narrow 18 to 20% W range (Fig. 4a).

(i) quite constant e in the 0 to 15% W domain (zero shrinkage)

(ii) concave curve in the 15 to 20% W domain (residual shrinkage)

(iii) linear shrinkage in the 20 to 40% W domain (proportional shrinkage)

(iv) convex curve in the W > 40% domain (structural shrinkage).

[13]

In a simplified linear segment of the W profile, the variation of volume V at z depth may be calculated as follows:

[14]

At the same time, the heights of the samples were measured using comparators at successive water contents. Each height is the average value of five equidistant measurements on the upper face of the cylindrical samples. The precision of the measurement is 0.01 mm. The results are represented in a normalized height–water content diagram (Fig. 4b). Heights are normalized by the heights of the dried samples.

The comparison between the measured heights and the heights calculated following the polynomial curve (Eq. [8]) shows three domains (Fig. 4b):

(i) in the 0 to 20% W domain, the calculated h are lower than the measured h

(ii) in the 20 to 40% W domain, the calculated h accord with the measured h and can be approximated by the linear relation

[15]

(iii) for W > 40%, the measured h values are lower than calculated h.

Field Observations
The wet density (_b) was measured on samples by the method of double weighing with paraffin coating (American Society for Testing and Materials, 1999; Normes Françaises, 1991). Gravimetric water content was determined after drying at 105°C for 24 h:

[16]

where M_w and M_d (g) are the wet and dry masses of the sample.

In the grassland field P2, the W profiles exhibit two vertical layers. In the upper layer (0–0.70 m), the W values evolve on the surface from 18 to 32% from the dry to the wet season, respectively, whereas they are quite constant at 40% at the depth of 0.70 m. Between the depths of 0.70 and 2.00 m, the W profiles are quite constant through the seasons (Fig. 5). Thus the W profiles can be simplified by only two linear segments representative of the upper (0–0.70 m) and lower (0.70–2.00 m) layers. In the sunflower field P1, the W profiles also show two main superimposed layers: the upper layer from the surface to a depth of 1.50 m, which follows the seasonal W variations, and the lower layer between a depth of 1.50 and 2.00 m quite unchanged through the seasons (Fig. 5). Nevertheless, the W profiles are complicated by the presence of the paleosol between 1.30- and 1.50-m depth and by the plowing effect observed from the surface to the depth of 0.50 m (Fig. 5). Thus the 0- to 1.50-m zone has to be subdivided into three superimposed layers: 0 to 0.50, 0.50 to 1.30, and 1.30 to 1.50 m. In the sunflower and grassland fields, the dry and wet season W profiles have been modeled according to successive linear segments: W = (z – d)/c for each layer (Fig. 5; Table 5).

On the surface of the grassland field, the volume percentage of the prismatic network of cracks, calculated from the differences between the water contents of the wet and dry seasons, is 12% (Fig. 6). It is equivalent to apertures of prismatic joints of 0.4 cm calculated for prisms with hexagon side lengths of 7 cm (Fig. 6). These are crack widths equivalent to those calculated by Bruand et al. (2001) for soils of Western Australia in the same 1.70 to 1.95 wet density range. The crack porosity calculated referring to the referential W_p reaches 18% and agrees with the equivalent macroporosity measured by Velde (1999) in soils of the Marais Poitevin.

On the surface of the sunflower field, the plowing effect on the soil structure induces an increase in the macroporosity of up to 19% in volume. The equivalent joint aperture reaches 1.3 cm with hexagon side lengths of 13 cm (Fig. 6).

	DISCUSSION

TOP ABSTRACT INTRODUCTION SITE DESCRIPTION THEORY RESULTS DISCUSSION CONCLUSIONS APPENDIX 1 REFERENCES

 
In the two studied fields P1 and P2, according to the W profiles and Atterberg limits, three domains can be identified from the surface to depth (Fig. 3, 4, and 5):

(i) The surface solid domain (W < W_p), unsaturated (W < W_s), or saturated (W_s < W < W_p). The in situ measured W are always greater than or equal to W_s. They characterize saturated states within the prisms. The in situ wet densities are maximum (1.90–1.95 g cm^–3).

(ii) The intermediate saturated and plastic domain (W_p < W < W_l). The wet density of the sediment decreases according to the porosity increase.

(iii) The lower "pseudo liquid" domain (W > W_l) characterized by very high W values, which reach 100% at a depth of 2.0 m in P2.

The isotropic shrinkage properties of the clay material in the W_s to W_p domain suggest a simplified calculation of the soil subsidence from the vertical water content profiles. In fact, this calculation of subsidence has to be corrected by the possible propagation of subhorizontal cracks and fissures between peds (Hallaire, 1988b). Without the measurement and quantification of the horizontal cracks within prisms, we decided not to take into account the horizontal crack network in our model. The material is modeled as an assemblage of prisms with only clay-matrix microporosity and vertical interprism joints taken as macroporosity. Thus this preliminary model of the subsidence deduced from the W profiles uses a simple shrinkage geometry factor r = 3 in the upper W < W_p layer.

The interseasonal subsidence calculated from the differences between the W profiles of the dry and wet seasons are 2.3 and 7.2 cm in the grassland and sunflower fields, respectively. These values agree with the vertical compaction measured by Hallaire (1987), using his transductor in alluvial deposits on the site of Vignère. Our calculated values of subsidence are lower than the topographic variations of 4 and 11 cm measured in the grassland and sunflower fields, respectively. These subsidence calculations are based only on the interseasonal behavior of the upper layer (0–W_p), referring to a constant depth of W_p. They do not take into account the variation in the depth of W_p, which can be induced by the water table variation in the two studied fields, or the farm machinery compaction in the plowing zone of the sunflower field.

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION SITE DESCRIPTION THEORY RESULTS DISCUSSION CONCLUSIONS APPENDIX 1 REFERENCES

 
The specificity of the marsh of St Laurent de la Prée offers the possibility of investigating in situ a clay-dominant soil in the 20 to 100% W range. Chronologically, the structural maturation of the sediment has operated following two stages: (i) the primary consolidation of the muddy and salt-clay-dominant sediment, and (ii) the current wetting–drying interseasonal cycles.

The compaction of the clay-dominant soil in a saturated state and desiccation up to the unsaturated state have similar consequences for the closing of the microporosity. Thus, the recording of simple _b and W profiles show that the soil structures are developed down to depths of 1.50 and 0.70 m in the sunflower and grassland fields, respectively. In the studied profiles, these depths are characterized by W = W_p: they mark the inferior limit of the shrinkage crack propagation. The shrinkage curves obtained by drying the intact samples agree with the shrinkage lines obtained on the fraction <400 µm. In the 20 to 40% W domain, they validate the isotropic shrinkage of the clayey material.

The soil consolidation, the prismation, and the subsidence are explained and modeled taking into consideration two layers: the subsurface layer characterized by a clay-rich material in solid state (W < W_p) and the deeper layer characterized by the sediment in plastic or "pseudo liquid" state (W > W_p). In the surface layer, the shrinkage geometry factor (r = 3) characterizes the isotropic volume change: shrinkage and subsidence operate simultaneously. In the deeper layer the shrinkage geometry factor is equal to 1-only the subsidence mechanism operates.

The porosity of the sediment is restricted to a microporosity of the clay matrix when W > W_p. This microporosity increases with depth up to 73% at 2.00 m deep (Fig. 2). At the surface, the global porosity has to be separated (or simplified in our calculation) into the macroporosity of the crack network and the microporosity of the matrix within the prisms. During the drying stages, the crack macroporosity increases, whereas the microporosity within the prisms decreases simultaneously. The maximum of wet density after shrinkage of 1.95 to 2.05 g cm^–3 within prisms suggests their saturation even in the dry season.

The shrinkage curves usually represented in the e–W diagram or in the specific volume–water content diagram are determined from the laboratory drying tests. The _b and W profiles recorded down to a depth of 2.00 m in the marsh of St Laurent de la Prée allow the comparison of the in situ soil structure behavior in the 0 to 100% W range with the shrinkage curves measured in the laboratory. The study points out the role of the W_p depth in the downward progression of shrinkage cracks and allows a preliminary model of the in situ shrinkage behavior of the soil.

	APPENDIX 1

TOP ABSTRACT INTRODUCTION SITE DESCRIPTION THEORY RESULTS DISCUSSION CONCLUSIONS APPENDIX 1 REFERENCES

 
Equations of the Vertical Variations of Volume
The linear relationship between the volume and water content demonstrated in the proportional shrinkage domain of Braudeau et al. (1999) is

[A1]

The reference volume is calculated for W₁₀₀ (W = 100%) as follows:

[A2]

The volumetric shrinkage (%) between V_ref and V_z (volume at z depth) is

[A3]

[A4]

where W_z is the water content at z depth. So,

[A5]

[A6]

The volumetric shrinkage (V) between z₁ depth and z₂ depth is

[A7]

Thus, for each linear segment, the V of one unitary volume located between the z₁ and z₂ depths can be calculated as follows:

[A8]

where the segment equation of water content vs. depth is W = (z – d)/c, z [z₁; z₂].

	ACKNOWLEDGMENTS

 
This study was supported by the Région Poitou-Charentes and the Parc Interrégionnal du Marais Poitevin.

Received for publication August 5, 2005.

	REFERENCES

TOP ABSTRACT INTRODUCTION SITE DESCRIPTION THEORY RESULTS DISCUSSION CONCLUSIONS APPENDIX 1 REFERENCES

 

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