Study of the Design and Mechanical Properties of the Mix Proportion for Desulfurization Gypsum–Fly Ash Flowable Lightweight Soil

Abstract

In order to solve the global problem of bridge head jumping caused by the insufficient compaction of the roadbed in the transition section of highways and bridges, a desulfurization gypsum–fly ash flowable lightweight soil without vibration, capable of self-compaction, low bulk density, and economic and environmental protection, has been developed. This study selected low-grade cement, industrial waste (fly ash and desulfurization gypsum), and Yellow River silt as the raw materials for the design of the mix ratio of a desulfurization gypsum–fly ash flow-state lightweight soil mix. Through multiple indoor experiments, the influence of cement content, silt content, and the fly ash/desulfurization gypsum quality ratio on its fluidity and mechanical properties was systematically studied. The stress–strain relationship under uniaxial compression was analyzed and the strength formation mechanism was revealed through scanning electron microscopy (SEM). The results show that the mechanical properties of the prepared desulfurization gypsum–fly ash flowable lightweight soil meet the engineering requirements. Increasing both the cement and fly ash content results in the decreased fluidity of the desulfurization gypsum and fluidized fly ash. However, as the mass ratio of fly ash to desulfurization gypsum increases, the fluidity reaches its maximum when the mass ratio of fly ash to desulfurization gypsum is 2:1. Based on the stress–strain relationship test results, a uniaxial compressive constitutive model of the desulfurization gypsum–fly ash flowable lightweight soil was proposed. The model was fitted and analyzed with the test results, and the correlation was greater than 0.96. The high degree of agreement showed that desulfurization gypsum can promote the disintegration of fly ash, thereby increasing the specific surface area. This provides more contact points, promotes the hardening process, and enhances the interlocking force between particles and the formation of cementitious substances, further enhancing strength.

1. Introduction

As an important component of the highway structure, the subgrade usually needs to be connected to bridges, culverts, retaining walls, etc. The part of the subgrade that connects with the sides of bridges and culverts, as well as the back of retaining walls, is known as the “Three Structures’ Fill”. Due to significant differences in material strength and stiffness between the subgrade and the structures, as well as limited construction space at the “Three Structures’ Fill”, insufficient compaction often occurs due to the inability to use heavy compaction machinery on the subgrade. This easily leads to differential settlement issues between the subgrade and the structures, significantly impacting the comfort and safety of highway operation. Therefore, controlling the post-construction and differential settlement of the subgrade and improving the convenience of subgrade construction are essential prerequisites and foundations for ensuring the construction and safe operation of highways.

In recent years, numerous scholars have conducted significant research addressing the problem of subgrade soil treatment in the “Three Structures’ Fill”. The prevailing approach utilized at present is the application of lightweight subgrade fill materials. Flowable fly ash serves as a characteristic Controlled Low Strength Material (CLSM) [1]. It is predominantly composed of cement, fly ash, and water mixed in specific proportions to create a highly flowable mixture. Following the appropriate curing process, it solidifies into a blended material with a certain level of strength [2]. Yuan Xiaoya [3] found that fly ash has the characteristic of dispersing the cement particle aggregation structure and promoting particle dispersion, thereby improving the internal microstructure of cement-based materials. This improves its mechanical properties. Jia Yan [4] demonstrated in their research that a cement–fly ash slurry exhibited high fluidity and good strength after consolidation, making it suitable for backfilling in subgrade construction. Huang Zhiqin and Yu Yunyan [5] investigated the use of fly ash as an additive in red mudstone and found that it effectively promotes particle aggregation, enhances the unconfined compressive strength, and significantly improves the deformation resistance of the soil. Considering the favorable crack resistance of fly ash concrete, many researchers have focused on increasing the proportion of fly ash in concrete in recent years [6,7,8,9]. Ma Chengchang et al. [10] showed that the tensile creep of concrete increases with the increase in fly ash content under the same loading age. Liu Jun et al. [11] studied the mechanical properties of lightweight aggregates under different curing conditions using SEM, X-ray analysis, and other microscopic analysis techniques, considering factors such as aggregate physical and chemical properties. Janardhanatn R et al. [12] found in their study on the mix proportion of flowable fly ash that a fly ash content as high as 90% still met the usage requirements after 14 freeze–thaw cycles, demonstrating its feasibility. Wang Yanzhang [13,14,15] created a mix proportion design for flowable fly ash. They analyzed the mechanisms of strength development and systematically studied the effects of various raw material proportions on consistency, strength, and shrinkage. Additionally, they performed post-construction settlement calculations, stability analysis, and field tests. Lin et al. [16] conducted laboratory tests to analyze the influence of water content, cement content, and curing environment on the flowability and mechanical properties of flowable fly ash and proposed evaluation indicators. Yang Chunfeng [17,18,19,20] carried out a mix proportion design for flowable fly ash, summarized and analyzed the optimal water content for liquid fly ash, and conducted field tests in a reconstruction and expansion project. Sun Jishu et al. [21] designed foam fly ash by incorporating a foaming agent and provided recommended mix proportions. Zhen Wukui et al. [22,23,24] redesigned the mix proportion of flowable fly ash by adding lime and investigated its engineering properties and freeze–thaw resistance. Although flowable fly ash has shown good performance in subgrade backfilling, it has not been widely promoted in China. The main reason is the rising cost of fly ash in recent years. To better promote the use of flowable fly ash and reduce its production cost, inexpensive coarse aggregates can be added to the mixture. Coarse aggregates can serve as a reinforcing framework and reduce volume changes [25]. Gabr et al. [26] added different amounts of mine tailings pond sludge (AMD) to flowable fly ash and found that it increased the compressive strength by 10–70%. Do et al. [27] discovered that substituting some of the cement in flowable fly ash with reddish clay reduced its fluidity and shortened the setting time. When the substitution rate reached 15%, the 28-day compressive strength increased by 6.3%. In their study, Wu et al. [28] discovered that the inclusion of paper mill sludge at 5% and 10% reduced the strength of flowable fly ash by approximately 20% and 40%, respectively. Additionally, this inclusion led to a decrease in fluidity.

Due to considerations regarding material costs and environmental issues, the use of locally sourced aggregates for the preparation of flowable fly ash has gained widespread attention. Researchers such as Do et al. [29] have studied the use of ponded ash (PA) and excavated soil (ES) as aggregates, and experimental results show that the compressive strength and fluidity of flowable fly ash decrease while the initial setting time lengthens with a decrease in the PA/ES ratio. Tuerkel [30] prepared flowable fly ash by adding limestone sand with particle sizes of 0–5 mm, and the results showed that as the limestone sand content increased, the water absorption of the flowable fly ash increased. Chittoori [31,32,33,34] prepared flowable fly ash by adding two types of clay, high-plasticity clay and a 1:1 mixture of high- and low-plasticity clay, and a comparative analysis revealed that flowable fly ash with only high-plasticity clay exhibited better overall performance. It can be seen that adding soil as an aggregate to flowable fly ash is feasible, but the type and nature of the soil have a significant impact on its properties.

Desulfurized gypsum and fly ash are two types of industrial waste that have a significant impact on the environment due to their large output. However, the current utilization rate of these waste materials is very low. Therefore, it is crucial to find rational ways to utilize them in order to protect the environment effectively. In this study, a new type of flowable lightweight soil, called desulfurized gypsum–fly ash flowable lightweight soil, was formulated using fly ash, industrial waste desulfurized gypsum, and powdered soil as a roadbed improvement filling material. Performance tests on different mix proportions were conducted and the effects of factors such as the dosage of each raw material and curing time on the flowability and mechanical properties of the soil were analyzed. This systematic understanding provides valuable insights. Furthermore, by performing uniaxial compressive strength tests, the stress–strain response of the material was plotted and analyzed, and a constitutive model was established. These findings have significant implications for the engineering application and promotion of desulfurized gypsum–fly ash flowable lightweight soil.

2. Test Materials and Test Plans

2.1. Material

2.1.1. Fly Ash

This experiment focused on the secondary fly ash obtained from Shandong Huaneng Jinan Huangtai Power Generation Co., Ltd. (Jinan, China). The chemical composition and performance indicators of this fly ash are presented in

Table 1. Chemical composition of fly ash.

Chemical Composition	Fe2O3	CaO	SO3	Al2O3	SiO2
Mass fraction/%	7.50	4.63	1.50	23.67	56.96

and

Table 2. Performance indicators of fly ash.

Density/(kg·m−3)	Specific Surface Area/(m2·kg−1)	Fineness/%	Loss on Ignition/%
2389	467	16.8	7.5

(provided by the supplier). Figure 1 illustrates the macro and micro diagrams of the fly ash, revealing that it primarily consists of spherical particles with a minor presence of impurities. The particle size of spherical particles under SEM is between 0.92 microns and 31 microns. A ZEISS sigma 500 SEM (Shandong Wusheng Information Technology Co., Ltd. Jinan, China) was chosen to observe the microscopic morphology of the fly ash and desulfurization gypsum with an acceleration voltage of 4 kV and a working distance of 6.3 mm. Figure 2 shows the XRD pattern of fly ash. A BRUKER D8 Advance XRD (Jinan Mengmai International Trade Co., Ltd. Jinan, China) was selected for ex situ testing of the fly ash and desulfurization gypsum at room temperature with a 2θ range of 10–80° in steps of 0.02° at 10°/min. Its main crystalline phases are SiO₂ and Al₆Si₂O₁₃.

2.1.2. Desulfurization Gypsum

This study focused on the waste generated from flue gas desulfurization at Shandong Huaneng Jinan Huangtai Power Generation Co., Ltd. The results are presented in Figure 3 and Figure 4, which illustrate the macro and micro characteristics of the desulfurization gypsum, as well as the XRD pattern. It is evident from the figures that the desulfurization gypsum used in this study has a brownish-yellow powder appearance and is primarily composed of elongated blocks. The crystal phase of the gypsum is identified as Ca₂SO₄·2H₂O.

2.1.3. Cement

This experiment used P.O.42.5 ordinary Portland cement. Its performance indicators are shown in

Table 3. Cement performance indicators.

Water Requirement of Normal Consistency/%	Setting Time/min		Flexural Strength/MPa			Compressive Strength/MPa
	Initial	Final	3 d	7 d	28 d	3 d	7 d	28 d
26.9	205	265	5.6	7.5	9.6	30.2	36.7	48.4

(provided by the supplier).

2.1.4. Silt

This study focused on the selection of silt from the experimental section of the Beijing Taiwan Expressway renovation and expansion project. Silt is not commonly used as a roadbed filling material due to its unique properties, including low plasticity, poor viscosity, low strength, difficulty in compaction, and susceptibility to liquefaction and erosion. The analysis of

Table 4. The grading criteria of clay soil.

Control Grain Size d60/mm	Effective Grain Diameter d10/mm	Median Diameter d30/mm	Coefficient of Nonuniformity Cu	Coefficient of Curvature Cc
0.092	0.013	0.087	7.1	6.3

and Figure 5 reveals that the distribution range of silt particle groups in the experimental section of this project is relatively wide; however, the particle matching is inadequate.

2.2. Material Preparation and Mix Ratio Plan

2.2.1. Material Preparation

Due to the small particle sizes of various raw materials, agglomeration is likely to occur during the preparation process. This makes it difficult for water to mix into the solid material, resulting in uneven mixing of the mixture. In this study, the following steps were used for blending: Firstly, weigh the raw materials according to the design mix comparison. Pour the weighed fly ash, desulfurization gypsum, cement, and powder soil into a mixer and mix for about 1 min. Then, add 50% of the required water and stir for 30 s. After that, add all the remaining water and stir for about 3 min. This process forms a desulfurization gypsum–fly ash flowable lightweight soil slurry. Finally, pour the slurry into the trial mold for pouring. The reason for using the method of adding water in stages is that it solves the problem of easy splashing when mixing with water once, which is caused by the difficulty of stirring due to the solid materials and water layers. The specific preparation process is shown in Figure 6.

In this study, two types of specimens were made using desulfurization gypsum and fluidized fly ash. Unconfined compressive strength testing was conducted on 70.7 mm × 70.7 mm × 70.7 mm cube specimens, while uniaxial compression tests were performed on φ 50 mm × 100 mm cylindrical specimens. No vibration was required after pouring the desulfurization gypsum and fluidized fly ash. Once the surface moisture dried slightly, any excess slurry above the mold was flattened using a scraper and the surface was covered with a damp cloth. Next, the specimens were placed in an environment with a room temperature of 20 ± 5 °C and a relative humidity greater than 50%. They were left to stand for 1–2 days before demolding and labeling. After demolding, the specimens were subjected to standard curing conditions. Relevant tests were conducted after 7 or 28 days of curing.

2.2.2. Mix Proportion Design Plan

A mix proportion design plan was adopted to investigate the effects of the mass ratio of fly ash to desulfurization gypsum, cement content, and silt content on the flowability and unconfined strength of the desulfurization gypsum–fluidized fly ash. On the basis of a large number of preliminary trial tests, a fixed water solid ratio of 0.34 was selected, and mass ratios of fly ash to desulfurization gypsum of 1:1, 2:1, and 3:1 were selected. Cement contents of 6%, 8%, and 10% were selected, and silt contents of 0, 20%, 40%, and 60% were selected. The external mixing method was adopted for the silt, and the specific mix design is shown in

Table 5. Mix ratio of desulfurization gypsum–fly ash flowable lightweight soil.

Sample	Mass Ratio of Fly Ash to Desulfurization Gypsum	Cement Content	Silt Content	Composition of Fluidized Fly Ash/m3
				Cement/kg	Desulfurization Gypsum/kg	Fly Ash/kg	Silt/kg	Water/kg
1	1:1	6%	0%	77.02	603.34	603.34		436.46
2			20%	64.94	508.70	508.70	216.47	441.60
3			40%	56.14	439.73	439.73	374.24	445.34
4			60%	49.43	387.22	387.22	494.33	448.19
5		8%	0%	103.02	592.39	592.39		437.85
6			20%	86.82	449.22	449.22	217.05	442.78
7			40%	75.02	431.37	431.37	375.11	446.38
8			60%	66.04	379.76	379.76	495.34	449.11
9		10%	0%	129.19	581.36	581.36		439.25
10			20%	108.82	489.68	489.68	217.64	443.98
11			40%	93.99	422.98	422.98	375.98	447.42
12			60%	82.73	372.27	372.27	496.35	450.03
13	2:1	6%	0%	77.96	814.20	407.10		441.75
14			20%	65.60	685.18	342.59	218.68	446.10
15			40%	56.63	591.46	295.73	377.53	449.26
16			60%	49.82	520.30	260.15	498.16	451.66
17		8%	0%	104.25	799.24	399.62		443.06
18			20%	87.69	672.28	336.14	219.22	447.21
19			40%	75.67	580.13	290.06	378.34	450.23
20			60%	66.55	510.19	255.10	499.10	452.52
21		10%	0%	130.70	784.20	392.10		444.38
22			20%	109.89	659.31	329.66	219.77	448.33
23			40%	94.79	568.74	284.37	379.16	451.2
24			60%	83.34	500.05	250.02	500.05	453.38
25	3:1	6%	0%	78.43	921.56	307.19		444.44
26			20%	65.94	774.78	258.26	219.80	448.39
27			40%	56.88	668.34	222.78	379.20	451.25
28			60%	50.01	587.61	195.87	500.10	453.42
29		8%	0%	104.87	904.52	301.51		445.71
30			20%	88.13	760.12	253.37	220.32	449.46
31			40%	76.00	655.47	218.49	379.98	452.18
32			60%	66.80	576.15	192.05	501.00	454.24
33		10%	0%	131.47	887.40	295.80		446.99
34			20%	110.42	745.39	248.46	220.85	450.54
35			40%	95.19	642.55	214.18	380.77	453.12
36			60%	83.65	564.65	188.22	501.92	455.07

.

2.3. Experimental Plan

2.3.1. Flowability Test Method and Evaluation Index

Flowability Test Method

This test was conducted in accordance with ASTM D6103-2004 [35] “Standard Test Method for Flow Continuity of Controllable Low Strength Materials”. The fluidity of the slurry is characterized by its free diffusion expansion under self-weight, as shown in Figure 7. Considering that in practical engineering applications, there may be situations where tank truck transportation and other reasons may result in delayed pouring, this study also conducted tests on its flowability over time: that is, testing the flowability after mixing for 0 and 30 min of standing time. After each test of flowability, the desulfurization gypsum–fly ash flowable lightweight soil slurry was loaded back into the container and covered with a damp cloth. It was necessary to stir it again for 1 min before conducting a flowability test.

Liquidity Evaluation Indicators

The research on mobility in this study adopts the internationally recognized CLSM mobility testing procedure ASTM D6103-2017 [36]. This experimental procedure was specifically developed by the American Society for Testing and Materials for CLSM. Based on the results of the tested flowability test, this regulation divides liquidity into three levels of evaluation, as shown in

Table 6. CLSM flowability evaluation level.

Level	Flowability/mm	Applicability
Low flowability	<150	Reclamation work for large-scale pipe trenches, roadbeds, etc.
Average flowability	150–200	General backfilling project
High flowability	>200	Backfilling projects with narrow operating space or dead corners

.

2.3.2. Unconfined Compressive Strength Test

This experiment is based on the compressive strength testing method for building mortar cubes in JCJ/T70-2009 [37] “Standard for Basic Performance Testing of Building Mortar”. Unconfined compressive strength testing was conducted on desulfurization gypsum–fly ash flowable lightweight soil. The preparation and curing of the test piece refer to the method described in Figure 6. After the specimen was cured to the specified age (7 days or 28 days), a YAW-300 pressure testing machine(Jinan Zhongluchang Testing Machine Manufacturing Co., Ltd., Jinan, China) was used for continuous and uniform loading, and the loading rate was maintained at 1 mm/min, as shown in Figure 8. The formula for calculating unconfined compressive strength is shown in Equation (1).

$$f_{cu}=\frac{N_u}{A}$$

(1)

where $f_{cu}$ is compressive strength, $N_u$ is failure load, and $A$ is the pressure bearing area.

2.3.3. Uniaxial and Biaxial Compressive Test

To evaluate the stiffness characteristics of the desulfurization gypsum–fly ash flowable lightweight soil, we explored the influence of various raw material dosages on their strength and deformation characteristics. The stress–strain test plan was developed, as shown in

Table 7. Uniaxial compression test plan.

Sample	Mass Ratio of Fly Ash to Desulfurization Gypsum	Cement Content	Silt Content
Y1	1:1	6%	20%
Y2		8%
Y3		10%
Y4	2:1	8%
Y5	3:1
Y6	1:1		0%
Y7			40%
Y8			60%

. The MTS810 electro-hydraulic servo testing machine(Jiangsu Donghua Testing Technology Co., Ltd., Jiangsu, China) was used in this experiment, and the loading rate was controlled at 1 mm/min. The selection of test pieces, φ 50 mm × 100 mm cylindrical specimens with 3 formed specimens in each group, were tested after curing for 28 days.

3. Results and Discussion

3.1. Flowability Research

3.1.1. The Influence of Cement Content and Silt Content on Fluidity

In this study, flowability tests were conducted on the design mix proportion in Section 2.3.1 to investigate the influence of cement content and silt content in the cementitious material on the flowability of the desulfurization gypsum–fly ash flowable lightweight soil. The relationship between cement content, silt content, and fluidity was analyzed, as shown in Figure 9.

From Figure 9, it can be seen that when the content of other raw materials is constant, the flowability of the desulfurization gypsum–fly ash flowable lightweight soil gradually decreases with the increase in cement content. There is a negative correlation between the two. In Figure 9a, the silt content is 40%. When the cement content increases from 6% to 10%, the fluidity decreases from 218 mm to 192 mm. At this point, the relative decrease in mobility is the largest. But the decline rate is only about 6.3%. Although the flowability of the desulfurization gypsum–fly ash flowable lightweight soil decreases with the increase in cement content, the decrease is relatively small. The main reasons for this phenomenon are the following:

(1)

Cement has high activity. The hydration reaction can take place in a relatively short time, and the more hydration products generated, the more unfavorable the flowability of the desulfurization gypsum–fly ash flowable lightweight soil.

(2)

When the water solid ratio is fixed, the specific surface area of cement is relatively large. An increase in cement content will lead to a decrease in the fluidity of the slurry.

(3)

The cement content selected in this study is relatively small, and the increasing gradient of the content is only 2%. Therefore, the influence of cement content on the fluidity of the slurry is also relatively small.

In Figure 9, the condition of a fixed mass ratio of fly ash to desulfurization gypsum and constant cement content can be seen. The flowability of the desulfurization gypsum–fly ash flowable lightweight soil also shows a decreasing trend with the increase in fly ash content. When the content of silt increases from 0% to 20%, the maximum decrease in flowability is 15 mm, with an average decrease rate of 7%. When the content of silt increases from 20% to 60%, the relative decrease in fluidity is relatively small, with an average decrease rate of 3%. The increase in silt content leads to a significant decrease in fluidity. The fine soil particles cause a decrease in the fluidity of the desulfurization gypsum–fly ash flowable lightweight soil, mainly due to their small particle size and large specific surface area. Therefore, the soil mixture has strong water absorption ability.

3.1.2. The Influence of the Mass Ratio of Fly Ash to Desulfurization Gypsum on Fluidity

We investigated the influence of the mass ratio of fly ash to desulfurization gypsum on the flowability of the desulfurization gypsum–fly ash flowable lightweight soil. Based on the test results in Section 3.1.1, the relationship between the mass ratio of fly ash to desulfurization gypsum and flowability was analyzed, as shown in Figure 10.

As shown in Figure 10, ceteris paribus, the fluidity of the desulfurization gypsum–fly ash flowable lightweight soil increases first and then decreases with the increase in the mass ratio of fly ash to desulfurization gypsum. When the mass ratio of fly ash to desulfurization gypsum increases from 1:1 to 2:1, its fluidity increase rate is about 5%. But when the cement content is 10%, the increase rate is about 10%. When the mass ratio of fly ash to desulfurization gypsum increases from 2:1 to 3:1, its fluidity decreases by about 23%, with a significant decrease. Especially when the cement content is 10% and the silt content is 60%, the fluidity decreases to 150 mm, with a decrease rate of 27%. A reasonable explanation for this is that the water in the mixture exists in two forms: filling water and free water. Filling water does not affect its fluidity. The fluidity of the slurry mainly depends on free water. Due to the morphological effect and micro-aggregate effect of fly ash, adding an appropriate amount of fly ash can change the filling water between particle voids into free water. This has led to an increase in the proportion of free water. In addition, an appropriate amount of fly ash also acts as a “rolling ball” in the slurry. This reduces the friction between solid particles. As a result, the fluidity of the slurry is improved. However, due to the large specific surface area of fly ash, excessive fly ash requires a large amount of free water consumption. Under the condition of a constant water to solid ratio, the phenomenon of reduced fluidity occurs when the amount of coal powder added is too high.

3.2. Research on Unconfined Compressive Strength

The Influence of Age and Mass Ratio of Fly Ash to Desulfurization Gypsum on Compressive Strength

The relationship between the compressive strength and the mass ratio of fly ash to desulfurization gypsum of specimens with a curing age of 7 and 28 days was analyzed. The effects of age and the mass ratio of fly ash to desulfurization gypsum on the unconfined compressive strength of the desulfurization gypsum–fly ash flowable lightweight soil were explored, as shown in Figure 11. By analyzing the relationship between the age of the specimen and its compressive strength, the following conclusions can be drawn.

The compressive strength range of specimens with a 7 d curing period is 0.38 MPa to 2.89 MPa. The compressive strength range of specimens with a curing age of 28 d is 1.2~5.13 MPa, which meets the requirements (7 d ≥ 0.3 MPa, 28 d ≥ 0.6 MPa).

The compressive strength of the desulfurization gypsum–fly ash flowable lightweight soil increases with age. Compared to the compressive strength of specimens with a curing age of 7 days, when the cement content is 6%, the compressive strength of the specimens with a curing period of 28 days increases the fastest, with a growth rate of 58~136%. The growth rate ranges from 20% to 107% when the cement content is 8% and 10%. This is mainly because the fly ash volcanic ash reaction needs cement hydration products to provide an alkaline reaction environment, and its reaction rate is slow. When the cement content is low, the early strength of the specimen is mainly contributed by the cement hydration reaction. Its internal alkalinity is weak. The volcanic ash reaction time of fly ash is delayed, resulting in a high growth rate of compressive strength.

Fly ash and desulfurization gypsum are used as mineral admixtures. The activation effect of sulfate activity is one of the main sources of compressive strength of the desulfurization gypsum–fly ash flowable lightweight soil. From the compressive strength of the specimens with a curing age of 28 days in Figure 11, the following can be seen:

(1)

In Figure 11a,b, when the cement contents are 6% and 8%, the compressive strength of the specimen increases with the increase in the mass ratio of fly ash to desulfurization gypsum. It has a good positive proportional relationship. In Figure 11c, when the cement content is 10%, the compressive strength of the specimen first increases and then decreases with the increase in the mass ratio of fly ash to desulfurization gypsum. When the mass ratio is 2:1, the compressive strength is the highest.

(2)

When the mass ratio of fly ash to desulfurization gypsum increases from 1:1 to 2:1, the compressive strength of the specimen increases significantly. Its growth rate ranges from 5% to 29%. When the mass ratios are 2:1 and 3:1, the compressive strength of the specimen is relatively close. Its amplitude of change is very small.

Based on the above phenomenon, a conclusion can be drawn. As the mass ratio of fly ash to desulfurization gypsum increases, the content of fly ash in the fluidized lightweight soil matrix of desulfurization gypsum and fly ash for the volcanic ash reaction is relatively higher. Most of the unhydrated fly ash particles can effectively fill the gaps between their internal solid particles, gradually densifying the matrix structure. This improves the compressive strength of the specimen. When the mass ratio of fly ash to desulfurization gypsum is 2:1, the proportion of the two mineral admixtures is appropriate. Desulfurization gypsum has the highest degree of volcanic ash activity stimulation on fly ash. At this point, the strength increase provided by the volcanic ash reaction of fly ash is greater than the strength increase provided by its filling effect. This makes the compressive strength close to or even higher than the compressive strength at a mass ratio of 2:1. From this, it can be seen that when considering production costs and higher strength requirements, the optimal mass ratio of fly ash to desulfurization gypsum is 2:1.

3.3. Study on Stress–Strain Relationship under Uniaxial Compression

3.3.1. Complete Stress–Strain Curve

The stress–strain curve is the most basic indicator for describing the mechanical properties of materials. It can well reflect the strength and deformation performance of the desulfurization gypsum–fly ash flowable lightweight soil. Therefore, we explored the stress–strain relationship and failure mode of the desulfurization gypsum–fly ash flowable lightweight soil during the loading process. This is of great significance for fully understanding the mechanical properties of the desulfurization gypsum–fly ash flowable lightweight soil.

Figure 12a–c show the stress–strain curves of the desulfurization gypsum–fly ash flowable lightweight soil under different cement contents, mass ratios of fly ash to desulfurization gypsum, and fly soil contents, respectively. From the figure, it can be seen that the stress–strain development process of the desulfurization gypsum–fly ash flow-state lightweight soil can be roughly divided into four stages. The segmentation position is shown on the Y3 curve. To make the expression clear, only the Y3 curve was segmented and labeled. The following is the specific stage division:

(1)

The OA segment of the curve is in the linear elastic stage. The stress–strain curve of the desulfurization gypsum–fly ash flowable lightweight soil changes approximately in a straight line. At this stage, the desulfurization gypsum–fly ash flowable lightweight soil gradually hardens. The stress increases rapidly with strain. The stress at point A is the proportional limit.

(2)

The AB segment of the curve represents the plastic yield stage. The slope of the stress–strain curve gradually decreases. The strain growth rate has significantly accelerated. The increase in stress is relatively small. At this stage, cracks or micro defects begin to appear in the internal structure of the desulfurization gypsum–fly ash flowable lightweight soil, and its stress level is close to the material threshold. The stress at point B is the peak stress.

(3)

The BC segment of the curve is in the failure stage. The stress–strain curve shows a downward trend. The stress decays continuously with the increase in strain. At this stage, the desulfurization gypsum–fly ash flow-state lightweight soil specimen exhibits cracks and reaches failure.

(4)

The CD segment of the curve represents the residual strength maintenance stage. The stress–strain curve can be approximately represented as a horizontal straight line. During this stage, the stress of the desulfurization gypsum–fly ash flow-state lightweight soil is a relatively small and fixed value. The strain keeps on rising. The stress depicted in point D of the figure corresponds to residual strength.

It can be seen from Figure 12a that there is no significant difference in the effect of cement content on the rising section of the stress–strain curve of the desulfurization gypsum–fly ash flow-state lightweight soil. But as the cement content increases, its decreasing section gradually slows down significantly. The opening of the stress–strain curve gradually increases downwards. This indicates that an increase in cement content can significantly improve the ductility of the desulfurization gypsum–fly ash flowable lightweight soil.

It can be seen from Figure 12b that as the mass ratio of fly ash to desulfurization gypsum increases, the slope of the rising section of the stress–strain curve shows a decreasing trend, and its peak strain gradually increases. When the mass ratio of fly ash to desulfurization gypsum is 2:1, the slope of the descending section of the stress–strain curve is the highest. The stress–strain curve has the smallest downward opening. Therefore, its brittleness is maximum when the mass ratio is 2:1.

It can be seen from Figure 12c that as the amount of silt gradually increases, the slope of the rising section of the stress–strain curve significantly decreases. But the impact on the descending segment is not significant. The descending section of the stress–strain curve at each dosage is almost parallel. It is worth mentioning that as the amount of silt increases, the strain corresponding to its peak stress gradually increases. From this, it can be seen that an increase in the amount of silt significantly increases the deformation of the desulfurization gypsum–fly ash flow-state lightweight soil.

3.3.2. Elastic Modulus

The elastic modulus can be calculated from the slope of the stress–strain curve of the material. The stress–strain curves of the desulfurization gypsum–fly ash flowable lightweight soil under different mix ratios in this experiment are shown in Figure 12. The stress–strain relationship of the desulfurization gypsum–fly ash flowable lightweight soil exhibits nonlinear characteristics similar to that of cement soil. And its rising section has a good linear elastic relationship. Therefore, the elastic modulus calculation method for high–plasticity clay proposed by Li et al. [38] can be used. The slope of the line connecting the point corresponding to 0.5 times the peak stress in the rising segment and the origin was taken.

The calculation results of the elastic modulus of the desulfurization gypsum–fly ash flowable lightweight soil under different mix ratios are shown in

Table 8. Elastic modulus of desulfurization gypsum–fly ash flowable lightweight soil.

Sample	Elastic Modulus $\frac{{\mathit{E}}_{\mathbf{50}}}{\mathbf{M}\mathbf{P}\mathbf{a}}$
Y1	246.2
Y2	321.1
Y3	267.7
Y4	436.7
Y5	150.1
Y6	564.5
Y7	217.3
Y8	121.2

. The elastic modulus E₅₀ of the desulfurization gypsum–fly ash flowable lightweight soil ranges from approximately 120 MPa to 565 MPa. Its elastic modulus is about 2–18 times that of roadbed soil (the elastic modulus of roadbed soil is about 30~60 MPa). Through research by Feng et al. [39], it was found that roadbed materials with higher elastic moduli can significantly reduce the post-construction settlement and traffic load on the stress of pipelines in trench backfill engineering. Therefore, using a desulfurized gypsum–fly ash flowable lightweight soil for backfilling can reduce post-construction settlement. It can change the stress state of the abutment under traffic loads.

It can be seen from Table 8 that with the increase in cement content and the mass ratio of fly ash to desulfurization gypsum, the elastic modulus E₅₀ of the desulfurization gypsum–fly ash flowable lightweight soil first increases and then decreases, reaching its maximum when the cement content is 8% and the mass ratio of fly ash to desulfurization gypsum is 2:1. The elastic modulus E₅₀ decreases with the increase in silt content. This further indicates that an increase in the amount of silt can increase the deformation of the desulfurization gypsum–fly ash flowable lightweight soil.

3.3.3. Uniaxial Compressive Constitutive Model

Establishment of Constitutive Model

Based on the analysis above, the stress–strain relationship curve of the desulfurization gypsum–fly ash flowable lightweight soil falls between that of soil and concrete. Unlike soil, this curve exhibits a distinct linear elastic stage. However, it can undergo significant plastic deformation under a load, similar to concrete. Currently, research on the constitutive model of cement–soil primarily focuses on describing the direct or modified constitutive relationship between soil and concrete. In this study, a constitutive model of soil was selected to describe the constitutive relationship of the desulfurization gypsum–fly ash flowable lightweight soil.

Among the existing mathematical models for describing the stress–strain relationship of soil, the most influential one is the Duncan–Zhang model. This model is a nonlinear variable elasticity model. The parameters in the model can be determined and calculated very clearly. The original expression of the Duncan–Zhang model is as follows:

$$\left({\sigma }_1-{\sigma }_3\right)=\frac{\epsilon }{\frac{1}{E}-\frac{R_f \epsilon }{{\left({\sigma }_1-{\sigma }_3\right)}_f}}$$

(2)

where $({\sigma }_1-{\sigma }_3)$ is deviatoric stress, ε is axial strain, E is the initial tangent modulus, $R_f$ is the failure stress ratio, and $({\sigma }_1-{\sigma }_3{)}_f$ is the failure deviator stress.

During the uniaxial compression test, due to the fact that ${\sigma }_3$ = 0, based on the hypothesis of Hooke’s Law, Formula (2) can be expressed as follows:

$$\frac{\sigma }{{\sigma }_p}=\frac{\frac{\epsilon }{{\epsilon }_p}}{a+f{\left(\frac{\epsilon }{{\epsilon }_p}\right)}^b}$$

(3)

where ${\sigma }_p$ is peak stress, ${\epsilon }_p$ is the strain corresponding to peak stress, and f is the stress failure ratio, which is approximately $R_f$. As long as reasonable values are taken for the parameters a, f, and b in the formula, the stress–strain relationship of the desulfurization gypsum–fly ash flowable lightweight soil can be well described.

Analysis and Verification of Constitutive Models

To verify the accuracy of this constitutive model, the stress–strain curves of the desulfurization gypsum–fly ash flowable lightweight soil under different mix ratios were analyzed. They were calculated according to Equation (3) above. The fitting curve is shown in Figure 13, and the values of the three fitting parameters (a, f, and b) and their correlations are shown in Figure 13.

From Figure 13, it can be seen that the experimental data of the desulfurization gypsum–fly ash flow-state lightweight soil under different mix ratios are in good agreement with the calculated values of this model, and the correlation is greater than 0.96. Therefore, the modified Duncan–Zhang model can well describe the stress–strain relationship of the desulfurization gypsum–fly ash flowable lightweight soil. This has certain theoretical and practical significance.

3.4. Mechanism of Strength Formation of Desulfurization Gypsum–Fly Ash Flowable Lightweight Soil

Desulfurized gypsum–fly ash flowable lightweight soil is a high flowable roadbed backfill material made by uniformly mixing Portland cement, fly ash, and desulfurization gypsum as a ternary cementitious system with powder soil. The mechanism of strength formation is actually the complex process of microstructure formation in the system composed of composite cementitious materials and silt. The specific formation process is discussed and analyzed below.

3.4.1. Cement Hydration Reaction

After adding water to mix of the desulfurization gypsum–fly ash fluidized lightweight soil, the Portland cement will immediately start the hydration reaction. The hydration reaction generates gel products such as calcium silicate hydrate and calcium aluminate hydrate, and a large amount of Ca(OH)₂ will be generated at the same time.

3.4.2. Activation of Fly Ash Activity

Fly ash has volcanic activity, and its main components are Al₂O₃ and SiO₂. Based on Figure 1, it can be seen that fly ash mainly exists in the form of glass ball particles. In the alkaline environment created by the cement hydration reaction, the chemical bonds of Si-O and Al-O on the surface of the glass particles of fly ash break, leading to the activation of fly ash and enhancing the reaction rate of volcanic ash. The pozzolanic reaction of fly ash mainly involves the reaction of Ca²⁺ in Ca(OH)₂ with the active oxides Al₂O₃ and SiO₂ of fly ash, generating cementitious substances such as hydrated calcium aluminate and hydrated calcium silicate. The specific reaction formula is as follows:

$${\mathrm{Al}}_2{\mathrm{O}}_3+{n\mathrm{Ca}\left(\mathrm{OH}\right)}_2+{x\mathrm{H}}_2\mathrm{O}\to n\mathrm{CaO}·{\mathrm{SiO}}_2·{x\mathrm{H}}_2\mathrm{O}$$

(4)

$${\mathrm{SiO}}_2{+m\mathrm{Ca}\left(\mathrm{OH}\right)}_2{+y\mathrm{H}}_2\mathrm{O}\to m\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3·{y\mathrm{H}}_2\mathrm{O}$$

(5)

$${2\mathrm{SiO}}_2{+\mathrm{Al}}_2{\mathrm{O}}_3{+\mathrm{Ca}\left(\mathrm{OH}\right)}_2{+3\mathrm{H}}_2\mathrm{O}\to \mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3·{2\mathrm{SiO}}_2·{4\mathrm{H}}_2\mathrm{O}$$

(6)

3.4.3. Promoting Reaction of Desulfurization Gypsum

The primary component of desulfurization gypsum is CaSO₄·2H₂O. The presence of SO₄²⁻ not only facilitates the breaking of Si-O and Al-O chemical bonds on the surface of fly ash particles but also reacts with AlO²⁻ and Ca²⁺ to form ettringite. This reaction leads to a reduction in the AlO²⁻ content within the structural system, thereby enhancing the disintegration of fly ash particles. In addition, desulfurization gypsum can also provide sufficient Ca²⁺ for the reaction system, promoting the generation of more cementitious substances. The main reactions involved in desulfurization gypsum are as follows:

$${\mathrm{Ca}}^{2+}+{\mathrm{Al}}_2{\mathrm{O}}_3+{\mathrm{OH}}^{-}+{\mathrm{SO}}_4^{2-}\to 3\mathrm{CaO}·{\mathrm{Al}}_2{\mathrm{O}}_3·{3\mathrm{CaSO}}_4·{32\mathrm{H}}_2\mathrm{O}$$

(7)

To gain a more intuitive understanding of the strength formation process of the desulfurization gypsum–fly ash flowable lightweight soil, for the specimens with the first mix ratio (cement content of 8%, fly ash/desulfurization gypsum mass ratio of 2:1, and silt content of 20%), samples were taken for SEM testing at the curing ages of 7 and 28 days, as shown in Figure 14 and Figure 15.

Based on the findings in Figure 14, it is evident that after 7 days of curing, fly ash, desulfurization gypsum, and silt particles have been partially wrapped in flocculent and needle-like substances. However, complete wrapping has not yet occurred. Figure 14b further illustrates that the fly ash pellets are densely packed, with a visible disintegration gap in the glass layer. Notably, a significant amount of flocculent material is present around the gap. These observations indicate that the volcanic ash reaction of fly ash has commenced during the 7-day curing period. The figure primarily showcases the hydration reaction of cement, the interaction between fly ash and Ca(OH)₂, and the formation of hydrated calcium silicate and hydrated calcium aluminate.

According to Figure 15, it is evident that at a curing age of 28 days, the fluidized lightweight soil structure of the desulfurization gypsum–fly ash contains more flocculent substances. The fly ash, desulfurization gypsum, and powder soil particles are completely enveloped by a continuous network structure. Additionally, there is a needle-like substance known as ettringite present in the structure, indicating the involvement of desulfurization gypsum in the reaction. The different particles are interconnected and overlapped by flocs, resulting in the formation of a cohesive whole. This enhances the adhesion between particles and improves the structural density.

4. Conclusions

This article first explains the raw materials, testing methods, and mix design scheme. By evaluating the flowability and unconfined compressive strength of the desulfurization gypsum–fly ash flowable lightweight soil, each mix ratio is determined to meet the requirements of roadbed backfilling; in addition, the development process of its stress–strain curve was studied, and a uniaxial compressive constitutive model was proposed. The main conclusions are as follows:

(1)

When the cement content ranges from 6% to 10%, the fly ash/desulfurization gypsum mass ratio ranges from 1:1 to 3:1, and the fly ash content ranges from 0% to 60%. The flowability, 7 d compressive strength, and 28 d compressive strength of the desulfurization gypsum–fly ash flowable lightweight soil vary from 150 mm to 240 mm, 0.38 to 2.89 MPa, and 1.2 to 5.13MPa, respectively. It is recommended to select specific mix proportions based on actual engineering requirements.

(2)

The increases in cement content and silt content both lead to a decrease in the flowability of desulfurization gypsum–fly ash flowable lightweight soil. However, as the mass ratio of fly ash to desulfurization gypsum increases, the flowability reaches its maximum at a mass ratio of 2:1. The mass ratio of fly ash/desulfurization gypsum has the greatest impact on its fluidity, with a maximum decrease of 27% when it increases from 2:1 to 3:1; The flowability of desulfurized gypsum–fly ash fluidized lightweight soil shows a loss after standing for 30 min, with a decrease range of 1.36% to 5.13%.

(3)

The compressive strength of the desulfurization gypsum–fly ash flowable lightweight soil is positively proportional to the cement content and age and inversely proportional to the silt content. When the mass ratio of the fly ash/desulfurization gypsum increases from 1:1 to 2:1, its compressive strength increases significantly. When the mass ratios are 2:1 and 3:1, its compressive strength is very close. Considering production costs, it is recommended to choose a fly ash/desulfurization gypsum mass ratio of 2:1.

(4)

The development process of the stress–strain curve of the desulfurized gypsum–fly ash flowable lightweight soil can be divided into four stages: linear elastic stage, plastic yield stage, failure stage, and residual strength maintenance stage. Based on the stress–strain relationship test results, a uniaxial compressive constitutive model of the desulfurization gypsum–fly ash flowable lightweight soil was proposed. The model was fitted and analyzed with the test results, and the correlation was greater than 0.96, indicating a high degree of agreement.

(5)

Compared to traditional fluidized fly ash, the desulfurization gypsum in the fluidized lightweight soil of the desulfurization gypsum fly ash can promote the disintegration of fly ash, thereby increasing the specific surface area. This provides more contact points and promotes the hardening process, enhancing the interlocking force between particles and the formation of cementitious substances and further enhancing strength.