Simulation method for quantifying adsorbed water and free water in unsaturated soil porous medium

Abstract

The invention discloses a simulation method for quantifying adsorbed water and free water in an unsaturated soil porous medium, and relates to the technical field of molecular simulation, according to the method, a coarse graining molecular dynamics method is adopted, Wyoming sodium-based montmorillonite is selected as the unsaturated soil porous medium, microscopic water absorption and expansion behaviors of a Wyoming sodium-based montmorillonite system are studied, and then on the basis of the GB potential, the water absorption and expansion behaviors of the unsaturated soil porous medium are studied. The aging evolution and the structural response of the aggregate expansion stress of montmorillonite in the water absorption process are systematically analyzed, and the influence mechanism of the energy well depth on the expansion stress is disclosed from the angles of distribution and proportion of different types of pore water and arrangement change of laminates. According to the method, the coupling relation between the soil expansion stress and the bound water content and the coupling relation between the soil expansion stress and the total number of laminates in the unsaturated soil medium are quantitatively revealed, the mechanism of microcosmic hydration expansion of montmorillonite under the regulation and control of the energy well depth is clarified, and distinguishing of adsorbed water and free water and dynamic content quantification under the microscale are achieved.

Description

Technical Field

[0001] This invention relates to the field of molecular simulation technology, specifically to a method for quantifying the simulation of adsorbed water and free water in unsaturated porous soil media. Background Technology

[0002] In existing studies on water behavior in unsaturated soil media, the adsorption behavior of water in these media is often simulated starting from the atomic level. For example, using montmorillonite crystal layers as an unsaturated soil medium, the adsorption characteristics of water on the surface of the atomic crystal layer are studied. Although atomic-scale simulations can characterize the adsorption structure and local interactions of water on the surface of montmorillonite crystal layers, these results usually remain at the crystal layer or single-particle scale, lacking parameterized expressions that can be transferred to the aggregate or pore scale. Correspondingly, pore-scale or macroscopic models can only describe the water absorption and swelling process using empirical parameters or overall water content, and cannot reflect the two fundamentally different states of water: adsorption on the crystal layer surface and migration in the pores.

[0003] Furthermore, due to the lack of a consistent cross-scale description of water-soil interaction, existing methods can only characterize pore water holistically. Adsorbed water and free water cannot be distinguished in numerical models, and the migration capacity and confinement state of water are difficult to quantify. This mixture of states further leads to the simplification of aggregate pore structure to an idealized structure during modeling, making it difficult to incorporate the pore heterogeneity and mechanical constraints formed during soil compaction and rebound into the analysis.

[0004] Building upon the aforementioned issues, the water absorption and swelling behavior of unsaturated soil media can typically only be described by static swelling or the overall pressure-swelling relationship. The generation, release, and evolution of internal stresses during the swelling process lack microscopic support, limiting our understanding of soil swelling dynamics and local pore stress distribution. In summary, there is a lack of a transferable description of water-soil interactions from the atomic scale to the aggregate scale. Summary of the Invention

[0005] (a) Technical problems to be solved This invention provides a simulation method for quantifying adsorbed water and free water in unsaturated porous soil media, which can quantitatively analyze the dynamic evolution of water state and water behavior in unsaturated soil media sinks from the atomic scale to the aggregate scale.

[0006] (II) Technical Solution To achieve the above objectives, the present invention provides the following technical solution: a simulation method for quantifying adsorbed water and free water in unsaturated porous soil media, selecting Wyoming-type sodium-based montmorillonite as the target research object, including the following steps: S1: At the atomic scale, a simulated system of Wyoming-type sodium-based montmorillonite crystal layers and their intergranular water molecules and sodium ions was constructed to form two montmorillonite contact configurations: face-to-face and edge-to-edge. Using the center distance of the montmorillonite particles as the control variable, the interlayer spacing was gradually adjusted to generate adjacent configuration states, and the Gibbs free energy difference of each pair of adjacent states was calculated to obtain the free energy spacing relationship curve under the corresponding contact configuration. S2: Based on the free energy spacing relationship curve of each of the above, the anisotropic interaction parameters of montmorillonite particles are fitted by the Gay-Berne potential function; at the same time, multiple all-atomic water molecules between crystal layers are merged into a single coarse-grained water particle to construct a coarse-grained model of montmorillonite and water. S3: The interaction potential of the coarse-grained water particles is introduced into the simulation system, and the wetting behavior of the coarse-grained model and the change in montmorillonite interlayer spacing are used as constraints to adjust the energy well depth of the interaction between montmorillonite and water through parameter inversion. S4: Based on the energy well depth, a certain number of montmorillonite particles are filled into the three-dimensional simulation area, and structural relaxation is performed under constant particle number, volume and temperature conditions; then, different confining pressures are applied for isotropic compression loading, and the rebound process is simulated under low confining pressure conditions to obtain a montmorillonite aggregate configuration with pore compaction characteristics and mechanical stability after equilibrium. S5: Add coarse-grained water particles into the pores of the montmorillonite aggregate configuration, and use coarse-grained molecular dynamics to simulate the migration and distribution of water; after water absorption equilibrium is reached, perform kinetic relaxation under isothermal conditions. S6: Based on the trajectory results of the aforementioned dynamic relaxation, taking the configuration of montmorillonite aggregates with added coarse-grained water particles as a reference, the relative displacement evolution of water particles at different time scales is statistically analyzed; and the migration rate difference is analyzed by combining the well depth analysis of different montmorillonite-water interaction energies, so as to realize the distinction between adsorbed water and free water and the dynamic content quantification.

[0007] In some feasible embodiments, at the whole atomic scale, Wyoming-type sodium-based montmorillonite was selected as the research object, and montmorillonite crystal layers with face-to-face contact configuration and edge-to-edge contact configuration and simulation systems of intercrystalline water molecules and sodium ions were constructed respectively. In each contact configuration, the distance from the center of the montmorillonite particle is... As a geometric control parameter, it is based on a preset spacing increment. : ; according to A series of adjacent configuration states are generated, and molecular dynamics equilibrium simulations are performed on the system in each configuration state; After obtaining the equilibrium configuration of adjacent configuration states, the potential energy affected by the spacing perturbation is calculated and recorded based on a simple overlap sampling method. Changes, and through: ; in, The unit cell parameters of montmorillonite particles in the dry state are obtained by calculating the difference in free energy between adjacent states. We obtained curves showing the change of the free energy of montmorillonite particles with the center distance under different contact configurations.

[0008] In some feasible embodiments, based on the obtained free energy and spacing relationship curves under different contact configurations, the Gay–Berne potential function is introduced to perform parameter fitting on the anisotropic interaction between montmorillonite particles; wherein, for the face-to-face contact configuration and the edge-to-edge contact configuration, the energy well depth, minimum action radius and cutoff radius of montmorillonite particles under different scale conditions are determined respectively.

[0009] In some feasible embodiments, multiple all-atomic water molecules are merged into a single coarse-grained water particle. Based on the all-atomic water system, configuration states with different water particle spacings are generated, and the free energy difference between adjacent states is calculated by the free energy perturbation method to fit the interaction potential parameters between water particles. After completing the fitting of the montmorillonite-montmorillonite and water-water interaction parameters, a unified coarse-grained montmorillonite-water interaction model was constructed.

[0010] In some feasible embodiments, based on the constructed unified model of interaction between coarse-grained montmorillonite and water, the interaction potential between montmorillonite particles and coarse-grained water particles is introduced, and the well depth of the montmorillonite-water interaction energy is used as a parameter to be determined. Under the given energy well depth conditions, montmorillonite system configurations containing coarse-grained water particles were constructed respectively, and coarse-grained molecular dynamics simulations were carried out to obtain the wetting process evolution characteristics and montmorillonite interlayer spacing changes under the corresponding conditions. Using the wetting behavior characteristics obtained at the full atomic scale and the variation of montmorillonite interlayer spacing as inversion constraints, the simulation results under different energy well depth conditions are compared and screened. By using parameter inversion, the range of well depth values ​​for the montmorillonite-water interaction energy that makes the coarse-grained montmorillonite-water interaction model consistent with the all-atom results in terms of wetting process evolution and crystal layer expansion response were determined.

[0011] In some feasible embodiments, based on the determined montmorillonite-montmorillonite and montmorillonite-water coarsening interaction parameters, a certain number of montmorillonite particles are introduced into the three-dimensional simulation region, and the space is filled according to their shape and orientation properties to construct an initial set of montmorillonite particles. Under constant particle number, volume and temperature conditions, the montmorillonite particle assembly is subjected to molecular dynamics structural relaxation so that the interparticle interactions reach a stable equilibrium state. After structural relaxation was completed, different confining pressures were applied to conduct isotropic loading simulations on montmorillonite particle aggregates, causing the aggregate structure to undergo a compaction process. After the loading process reaches stability, the rebound process is simulated under low confining pressure to release some external constraints and obtain the equilibrium configuration of montmorillonite aggregates that simultaneously contains compaction history information and stable pore structure characteristics.

[0012] In some feasible embodiments, based on the equilibrium configuration of the montmorillonite aggregates, coarse-grained water particles are introduced into the pore space between the aggregate particles to construct an initial montmorillonite-water system. Using the coarse-grained interaction parameters determined in S2 and S3, the migration and distribution of water particles in the pores of aggregates were simulated using coarse-grained molecular dynamics under constant particle number, volume and energy conditions until the water absorption behavior of the system reached a stable state. After the water absorption process stabilizes, the montmorillonite-water system is subjected to dynamic relaxation under constant particle number, volume, and temperature conditions to eliminate transient fluctuations and obtain a stable structural and energy state. Under fixed volume conditions, the internal stress of the system is continuously calculated over time based on the virial theorem, and the time history characteristics of the expansion stress generated by montmorillonite aggregates during water absorption are extracted.

[0013] In some feasible embodiments, based on the dynamic trajectory results of the montmorillonite-water system, the system configuration at the beginning of the water absorption process is used as a reference state to extract the spatial displacement information of coarse-grained water particles at different time scales; within a given time window, the relative displacement distribution characteristics of water particles relative to the reference configuration are statistically analyzed to obtain the displacement statistics of pore water migration over time.

[0014] In some feasible embodiments, under different montmorillonite-water interaction energy well depth parameters, the relative displacement distribution and mobility of water particles are compared and analyzed to identify water particles that stay in the displacement-restricted area for a long time and water particles that have greater migration ability in the pore network. Based on the differences in water particle migration behavior, adsorbed water and free water are classified, and their quantity ratio and dynamic evolution characteristics over time are further statistically analyzed to achieve the distinction and quantitative characterization of adsorbed water and free water in unsaturated soil porous media.

[0015] (III) Beneficial Effects: Compared with the prior art, this invention has the following beneficial effects: This invention, based on the GB potential model, focuses on the microscopic wetting process and structural response of aggregates of saturated Wyoming sodium-based montmorillonite (in unsaturated soil media), by determining a reasonable range for the energy well depth of montmorillonite-water. Subsequently, the evolution of the aggregate swelling stress and its correlation with pore water distribution and the arrangement of the stratified structure are analyzed. Furthermore, the coupling relationship between soil swelling stress, bound water content, and the total number of strata in unsaturated soil media is quantitatively revealed, elucidating the mechanism of microscopic hydration swelling of saturated montmorillonite under the regulation of energy well depth, and achieving the distinction and dynamic quantification of adsorbed water and free water at the microscopic scale. Attached Figure Description

[0016] Figure 1 A flowchart illustrating the steps of the simulation method for quantifying adsorbed water and free water in unsaturated porous soil media provided in this embodiment of the invention. Figure 2 This is a schematic diagram of coarse-grained modeling of Wyoming sodium-based montmorillonite in the simulation method for quantifying adsorbed water and free water in unsaturated porous soil provided in the embodiments of the present invention. Figure 3 This is a schematic diagram of coarse-grained modeling of SPC water molecules in the simulation method for quantifying adsorbed water and free water in unsaturated soil porous media provided in the embodiments of the present invention. Figure 4 A schematic diagram of the CG modeling process of the microscopic montmorillonite-water system in the simulation method for quantifying adsorbed water and free water in unsaturated porous soil media provided in the embodiments of the present invention. Figure 5 This is a schematic diagram illustrating the changes in total energy and potential energy over time in the simulation system of the simulation method for quantifying adsorbed water and free water in unsaturated porous soil media provided in this embodiment of the invention. Figure 6 A schematic diagram illustrating the change in pore water distribution during the water absorption-swelling process in the simulation method for quantifying adsorbed water and free water in unsaturated soil porous media provided in this embodiment of the invention. Figure 7 This is a schematic diagram illustrating the fitting relationship between aggregate expansion stress and bound water content in the simulation method for quantifying adsorbed water and free water in unsaturated porous soil provided in this embodiment of the invention. Figure 8 This is a schematic diagram illustrating the fitting relationship between the total number of layers and the content of bound water and free water in the simulation method for quantifying adsorbed water and free water in unsaturated porous soil provided in this embodiment of the invention. Detailed Implementation

[0017] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0018] It should be noted that, where there is no conflict, the features in the embodiments of the present invention can be combined with each other.

[0019] Combination Figures 1 to 8 The method presented here is a simulation of adsorbed and free water in unsaturated porous soil media. This method employs coarse-grained molecular dynamics to systematically study the microscopic water absorption and swelling behavior of saturated Wyoming sodium-based montmorillonite systems. Based on the GB potential, the time-dependent evolution of aggregate swelling stress and its structural response during water absorption are systematically analyzed. Furthermore, the influence mechanism of energy well depth on swelling stress is revealed from the perspectives of the distribution and proportion of different types of pore water and the changes in the arrangement of layers. By quantifying the correlation between swelling stress and bound water content and the total number of layers, the microscopic hydration and swelling mechanism of saturated montmorillonite aggregates is elucidated in depth.

[0020] In step S1, the structure of Wyoming-type sodium-based montmorillonite is first modeled at the atomic scale to clarify its cell structure, atomic composition and the distribution of exchangeable sodium ions between layers.

[0021] Specifically, commercial sodium montmorillonite (95%) was selected, with the molecular formula: ; This sodium-based montmorillonite has an average specific gravity of 2.76, a liquid limit of 520%, and a plastic limit of 42%. Based on experiments using the hexaamminecobalt ion exchange method and the BET method, the cation exchange capacity (CEC) and specific surface area are 111.12 mmol / 100 g and 31.552 m² / g, respectively. Particle size distribution, measured using a laser particle size analyzer (Mastersizer 3000, UK), ranges from approximately 0.05 μm to 4.73 μm. 72% of the particles are smaller than 2 μm.

[0022] The initial unit cell of sodium-based montmorillonite belongs to the C2 / m monoclinic system. In the dry state, its unit cell parameters are as follows: , = 99 °, ( ), ( ), ( ) 。

[0023] To avoid boundary effects, the model uses a three-dimensional periodic boundary, and the spatial group of the simulated environment is set as P1. According to... Figure 2 In the embodiments of this invention, the geometric characteristics of the montmorillonite layers are described, with the single-layer montmorillonite coarsened into ellipsoidal particles with a size set to 2a=2b=104.12 ( ). ), 2c = 9.62 ( Each coarse-grained montmorillonite particle has a mass of 86,000 amu, equivalent to the mass of a full-atom sodium-based montmorillonite of the corresponding size. The coarsening of water molecules was performed using a thermodynamic perturbation method, mapping five full-atom SPC water molecules to a spherical GB water particle. The mass of the coarse-grained water particle remained consistent with the full-atom model, with dimensions and masses of 2a=2b=2c=4 (…). ), 90 amu. Model structures of sodium-based montmorillonite and water molecules before and after coarsening are as follows: Figure 3 As shown.

[0024] Based on this, two typical configurations of montmorillonite particles with face-to-face contact and edge-to-edge contact were constructed, and water molecules and sodium ions were introduced around the configurations to form a complete montmorillonite-water molecule-sodium ion system.

[0025] Subsequently, using the center-to-center distance of montmorillonite particles as the sole geometric control variable, a series of discrete center-to-center distance values ​​were set for each contact configuration. Adjacent configuration states were generated step-by-step by applying small distance perturbations to the previous equilibrium configuration. It is important to note that for each configuration state, sufficient relaxation was performed through molecular dynamics simulations to ensure the system reached thermodynamic equilibrium under the corresponding center-to-center distance conditions.

[0026] After obtaining the equilibrium trajectories of adjacent configuration states, the Simple Overlap Sampling (SOS) method is used to statistically analyze the changes in potential energy of the system before and after the perturbation, and the free energy difference between adjacent states is calculated according to the following formula. : ; in, For the set spacing increment - ; The potential energy affected by the spacing perturbation is calculated and recorded based on the simple overlap sampling method described above.

[0027] By accumulating the free energy differences of all adjacent states, the free energy-space relationship curve of montmorillonite particle interaction as a function of center distance is finally obtained under face-to-face and edge-to-edge contact conditions.

[0028] Based on the above, it can be understood that the core function of this step is not to simulate water absorption, but to establish a quantitative description of the interaction energy directly at the atomic scale, specifically manifested in three levels: Face-to-face and edge-to-edge configurations differ fundamentally in terms of interlayer water, ion distribution, and charge environment. This step treats the two configurations separately to avoid averaging anisotropic interactions in the future. Characterizing interactions using free energy rather than instantaneous force or potential energy allows the results to naturally include thermodynamic contributions such as water molecule rearrangement and ion shielding, providing a stable energy benchmark for subsequent coarse-grained modeling. The free energy-space relationship curve is the direct basis for fitting all subsequent coarse-grained potential parameters, ensuring that the coarse-grained model is not empirically set, but traceable to behavior at the entire atomic scale.

[0029] Step one (S1) yields the following results, which can be directly used in subsequent steps: Free energy-center distance relationship curves for face-to-face and edge-to-edge contact configurations; The differences in interaction energy with distance under different configurations; The above are the objective function and constraint data provided by the Gay–Berne potential parameter fitting.

[0030] Understandably, these results will be used as is in subsequent processes to construct an anisotropic interaction model of coarse-grained montmorillonite particles, rather than being repeated at the full atomic scale.

[0031] In step one (S1), the free energy-center distance relationship curves of montmorillonite particles under face-to-face contact and edge-to-edge contact conditions have been obtained respectively. These curves fully reflect the intensity, range and anisotropic characteristics of particle interaction under different configurations in the form of free energy.

[0032] In the implementation of step two (S2), the free energy-spacing relationship curve obtained in step one is first used as the fitting target, and the Gay-Berne (GB) potential function is introduced to parametrically describe the anisotropic interaction between montmorillonite particles.

[0033] The GB potential is a single-point interaction potential applicable to rigid ellipsoids, biaxial, or spherical coarse-grained particles, effectively characterizing anisotropic interactions between non-spherical particles. This potential function comprehensively considers van der Waals interactions and electrostatic effects, and its basic expression is as follows:

[0034] ; in, (kJ / mol) represents the potential energy well depth. ( ( ) represents the effective interaction radius between atoms. This is a factor (usually 1) used to control the offset of the minimum potential energy value. ( () indicates the closest distance between the surfaces of two particles. Used to characterize the anisotropic effect caused by particle shape, This reflects the anisotropy of the system's free energy. Both of these dimensionless parameters depend on the relative well depths of face-to-face, side-to-side (equivalent to face-to-face), and edge-to-edge particles: , , , , and ,and = , = .

[0035] In addition, the potential function also includes the cutoff distance. ( (This is used to define the effective range of the interaction, thereby accurately reproducing the relationship between energy and particle separation distance.)

[0036] Specifically, for the two types of contact configurations, face-to-face and edge-to-edge, coarse-grained montmorillonite particle models of different scales (such as different equivalent plane dimensions) are selected. By adjusting the energy well depth, minimum interaction distance, cutoff radius and orientation-related parameters in the GB potential, the interaction energy given by the GB potential under different relative orientations and center distances is made consistent with the free energy curve obtained in step one in terms of both numerical value and trend.

[0037] While fitting the montmorillonite-montmorillonite interaction parameters, the water molecules were coarsened. Specifically, multiple all-atomic water molecules were merged into an equivalent coarsened water particle, and configuration states with different center distances of water particles were constructed based on the all-atomic water system. The free energy difference between adjacent configuration states was calculated using the free energy perturbation method to obtain the free energy-distance relationship between water particles, and the water-water interaction potential parameters were fitted accordingly.

[0038] After the above two processes are completed, a unified coarse-grained model is formed that simultaneously includes descriptions of montmorillonite-montmorillonite and water-water interactions.

[0039] Regarding S2, this step can be understood as a scale mapping process, which compresses the complex atomic-level information of atoms, molecules, and ions into: A coarse-grained montmorillonite particle; A coarse-grained water particle; And their interactions described by the GB potential function.

[0040] For example, in a face-to-face configuration, if the free energy curve shows a significant free energy minimum near a certain center distance, then during the GB potential fitting process, by adjusting the energy well depth and the minimum action distance, the coarse-grained montmorillonite particles can also exhibit stable attraction behavior within the same distance range. In an edge-to-edge configuration, the free energy change is more gradual, so by reducing the attraction intensity in the corresponding direction through orientation-related parameters, the configurational differences are preserved at the coarse-grained level.

[0041] In summary, step two yields the absolute trajectories of water particles throughout the simulation. However, considering that these trajectories are minor rearrangements of the aggregates themselves and that local porosity differences exist, directly using absolute coordinates for analysis would present two problems: First, different aggregates and different confinement histories are not comparable; Secondly, is the water moving, or is the overall structure undergoing minor adjustments? It's difficult to distinguish.

[0042] Therefore, in the embodiments of the present invention, this third step first involves adding coarse-grained water particles to a system consisting of a single montmorillonite particle or a small number of particles. The montmorillonite-water interaction potential is expressed as a GB potential or an equivalent coarse-grained potential, with an energy well depth. These are parameters to be determined.

[0043] For each candidate To determine the optimal values, a coarse-grained montmorillonite-water system was constructed to ensure uniform distribution of water particles within the montmorillonite interlayers and on the particle surface. Subsequently, coarse-grained molecular dynamics simulations were performed to obtain the corresponding values. The evolution of the wetting process and the trajectory of interlayer distance changes under the given conditions.

[0044] Comparing the wetting behavior characteristics (such as interlayer water molecule adsorption and arrangement) and the curves of interlayer spacing evolution with water adsorption obtained from the all-atom simulation in step one, the coarse-grained system under different conditions was calculated. The difference between the simulation results under the given conditions and the all-atom results is evaluated. The degree of matching of values.

[0045] Finally, filter by matching degree. This allows the coarse-grained model to maintain consistency with the all-atomic behavior in terms of wetting behavior and crystal layer expansion response, and outputs the montmorillonite-water interaction energy well depth range that can ultimately be used for aggregate construction.

[0046] In step three, the calibrated coarse-grained montmorillonite-montmorillonite and montmorillonite-water interaction parameters have been obtained. The goal of step four is to construct an equilibrium configuration of montmorillonite aggregates that can be used for water absorption and swelling simulations, and the specific operations are as follows.

[0047] First, select a certain number of coarse-grained montmorillonite particles (different sizes can correspond to different scale aggregates). Based on the center position and orientation properties of each particle (such as the quaternion description obtained from step two), fill the space in a cubic simulation box to ensure that there is no serious overlap between the particles initially, but maintain a certain degree of proximity to simulate the real stacking state. Specifically, fill multiple montmorillonite particles into a 5000 × 5000 × 5000 nm³ simulation box in a similar lattice manner.

[0048] To simulate the water absorption and swelling process of saturated montmorillonite aggregates, this paper is based on Figure 4 The initial structure shown was first simulated for water absorption over 25 ns under the NVE (constant number, volume, and energy) ensemble, driving the migration and distribution of water molecules between particles. After the water absorption process reached equilibrium, the aggregate system was subjected to 75 ns of kinetic relaxation under the NVT (constant number, volume, and temperature) ensemble with a time step of 0.5 fs to ensure sufficient stability of the system's energy, temperature, and geometry. Throughout this process, the evolution of expansion stress under fixed volume conditions was continuously monitored.

[0049] like Figure 5 As shown, in both the water absorption stage (NVE stage) and the expansion stress response stage (NVT stage), the total energy and potential energy of the system decrease and tend to stabilize over time, with potential energy dominating the total energy. With the increase of the montmorillonite-water energy well depth, the system energy reaches equilibrium more quickly and the energy level increases in the NVT stage, reflecting a strong clay-water interaction effect.

[0050] Under constant particle number, volume, and temperature conditions, molecular dynamics simulations were performed on the filled aggregates to gradually balance the interparticle interactions and bring the system to a thermodynamically stable state. Specifically, a 120 ns simulation was conducted at 298 K and a time step of 40 fs to stabilize the system's energy, temperature, and geometry. During this process, the particles may undergo slight rotation, translation, and local rearrangement to eliminate the non-physical stresses introduced by the initial artificial stacking.

[0051] Based on the equilibrium configuration after relaxation, the isotropic loading process of aggregates under actual soil compaction conditions is simulated by controlling the NPT ensemble to apply different confining pressures (such as 0.01, 0.1, 0.5, 1, 5 GPa). Specifically, different confining pressures are applied for 50 ns of isotropic loading to simulate the compaction process of aggregates in the soil under external pressure. At this time, the interparticle interactions are locally rearranged under high pressure, and the pore structure of the aggregates is compressed to form a more compact packing state.

[0052] After the high-pressure loading reaches a stable state, the confining pressure is gradually reduced to lower levels (e.g., 10, 1, 0.1 MPa) to simulate the rebound process of the aggregates after releasing external pressure. These operations ensure that the aggregates have both a physical compaction history and form a stable pore network, which can be directly used for water absorption and expansion simulation.

[0053] This process yields a final equilibrium aggregate configuration that retains both compaction history information and stable pore structure characteristics.

[0054] In step four, an equilibrium configuration of coarse-grained montmorillonite aggregates, including compaction history and stable pore structure, has been constructed. The core tasks of steps five and six are to introduce coarse-grained water particles into the pores of this aggregate, simulate water migration, distribution, and aggregate expansion, and ultimately identify the content and dynamic evolution characteristics of adsorbed water and free water.

[0055] To fill the pores of the aggregates with coarse-grained water droplets, a face-centered cubic arrangement is typically used to ensure uniform filling. Based on the center position and shape parameters of each montmorillonite particle, a spherical exclusion zone is constructed to remove water droplets that may overlap with the particles, ensuring that the water particles do not physically overlap with the montmorillonite in their initial state.

[0056] Under constant particle number, volume, and energy conditions, coarse-grained molecular dynamics was run to drive the migration and redistribution of water particles within pores. The simulation lasted approximately 100 ns until water molecules reached thermodynamic equilibrium within the pores. During this process, interparticle interactions and water-montmorillonite interactions ensured that water could both adsorb onto the crystal surface and fill free pores. Specifically, in a 5000×5000×5000 nm³ aggregate pores were filled with coarse-grained water particles, and the motion of water particles between pores and crystal layers was captured under the NVE ensemble for 100 ns.

[0057] After the above simulation steps, with the initial simulation state as a reference, the relative displacement distribution of water particles at different time scales is statistically analyzed using visualization and trajectory analysis software (such as OVITO). In some embodiments of the present invention, the movement of water particles can be visualized through color coding or probability distribution.

[0058] The relative displacement of water particles and the energy well depth of montmorillonite-water interaction. Correlation analysis was conducted, in which water particles with a migration amplitude close to zero were identified as adsorbed water, which are firmly bound to the surface of the crystal layer; water particles with a larger migration amplitude were identified as free water, which are mainly distributed in the pores of the aggregates.

[0059] To clarify the dynamic evolution of bound water and free water content during the wetting process of montmorillonite aggregates. Figure 6The relative displacement distribution curves of pore water at different times are shown. It can be clearly observed that as the water absorption-swelling process progresses, the shape of the distribution curves undergoes the following significant changes.

[0060] In the initial stage (5 ns), the main peak of the curve is sharp and concentrated in a relatively small displacement range, reflecting that the system is dominated by bound water. As the aggregates continue to absorb water, the main peak gradually shifts to the right and the peak value continues to decrease, indicating that the proportion of bound water is decreasing and the content of free water is gradually increasing.

[0061] By 50 ns, the distribution curve showed obvious peaks and inflection points at larger displacements, indicating that the partitioning of bound water and free water was gradually established.

[0062] After 75 ns, the curve is at 125 ( A distinct plateau forms at the relative displacement, and the overall morphology tends to stabilize: the position and width of the main peak and the height of the high-displacement section remain basically unchanged. This indicates that the ratio of bound water to free water has reached dynamic equilibrium, and the migration and reorganization of pore water within the system are approximately complete.

[0063] After water absorption and migration reach equilibrium, the system is switched to isothermal conditions (NVT ensemble), and the entire aggregate system is relaxed for approximately 100 ns using a time step of 0.5 fs. During this period, the evolution of expansion stress of the aggregate under fixed volume conditions is monitored over time using the virial theorem, generating expansion force time history curves to capture the dynamic response of the aggregate. This allows for the analysis of the aggregate expansion characteristics under different confining pressures and water contents.

[0064] Considering the potential correlation between the microscopic expansion stress of aggregates and the bound water content (Pb), therefore, Figure 7 A quantitative correlation between the two was fitted. The results show that the micro-expansion stress ( The relationship between microscopic expansion stress and bound water content follows an exponential relationship. The relationship between the expansion stress and bound water content is approximately linear, indicating that the expansion stress of the aggregates is largely dominated by the bound water content of the system. This is especially true at low... Under these conditions, an increase in bound water content will significantly enhance microscopic expansion stress.

[0065] Furthermore, the total number of layers was fitted separately. With bound water ( ), free water content ( The functional relationship between them.

[0066] refer to Figure 8 Obviously, when When ≤350 kcal / mol, and Linear positive correlation; when When ≥400kcal / mol, and They are linearly positively correlated.

[0067] This result indicates that at lower Down, Primarily dependent on bound water, an increased proportion of bound water promotes the fragmentation of large-sized laminates. At higher... Down, Primarily controlled by free water, a higher proportion of free water promotes smaller-sized laminates and an increase in the number of edge-to-face contacts. Therefore, with... The changes in the ratio of water to free water regulate the quantity and structural characteristics of the laminate, thereby affecting the evolution of expansion stress.

[0068] In summary, steps five and six play a core analytical and final output role in the entire simulation scheme. Step five obtains the swelling force time history and water distribution, while step six uses water particle mobility analysis to identify adsorbed water and free water and calculate their dynamic content. The output water mobility distribution, the ratio of adsorbed water to free water, and the evolution curve can be directly used to study the hydrodynamic characteristics of unsaturated soil porous media.

[0069] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. The scope of protection of the present invention is defined by the claims. Similarly, any equivalent structural changes made based on the description and drawings of the present invention should also be included within the scope of protection of the present invention.

Claims

1. A simulation method for quantifying adsorbed water and free water in unsaturated porous soil media, characterized in that, Wyoming-type sodium montmorillonite was selected as the target research object, and the following steps were performed: S1: At the atomic scale, a simulated system of Wyoming-type sodium-based montmorillonite crystal layers and their intergranular water molecules and sodium ions was constructed to form two montmorillonite contact configurations: face-to-face and edge-to-edge. Using the center distance of the montmorillonite particles as the control variable, the interlayer spacing was gradually adjusted to generate adjacent configuration states, and the Gibbs free energy difference of each pair of adjacent states was calculated to obtain the free energy spacing relationship curve under the corresponding contact configuration. S2: Based on the free energy spacing relationship curve of each of the above, the anisotropic interaction parameters of montmorillonite particles are fitted by the Gay-Berne potential function; at the same time, multiple all-atomic water molecules between crystal layers are merged into a single coarse-grained water particle to construct a coarse-grained model of montmorillonite and water. S3: The interaction potential of the coarse-grained water particles is introduced into the simulation system, and the wetting behavior of the coarse-grained model and the change in montmorillonite interlayer spacing are used as constraints to adjust the energy well depth of the interaction between montmorillonite and water through parameter inversion. S4: Based on the energy well depth, a certain number of montmorillonite particles are filled into the three-dimensional simulation area, and structural relaxation is performed under constant particle number, volume and temperature conditions; then, different confining pressures are applied for isotropic compression loading, and the rebound process is simulated under low confining pressure conditions to obtain a montmorillonite aggregate configuration with pore compaction characteristics and mechanical stability after equilibrium. S5: Add coarse-grained water particles into the pores of the montmorillonite aggregate configuration, and use coarse-grained molecular dynamics to simulate the migration and distribution of water; after water absorption equilibrium is reached, perform kinetic relaxation under isothermal conditions. S6: Based on the trajectory results of the aforementioned dynamic relaxation, taking the configuration of montmorillonite aggregates with added coarse-grained water particles as a reference, the relative displacement evolution of water particles at different time scales is statistically analyzed; and the migration rate difference is analyzed by combining the well depth analysis of different montmorillonite-water interaction energies, so as to realize the distinction between adsorbed water and free water and the dynamic content quantification.

2. The method for simulating the adsorbed water and free water in unsaturated porous soil media according to claim 1, characterized in that, At the atomic scale, Wyoming-type sodium-based montmorillonite was selected as the research object. Simulation systems of montmorillonite crystal layers with face-to-face contact configuration and edge-to-edge contact configuration, as well as intercrystalline water molecules and sodium ions, were constructed respectively. In each contact configuration, the distance from the center of the montmorillonite particle is... As a geometric control parameter, it is based on a preset spacing increment. : ； according to A series of adjacent configuration states are generated, and molecular dynamics equilibrium simulations are performed on the system in each configuration state; After obtaining the equilibrium configuration of adjacent configuration states, the potential energy affected by the spacing perturbation is calculated and recorded based on a simple overlap sampling method. Changes, and through: ； in, The unit cell parameters of montmorillonite particles in the dry state are obtained by calculating the difference in free energy between adjacent states. We obtained curves showing the change of the free energy of montmorillonite particles with the center distance under different contact configurations.

3. The method for simulating the adsorbed water and free water in unsaturated porous soil media according to claim 1, characterized in that, Based on the obtained free energy and spacing relationship curves under different contact configurations, the Gay–Berne potential function is introduced to perform parameter fitting on the anisotropic interaction between montmorillonite particles; wherein, for the face-to-face contact configuration and the edge-to-edge contact configuration, the energy well depth, minimum action radius and cutoff radius of montmorillonite particles under different scale conditions are determined respectively.

4. The method for simulating the adsorbed water and free water in unsaturated porous soil media according to claim 3, characterized in that, Multiple all-atomic water molecules are merged into a single coarse-grained water particle. Based on the all-atomic water system, configuration states with different water particle spacings are generated. The free energy difference between adjacent states is calculated by the free energy perturbation method, and the interaction potential parameters between water particles are fitted. After completing the fitting of the montmorillonite-montmorillonite and water-water interaction parameters, a unified coarse-grained montmorillonite-water interaction model was constructed.

5. The method for simulating the adsorbed water and free water in unsaturated porous soil media according to claim 4, characterized in that, Based on the unified interaction model between coarse-grained montmorillonite and water, the interaction potential between montmorillonite particles and coarse-grained water particles is introduced, and the well depth of the montmorillonite-water interaction energy is used as a parameter to be determined. Under the given energy well depth conditions, montmorillonite system configurations containing coarse-grained water particles were constructed respectively, and coarse-grained molecular dynamics simulations were carried out to obtain the wetting process evolution characteristics and montmorillonite interlayer spacing changes under the corresponding conditions. Using the wetting behavior characteristics obtained at the full atomic scale and the variation of montmorillonite interlayer spacing as inversion constraints, the simulation results under different energy well depth conditions are compared and screened. By using parameter inversion, the range of well depth values ​​for the montmorillonite-water interaction energy that makes the coarse-grained montmorillonite-water interaction model consistent with the all-atom results in terms of wetting process evolution and crystal layer expansion response were determined.

6. The method for simulating the adsorbed water and free water in unsaturated porous soil media according to claim 3, characterized in that, Based on the determined montmorillonite-montmorillonite and montmorillonite-water coarsening interaction parameters, a certain number of montmorillonite particles are introduced into the three-dimensional simulation region, and the space is filled according to their shape and orientation properties to construct an initial set of montmorillonite particles. Under constant particle number, volume and temperature conditions, the montmorillonite particle assembly is subjected to molecular dynamics structural relaxation so that the interparticle interactions reach a stable equilibrium state. After structural relaxation was completed, different confining pressures were applied to conduct isotropic loading simulations on montmorillonite particle aggregates, causing the aggregate structure to undergo a compaction process. After the loading process reaches stability, the rebound process is simulated under low confining pressure to release some external constraints and obtain the equilibrium configuration of montmorillonite aggregates that simultaneously contains compaction history information and stable pore structure characteristics.

7. The method for simulating the adsorbed water and free water in unsaturated porous soil media according to claim 1, characterized in that, Based on the equilibrium configuration of the montmorillonite aggregates, coarse-grained water particles are introduced into the pore space between the aggregate particles to construct an initial montmorillonite-water system. Using the coarse-grained interaction parameters determined in S2 and S3, the migration and distribution of water particles in the pores of aggregates were simulated using coarse-grained molecular dynamics under constant particle number, volume and energy conditions until the water absorption behavior of the system reached a stable state. After the water absorption process stabilizes, the montmorillonite-water system is subjected to dynamic relaxation under constant particle number, volume, and temperature conditions to eliminate transient fluctuations and obtain a stable structural and energy state. Under fixed volume conditions, the internal stress of the system is continuously calculated over time based on the virial theorem, and the time history characteristics of the expansion stress generated by montmorillonite aggregates during water absorption are extracted.

8. The method for simulating the adsorbed water and free water in unsaturated porous soil media according to claim 7, characterized in that, Based on the dynamic trajectory results of the montmorillonite-water system, the system configuration at the beginning of the water absorption process is used as a reference state to extract the spatial displacement information of coarse-grained water particles at different time scales; within a given time window, the relative displacement distribution characteristics of water particles relative to the reference configuration are statistically analyzed to obtain the displacement statistics of pore water migration over time.

9. The method for simulating the adsorbed water and free water in unsaturated porous soil media according to claim 8, characterized in that, Under different montmorillonite-water interaction energy well depth parameters, the relative displacement distribution and mobility of water particles were compared and analyzed to identify water particles that stay in the displacement-restricted area for a long time and water particles with greater migration ability in the pore network. Based on the differences in water particle migration behavior, adsorbed water and free water are classified, and their quantity ratio and dynamic evolution characteristics over time are further statistically analyzed to achieve the distinction and quantitative characterization of adsorbed water and free water in unsaturated soil porous media.

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