Experimental and numerical analysis of soil desiccating cracks in compacted and non-compacted specimens

. This paper presents the results and analysis of two cracking tests carried on specimens of silty clay. One specimen was prepared in slurry conditions without applying energy and the other specimen was compacted. They were dried in an environmental chamber at a constant temperature and relative humidity to study the effect of the initial consistency on the cracking behaviour. Weight measurements and photographic images taken at regular intervals documented the evolution of the specimens. THM models were then carried to capture the unsaturated flow in the porous medium due to evaporation, and its resulting shrinkage. All the numerical analyses were coupled, incorporating the effect of porosity change on the balance equations and the constitutive model. The transfer coefficients in the imposed drying boundary condition were based on calculations of aerodynamic surface resistances, taking into consideration the new fronts for evaporation created by the cracks. The constructed numerical model results capture the gravimetric water content loss and the occurring shrinkage for both specimen conditions.


Introduction
Laboratory experiments on desiccation cracking of soils are commonly conducted to study the impact of cracks on many geotechnical works such as landfills, embankments, earth dams, and waste cover reservoirs. The generation of cracks will eventually induce changes in the hydromechanical behaviour. Currently, the analysis of cracking in desiccating soils is far from being a routine and specific experiments must be developed to understand the processes involved in this phenomenon. Also, cracking alters the boundary conditions between the soil and the atmosphere. This must be taken into account when updating the boundary conditions in numerical models [1,2]. These models must consider the dynamic boundary conditions in the open crack surface, in which the vapour flux varies according to the aerodynamic resistance. This paper presents part of an ongoing research project exploring the effect of water content and compaction on the crack pattern of desiccating soils. Two specimens of silty clay prepared with different initial conditions are presented. One specimen was prepared in slurry conditions without applying energy and the other specimen was compacted on the dry side of Proctor standard. It appears from the experiments that specimens compacted on the dry side are less sensitive to cracking, which could be related to the stiffness of soils compacted using low water content [3]. However, the complete picture of the relationship between compaction water content and cracking potential will be obtained after performing all the planned experiments.

Soil properties
The soil used in the experiments was a silty clay from the Agròpolis site (Llobregat River delta near Barcelona, Spain), whose more relevant parameters for soil classification are given in Table 1.
The soil used was air dried and carefully crushed to destroy aggregates. Then, a 2 mm sieve was used to remove coarse particles. The resulting material was mainly silt and clay, with a fraction of fine sand also included. Liquid limit (w L ) 29% Plastic limit (w P ) 17% Unified soil classification system CL

Soil desiccation tests
Two soil specimens with different initial consistency were dried using an environmental chamber designed to study the desiccation response and behaviour of the soil under controlled or imposed environmental conditions controlling temperature (T) and relative humidity (RH). The specimens were prepared in cylindrical with grooved bases that limit the displacements at the bottom. One specimen was prepared in slurry conditions, without applying energy when pouri specimen was compacted. The trays were 10 cm in height and 80 cm in diameter for the slurry specimen but 40 cm in diameter for the compacted specimen are plans to perform several experiments with different diameters to check the size effect. Here, for both cases, the circular tray with the specimen was placed in the closed chamber and the desiccating process set by circulating dry air keeping the environmental chamber at RH = 30% and T ≈ 23°C, see Fig. 1. The drying process continued until the weight reached a ste condition.
The weight of the specimen was monitored to record the evolution of the global gravimetric water content, which is a measure of the water mass changes in the soil.
Photographs were taken at regular intervals to appraise the shrinkage and crack formation. The descriptor of the superficial cracking is the Crack Intensity Factor (CIF) [6], which is equal to the area of the formed cracks over the intact area. The images were processed using an image analysis technique in the literature [7] to determine the area of cracks and then calculate the CIF values. Fig. 2 shows initial and final surface of the two analysed soil specimens with different initial consistency were dried using an environmental chamber [5] specially desiccation response and cracking behaviour of the soil under controlled or imposed controlling temperature (T) in cylindrical trays the displacements at the in slurry conditions, pouring; the other specimen was compacted. The trays were 10 cm in ht and 80 cm in diameter for the slurry specimen but eter for the compacted specimen. There are plans to perform several experiments with different diameters to check the size effect. Here, for both cases, the circular tray with the specimen was placed in the closed chamber and the desiccating process set by circulating dry air keeping the environmental chamber at The drying process until the weight reached a steady-state The weight of the specimen was continuously monitored to record the evolution of the global gravimetric water content, which is a measure of the gular intervals to shrinkage and crack formation. The descriptor of the superficial cracking is the Crack which is equal to the area of . The images were technique explained to determine the area of cracks and Fig. 2 shows only the initial and final surface of the two analysed tests.
Environmental conditions setting on the chamber: temperature and relative humidity for slurry and compacted

Preparation of slurry specimen
The solid particles were mixed produce a liquid consistency at a water content higher than the liquid limit. The initial content for the slurry specimen This fluid mixture was carefully poured on the round tray avoiding air bubbles or addi specimen surface was levelled with a straight edge to get a uniform surface at the beginning of the test in Fig. 2a.

Preparation of compacted
The solid particles were mixed with enough water to produce the moisture according to the gravimetric water content required for the compaction process. moisture content for the compacted specimen was 12% below the optimum standard Proctor In this case, the specimen was compacted by a dynamic method using the hammer of the Proctor Marshall test. Five layers of 2 cm in high were adopted, and 68 hits on each one were applied. This compaction routine was defined to equalize the energy applied in the Standard Proctor test with th specimen. The surface of the compacted specimen was carefully levelled using a straight edge and filling holes to get a uniform initial surface, as shown in

Numerical simulations
The problem is THM-coupled in temperature, unsaturated flow in the porous medium due to evaporation, and changes in the stress field the resulting shrinkage. specimen solid particles were mixed with enough water to produce a liquid consistency at a water content higher than the liquid limit. The initial gravimetric water content for the slurry specimen was 43%.
fluid mixture was carefully poured on the round air bubbles or additional voids. The specimen surface was levelled with a straight edge to get a uniform surface at the beginning of the test, as shown compacted specimen solid particles were mixed with enough water to produce the moisture according to the gravimetric water compaction process. The initial moisture content for the compacted specimen was 12%, below the optimum standard Proctor. s case, the specimen was compacted by a dynamic method using the hammer of the Proctor Marshall test. Five layers of 2 cm in high were adopted, and 68 hits on each one were applied. This compaction routine was defined to equalize the energy applied in the Standard Proctor test with that used to prepare the The surface of the compacted specimen was carefully levelled using a straight edge and filling holes to get a uniform initial surface, as shown in Fig. 2c. initial condition of the slurry inal crack pattern from slurry nitial condition of the compacted inal crack pattern from compacted simulations coupled as it incorporates changes in temperature, unsaturated flow in the porous medium due to evaporation, and changes in the stress field due to Coupling all the behaviour seems necessary as the evaporation of water from the soil body produces matrix suction, which yields shrinkage and cracking. At the same time, shrinkage and cracking can contribute to the desiccation process as shrinkage forces water out of the soil matrix and cracks create new boundaries where water can evaporate.

Formulation
The problem was solved with the Finite Element Numerical model CODE_BRIGHT [8]. The theoretical framework consists of a multiphase approach (gaseous, liquid, and solid) and multispecies (dry air, water, and solid). The liquid phase may contain water and dissolved air, and the gas phase may contain water vapour and dry air. The formulation is based on 3 main components: balance equations, constitutive equations and balance restrictions. The state variables are: displacements in each direction, u (m); liquid pressure, (MPa); gas pressure, (MPa); and soil temperature T (°C). Thermal equilibrium is assumed between phases. Balance momentum for the medium is given by the stress equilibrium equation with the mechanical constitutive equation, while for the fluid phase the constitutive equations are Fick's and Darcy's laws.
The mass balance equations were established following the compositional approach, which is for species rather than phases. The total mass flux of a species in a phase is the sum of non-advective fluxes (diffusive/dispersive), and advective fluxes caused by both fluid and solid motions. An expression for porosity variation caused by volumetric deformation and solid density variation is obtained from the solid mass balance equation.
The basis for the comprehensive mechanical constitutive model are given in details in the papers describing the formulation of CODE_BRIGHT [8][9][10].

Boundary conditions
For the mechanical part, the classical approach is followed to impose external forces by means of a Cauchy type boundary condition, and a node-release technique to simulate the crack propagation [1]. The bottom boundary limited displacements in horizontal direction to replicate the experimental rough bottom conditions. On the other hand, the imposed drying on the specimens in the laboratory is applied numerically through a hydraulic boundary condition: a flow rate (outflow) of vapour mass fraction that represents the difference in relative humidity, RH, where is the flux of water vapour at the boundary, which depends on the prescribed vapour mass fraction and gas density and the current values at soil surface.
is the gaseous phase transfer coefficient factor. Replicating the experimental results requires applying similar boundary conditions to the recorded data in the environmental chamber at the laboratory. This process entails the conversion of RH and T values (Fig.1.) into and values by utilising the psychrometric and ideal gas laws: where is the maximum vapour concentration the air can hold at a given temperature, T, calculated using the vapour pressure at that given temperature and the molecular weight of water; is the air pressure (atm); is the molecular weight of dry air (kg·mol -1 ); and is the gas constant (J·mol -1 ·K -1 ).
The transfer coefficient necessary to impose the flux, , is obtained by comparing against the Latent Heat formula in the well-known surface energy equation. It can be then expressed in terms of aerodynamic (& ) and surface (& ) resistances (s·m -1 ).
According to Ohm's Law [11][12], measuring the mean wind velocity ' ( in the environmental chamber (0.3 m·s -1 ) at an altitude ) (0.7 m) from the soil surface is necessary to calculate the aerodynamic resistance where * is the von Karman's constant (0.41) [13] and ) is the roughness length for silty clay (0.001m) [14]. The wind speed is constant inside the chamber as long as the dehumidifier is operating (i.e. when RH inside the chamber is greater than 30%). Alternatively, & is dependent on the volumetric water content at the soil surface ϴ 0 [15]. It gains more significance as the specimen dries, thus hindering the advective fluxes in the soil-atmosphere boundary. The energy flux caused by mass inflow and outflow through the boundary is reduced to a Cauchy type term in the absence of heat flux. Conversely, by comparing against the Sensible Heat in the surface energy equation, the expression for energy transfer coefficient in the reduced prescribed energy flux equation is obtained.
The cracks will open a new pathway for soil-water evaporation [18]. The intensity of evaporation is contingent to the transfer coefficients assigned in the flux terms of the newly formed vertical hydraulic boundaries. The magnitude of the coefficients is governed by the wind velocity within the cracks which is expected to decrease with increasing depth, reaching null values at the bottom half of the experiment height. The decreasing crack width with depth furthermore hinders where ) 4 = ), and 5 is the diffusivity of water vapour in air at a temperature T (K).
Consequently, the model's constructed geometry is numerically divided into sequential vertical sections to reproduce the depreciating magnitude of increasing crack depth. A wind profile is assumed for each of the experiments, relying on physi observations of crack width and depth propagation with time. The newly assigned boundary condition at the crack vertical surfaces is triggered at coinciding with the first crack initiation specimen. The utilised profile is different in each case depending on the explained preceding conditions. heat transfer coefficient 1 2 however was applied equally to all surfaces of the specimen, considering the PVC holding tray to be conductive. The entire advancements in assigning representative governing equations for the soil-atmosphere interaction at the boundary is further explained in separate

Constitutive model
A set of necessary constitutive laws is associated with the formulation to establish the link between the unknowns in the balance equations and the dependant variables.
For the mechanical part, the volumetric strains are calculated in a reversible manner using a elasticity equation, based on the concept [19] [20].  Where κ and κ s are the slopes of the unload/reload curves in the 7 − ln :' and 7 − ln diagrams respectively. Recording the horizontal shrinkage using the Image Analysis technique allowed for estimating the volumetric deformations in the experiments, assuming isotropic conditions. Together with the gravimetric water content, the saturation the specimen can be computed, allowing determination of suction evolution (Fig.3). As a result, In the absence of ve fluxes become more prominent and the is then dependent upon the diffusivity of expressed as (7) is the diffusivity of water vapour he model's constructed geometry is vertical sections to reproduce the depreciating magnitude of with the increasing crack depth. A wind profile is assumed for each of the experiments, relying on physical observations of crack width and depth propagation with newly assigned boundary condition at the at specific times first crack initiation for each utilised profile is different in each case depending on the explained preceding conditions. The however was applied equally to all surfaces of the specimen, considering the PVC e entire procedure and representative set of atmosphere interaction separate papers.
A set of necessary constitutive laws is associated with formulation to establish the link between the unknowns in the balance equations and the dependant For the mechanical part, the volumetric strains are using a non-linear based on the concept of state surfaces is the mean effective stress and 8 + are constants lnE < + 0.1" 0.1 ⁄ G their values are obtained controlled triaxial and oedometer (9) are the slopes of the unload/reload lnE < + 0.1" 0.1 ⁄ G diagrams respectively. Recording the horizontal shrinkage using the Image Analysis technique allowed for estimating the volumetric deformations in the experiments, assuming isotropic conditions. Together with the gravimetric water content, the saturation ratio of the specimen can be computed, allowing determination As a result, H is obtained for both experiments. The compacted specimen exhibited a more consistent behaviour ( with regards to the slurry which w behaviour (from where the specimen's matrix suction was below 100 kPa and above it). An average value was obtained for the slurry (H = solution. As for shear deformations, the variable shear modulus G calculations were based on the of Poisson's ratio ν = 0.3 [21]. The hydraulic component used Generalized Darcy's law to represent the unsaturated advective flow in the deformable porous medium.
where K is the viscosity, is density, phase relative permeability defined by the generalized power law based on Corey's functions, and intrinsic permeability, assumed isotropic and dependent on porosity, φ , using the exponential law  To relate the suction ( saturation < during drying, the van Genuchten model [23] was used, accounting for shape parameter. for both experiments. The compacted specimen exhibited a more consistent behaviour (H = -0.0048) with regards to the slurry which witnessed a double behaviour (from where the specimen's matrix suction was below 100 kPa and above it). An average value was = -0.0816) to simplify the As for shear deformations, the variable shear calculations were based on the constant value . The hydraulic component used Generalized Darcy's law to represent the unsaturated advective flow in the is density, * J is the liquid phase relative permeability defined by the generalized power law based on Corey's functions, and k is the assumed isotropic and dependent nential law: are empirical parameters based on initial is the effective degree of saturation, hydraulic conductivity tests on porosity [22], and b is a factor accounting for the porosity influence on permeability. Where < J and < are the residual and maximum saturation respectively; is the air entry value; surface tension at a temperature T (°C); tension at temperature in which was measured; is a parameter for porosity influence on retention curve. The parameters were then acquired by fitting the curves to the experimental results from specimens with similar initial conditions for the same soil using the hygrometer and T5 Tensiometers in the laboratory (Fig.   Fig. 4. Soil Water Retention Curves for both initial conditions showing the fitted models. As for the non-advective fluxes of a species in a phase, they are composed of 2 components: molecular diffusion and mechanical dispersion. Fick's law describes the molecular diffusion of both vapour and air in the gaseous phase in terms of the particle's c of tortuosity, saturation degree and temperature. The residual and maximum is the air entry value; σ is the ; W is the surface was measured; and R is a parameter for porosity influence on retention curve. acquired by fitting the curves specimens with similar tions for the same soil using the hygrometer in the laboratory (Fig.4).
Water Retention Curves for both initial conditions used for the numerical simulations. advective fluxes of a species in a phase, they are composed of 2 components: molecular diffusion and mechanical dispersion. Fick's law describes the molecular diffusion of both vapour and air particle's coefficient of tortuosity, saturation degree and temperature. The mechanical dispersion tensors for vapour, dissolved air and heat are as well defined by Fick's law. the conductive heat fluxes are computed using the geometric weighted mean in on changes in porosity and saturation degree Table 2 sums up the numerical parameters used for each studied experiment.

Results
The models are processed based on the applied boundary conditions and the constitutive equations with the corresponding parameters. The gravimetric water content for each of the experiments was evaluated numerically by deducing the water content of each mesh from the computed vapour content and liquid saturation degree, and compared against the physical results from the laboratory. Figure 5 presents that comparison for both experiments showing a good agreement. The crack intensity factor is calculated as the area of cracks over the initial specimen area. The numerical model captures the volumetric desiccation. However, numerically the model assumes isotropic conditions and homogeneity. shrinkage is captured on the perimeter only. For the compacted specimen it did not illustrate a setback, since the physical results suggest the same behaviour of a mere perimeter crack. However, exhibited internal cracks in the laboratory experiment, whereas the simulation was only able to capture it as a horizontal shrinkage at the perimeter results for the slurry (Fig. 6). The simulation results exhibited a double-phase behaviour as suggested by (  3), where the numerical results at the first half of the test and elaborates its rate at the second half, but reaching similar residual values mechanical dispersion tensors for vapour, dissolved air and heat are as well defined by Fick's law. Additionally, the conductive heat fluxes are computed using the geometric weighted mean in Fourier's law, depending on changes in porosity and saturation degree [24] [25].
sums up the numerical parameters used for models are processed based on the applied boundary conditions and the constitutive equations with the corresponding parameters. The gravimetric water content for each of the experiments was evaluated numerically by deducing the water content of each mesh element from the computed vapour content and liquid saturation and compared against the physical results from Figure 5 presents that comparison for both experiments showing a good agreement.
Gravimetric water content evolution with time for both experiments, showing both the physical and numerical results.
The crack intensity factor is calculated as the area of cracks over the initial specimen area. The numerical model captures the volumetric shrinkage due to desiccation. However, numerically the model assumes isotropic conditions and homogeneity. Consequently, the shrinkage is captured on the perimeter only. For the compacted specimen it did not illustrate a setback, since s suggest the same behaviour of a However, the slurry specimen exhibited internal cracks in the laboratory experiment, whereas the simulation was only able to capture it as a horizontal shrinkage at the perimeter. This affected the 6). The simulation results phase behaviour as suggested by (Fig.  3), where the numerical results undermine the cracking at the first half of the test and elaborates its rate at the ilar residual values.

Conclusions
The paper presents two experiments on soil desiccation cracking in an environmental chamber departing from slurry and from compacted conditions, interpreted by means of a numerical finite element model considering the coupled THM phenomena involved. The numerical analyses simulate reasonably the measured desiccation rates and Crack Intensity Factor (compacted) and wet (slurry) specimens The desiccation and CIF rates are very different for the compacted and the non-compacted specimens. Desiccation rates in dry and wet specimens are affected by soil porosity, the amount of water available for evaporation and the mechanisms providing water to the surface (i.e. advection versus diffusion, which is slower). On the other hand, CIF rate is related to the stiffness of the material, which is much higher for the compacted specimen. This is part of an ongoing research project and further experiments and simulations with different initial conditions are being carried out in order to define a global picture of the desiccation and CIF rates for soils.