1. Introduction
Desulfurization gypsum–fly ash flowable lightweight soil is a composite material comprising industrial components like fly ash, desulfurization gypsum, cement, and soil. It exhibits high fluidity and density, effectively addressing uneven settlement issues caused by varying strength and stiffness of materials in roadbed construction. This material offers clear advantages for future roadbed development. A stable, robust roadbed is crucial for ensuring road surface quality. There has always been a phenomenon of “heavy road surface, light roadbed”, which has led to frequent pavement problems caused by roadbed diseases [
1]. Therefore, evaluating the macroscopic strength and material damage evolution of desulfurization gypsum–fly ash fluid lightweight soil is of significant importance.
In recent years, numerous scholars have extensively researched cement–fly ash materials. Yuan Xiaoya et al. [
2] found that fly ash has the characteristics of promoting the flocculation structure and particle diffusion of cement particles, which can improve the internal microstructure of cement-based materials and enhance their mechanical properties. Jia Yan’s research [
3] shows that cement–fly ash slurry has the characteristics of strong fluidity and high strength after setting, and can be used as a material for backfill of abutments. Huang Zhiqin [
4] discovered that incorporating fly ash as an additive into red bed mudstone can effectively enhance soil particle agglomeration and significantly improve the soil’s deformation resistance. Due to the excellent crack resistance of fly ash concrete, many experts and scholars have recently shifted their focus towards increasing the use of fly ash in concrete [
5,
6,
7,
8]. Research by Ma Chengchang et al. [
9] shows that under the same loading age, the tensile deformation of concrete increases with the increase in fly ash content. On a microscopic level, Liu Jun et al. [
10] utilized scanning electron microscopy, X-ray diffraction analysis, and other microscopic methods to investigate the mechanical properties of lightweight aggregates under varying curing conditions. Wang Jiabin et al. [
11] analyzed the correlation between the mechanical performance indicators of the multi-component gel material in the fly ash–cement–slag system. Their study revealed an exponential relationship between splitting compressive strength and compressive strength, establishing a mechanical performance model that considers the aggregate replacement rate.
Numerical simulation methods are a crucial tool for theoretical analysis in road engineering, allowing for the evaluation of macroscopic mechanics and mechanical response laws of structures. Zhang Yang et al. [
12] introduced a constitutive relationship model for fly ash concrete based on uniaxial compression tests, which was validated through a finite element method. Petcherdchoo et al. [
13] utilized the finite element method to develop a differentiated constitutive model, revealing that the initial shear modulus and unconfined compressive strength of Bangkok soft clay, enhanced by ordinary Portland cement and fly ash, increased with curing time. Cracks are identified as the primary cause of material performance deterioration [
14,
15,
16,
17]. In terms of crack evolution laws, Liang Dongxu [
18] conducted crack propagation experiments on prefabricated cross-fractured rock samples, demonstrating that the initiation and aggregation stress of rock cracks escalate with the angle between the main crack and the axial load.
The material structure of desulfurization gypsum–fly ash fluidized lightweight soil comprises interacting particles, although the microstructure exhibits discontinuity. Existing continuous element constitutive models based on the finite element method struggle to accurately depict the failure development of granular materials, leading to an unclear understanding of the material’s failure mechanism [
19]. This study presents a case analysis utilizing the discrete element method (DEM) numerical simulation to investigate the mechanical behavior of desulfurization gypsum–fly ash fluidized lightweight soil under uniaxial compression testing. The research aims to elucidate the failure mechanism of the material, assess crack evolution in conjunction with energy variations, and explore particle motion characteristics during testing. A two-dimensional discrete element numerical model was established based on a specified gradation, followed by the determination of micromechanical parameters for the contact model. The study analyzed strain and stress from numerical simulations and indoor experiments, focusing on crack evolution and its impact on the fracture surface. Cracks in the material were represented by a discrete fracture network (DFN) during numerical simulations of the failure process, enabling the identification of the failure mode of desulfurization gypsum–fly ash fluidized lightweight soil. The evaluation of damage in the material was conducted using energy indicators.
2. Materials and Methods
2.1. Material Parameters
The material utilized in this experiment is secondary fly ash (FA) from Shandong Huaneng Jinan Huangtai Power Generation Co., Ltd. (Jinan, China), with pertinent parameters detailed in
Table 1 and
Table 2. The cement used is P·O 42.5 ordinary Portland cement, taken from Jinan, China, with related parameters presented in
Table 3. Desulfurization gypsum (DG), a byproduct of flue gas desulfurization at Shandong Huaneng Jinan Huangtai Power Generation Co., Ltd. (Jinan, China), was employed. The silt was sourced from the trial section of the Beijing–Taiwan Expressway reconstruction and expansion project(Jinan, China), with related parameters presented in
Table 4 (the data in
Table 1,
Table 2,
Table 3 and
Table 4 are provided by the manufacturer).
2.2. Uniaxial Compressive Strength Test
Through SEM (Shandong Wusheng Information Technology Co., Ltd., Jinan, China) analysis, the particle sizes of each material were obtained as follows: the particle size of fly ash is between 0.92 µm and 31 µm; the particle size of desulfurization gypsum is between 90 µm and 200 µm; the particle size of silt is between 0.002 mm and 1 mm. Because the particle size of each raw material is small, it is easy to agglomerate in the preparation process, but it is difficult to mix water into the solid material and it is difficult to stir the mixture evenly. Following extensive preliminary trial mixing experiments, the subsequent mixing steps were employed in this study, as illustrated in
Figure 1.
Firstly, accurately weigh raw materials according to the design mix ratio. The weighed fly ash, desulfurized gypsum, cement and silt are poured into the mixer for dry mixing for about 1 min. Next, pour half of the weighed water and stir for 30 s, followed by adding the remaining water and mixing for about 3 min to create a desulfurization gypsum–fly ash fluidized lightweight soil slurry. Pour the slurry into a test mold for casting. By adding water in stages, the risk of layering solid materials and water (making it difficult to mix) is minimized, and it also prevents splashing during mixing. For small batches, a cement paste mixer is used, while a vertical concrete mixer is employed for larger quantities. The mix ratio test plan for desulfurization gypsum–fly ash fluidized lightweight soil is detailed in
Table 5, with 3 samples in each group.
Cylindrical specimens measuring 50 mm in diameter and 100 mm in length were utilized to generate the stress–strain curve through uniaxial compression. These samples were cured in a standard environment for 28 days before testing. Following a specific mix ratio, cylindrical specimens of the same dimensions were prepared for the compression tests. The tests were carried out using an MTS810 electro-hydraulic servo testing machine, with a constant loading rate of 1 mm/min. The computer recorded the axial load and displacement during the tests. Loading was halted once the strain rate reached 5%, at which point the stress–strain curve of the specimen was determined.
2.3. Establishment of Discrete Element Test Piece Model
In this study, a 50 mm × 100 mm discrete element particle model is created using circular shapes in PFC. To ensure the proper functioning of PFC2D, material gradation is first imported using the table command. Subsequently, the discrete element particle model with the corresponding gradation is generated using the ball distribute command. The upper and lower loading plates are created with the clump command, with the upper loading plate applying axial force. Displacement loading is employed to simulate the uniaxial compression process of desulfurization gypsum–fly ash fluidized lightweight soil, with the loading plates being vertically loaded at a rate of 1 mm/min.
The parallel bonding model is used to represent the contact model of desulfurization gypsum–fly ash fluidized lightweight soil, as shown in
Figure 2. This contact model consists of a bond model and a linear elastic model. When the bond force exceeds the bond strength, the bond model is fractured, and the stiffness related to the bond force and moment is removed from the model. However, the linear contact component always exists, and when all bonds are fractured, it can be considered as an unbonded linear elastic material.
Previous studies have demonstrated the challenges in directly determining the mesoscopic contact mechanical parameters of discrete element models in laboratory settings. Typically, a ‘trial and error method’ is employed to calibrate material parameters to ensure consistent simulation results with laboratory measurements. Building on this prior research, initial mesoscopic parameters of the contact model were established [
20], followed by a calibration of material parameters based on uniaxial compression test results. The final mesoscopic parameters of the contact model for desulfurization gypsum–fly ash fluidized lightweight soil are detailed in
Table 6. Given that the contact between silts mirrors the interaction of cementitious bonding on the silt surface, with all adhesive forces stemming from the cementitious material, the contact parameters for all particle interactions (silt–silt, silt–cementitious material, cementitious material–cementitious material) in this study remain constant.
During the discrete element simulation, the velocity of the upper loading plate was set to be consistent with the laboratory test of the uniaxial compression test model of desulfurization gypsum–fly ash fluidized lightweight soil. The contact force and displacement of the loading plate can be converted into the stress and strain of the specimen during the loading process. In the discrete element model of the specimen, all particles are applied with parallel bond contacts. The adhesion state of the bonded particles is monitored during the loading process. When the adhesion force is greater than the tensile strength or shear strength, the bond breaks. At this time, a DFN is inserted at the contact surface between the particles to represent a crack, and the direction of the DFN is parallel to the contact surface. During the loading process, the number of cracks is recorded in real time through the DFN, and the properties of particles at both ends of the broken bond contact are determined, and the type of crack is analyzed to evaluate the damage situation.