1 Introduction

Red clay is a typical kind of clay; it is difficult to compact as a filler in subgrades, and its dry shrinkage is severe. It easily adheres to cars and rollers during excavation and paving [1], and its water resistance limits the application of laterite in highway engineering. Phosphogypsum is a byproduct of the production of ammonium phosphate, i.e., approximately five tons of phosphogypsum are produced per ton of ammonium phosphate. The annual output of 1 million tons of ammonium phosphate in Guizhou generates approximately 5 million tons of phosphogypsum [2]. To date, phosphogypsum is mostly piled in stacks on land and dumped in rivers, lakes, and oceans. Phosphogypsum damages the land and vegetation, releases partially radioactive elements in acidic wastewater, causes pollution and endangers human health [3,4,5,6]. Methods to improve the engineering characteristics of red clay and recycle phosphite by applying it to roadbeds are still long-term issues for many scientific and technological workers. Cochranc [7] observed that adding phosphite to sandy soil increased the cohesion of particles and correspondingly improved the strength of the soil. Kumar [8] and other researchers found unexpected results after mixing lime, powdered coal and phosphite and conducting shear tests. MOTZ [9] and SINGH [10] found that phosphate can be used as a highway resurfacing material to achieve good results. Yong [11] incorporated industrial waste, including phosphogypsum, into cement to improve soil; their outdoor static load tests and mechanistic studies showed that this improved the strength of the soil and saved engineering costs. Feng [12] found that pure phosphate was not suitable for use as landfill, and phosphate-modified soil had good water resistance after curing. Qingqian et al. [13] found a material that is suitable for use as a roadbed filler. Through laboratory and field trials, phosphate was found to be a feasible material to use in pavement projects. Authors reported that the amount of phosphate expansion was small and water resistance satisfied requirements for roadbed fillers. The above studies showed that phosphate has good application prospects in highway engineering, but there has been less research on the mechanical properties and mechanism of phosphate-modified red clay. In this paper, cement is used as curing agent. According to the different proportion of phosphogypsum and red clay, the strength characteristics, dynamic characteristics, expansion characteristics and shrinkage characteristics of the mixture are studied, and the modification mechanism of the mixture is discussed from the perspective of microstructure and mineral composition. This study aims to provide a theoretical basis for the application of phosphogypsum in highway engineering and improve the engineering properties of red clay.

Firstly, the basic physical and chemical parameters of red clay, cement and phosphogypsum were presented in Sect. 1. In accordance with the preexisting researches and unconfined compressive strength test results, the mixture ratio and dynamic triaxial test plan were formulated in Sect. 2, respectively. Then, to ensure the repeatability of these tests, the test procedures of unconfined compressive strength test, expansion test, shrinkage test, dynamic characteristic test and microstructure test were described in detail in Sect. 3. Finally, the experimental results were presented and analyzed in Sect. 4, and the conclusions exhibited in Sect. 5 were obtained.

2 Raw material properties

In this study, samples of soil are obtained from Fuquan City. The soil is mainly yellowish brown, with a small amount of dark red clay. It is relatively uniform with dense structure and high natural water content. The basic physical and chemical characteristics of the soil are shown in Table 1. Phosphate is obtained from Fuquan City, Guizhou Province, and it has a high water content, dark brown or gray color, and chemical composition and basic physical characteristics as shown in Table 2. Cement is PO32.5, and its basic parameters are shown in Table 3.

Table 1 Basic physical and chemical analysis results of red clay
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Table 2 Basic physical indexes and chemical analysis results of phosphogypsum
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Table 3 Basic parameters of cement
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3 Mixture design method

According to the regulations on the composition of cement-modified materials for the construction of highway pavement bases [14] (JTG/T F20-2015), the recommended cement dosage is 6–14% for subbase soil with a plasticity index greater than 12. Considering that too much cement leads to an increase in subgrade shrinkage cracks and poor economy, the cement dosages are initially determined to be 3, 5 and 7%. Scholars [15,16,17,18,19,20] combined phosphogypsum with other inorganic binders as road fillers to explore the engineering properties of the mixture. Degirmenci [21] mixed phosphogypsum with fly ash and lime to explore the utilization potential of phosphogypsum in the construction industry, but in the above experiments, the content of phosphogypsum in the mixture was less than 20%, which could not effectively reduce the accumulation of phosphogypsum. Based on this, we not only set the mixing ratio of low content phosphogypsum, but also set the mixing ratio of high content phosphogypsum. The two mixing ratios are as follows. The first is set according to mass ratios of cement to phosphogypsum of 1:1, 1:2 and 1:3. The second is set according to mass ratios of phosphogypsum to soil of 1:1, 1:2 and 1:3. See Table 4 for the results. The mix proportion represent the percentage of each substance in the total mixture mass. According to the mixture design method in Table 4, unconfined compressive strength tests, expansion tests and shrinkage tests are carried out in the laboratory to analyze the mechanical properties of cement phosphogypsum-modified red clay. Additionally, XRD (Rigaku SmartLab, 2θrange varied between 5°and 90°, step size 0.02°, scan rate 10°/min) and SEM (Hitachi S-4800, measured at 5.0 kV) were used to explore the microstructure of the mixtures.

Table 4 Mix proportion design of mixture
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It should be illustrated that although the levels of F, P2O5 and other elements in phosphogypsum can limit its application in cement, phosphogypsum has not been pretreated in this paper, because the radioactivity of phosphogypsum used in this paper meets the specification requirements, and our work aims to effectively reduce the accumulation of phosphogypsum. Therefore, we continuously increase the content of phosphogypsum to find the optimal content of phosphogypsum, so as to ensure the quality of the project and control the construction cost while consuming phosphogypsum to the maximum extent.

The group of plain red clay with the largest unconfined strength, namely cement: phosphogypsum = 1:3 and the group of phosphogypsum: soil = 1:1 with the best water stability, is used for dynamic triaxial test. The ratio is shown in Table 5. The test load is a sine wave load, which is gradually increased by an equal difference sequence. The vibration times of each stage are taken as 10 times, the consolidation ratio is taken as 1.0, 2.0 and 3.0, the vibration frequency is taken as 2 Hz and 4 Hz, and the confining pressure is taken as 50 kPa, 100 kPa and 150 kPa. See Table 6 for the test scheme.

Table 5 Ratio of dynamic test
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Table 6 Dynamic test scheme
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4 Test method

4.1 Unconfined compressive strength test

Samples are prepared according to the test code for modified inorganic cementations materials in Highway Engineering (JTG E51-2009) [22]. Red clay and phosphogypsum are passed through a seive (2 mm), weighed according to the ratio in Table 4, and mixed evenly. Then, the predetermined quantity of water is added, the batch is mixed evenly, and simmered overnight. After the simmering is completed, cement is added, and the batch is stirred evenly before sample preparation. The sample preparation is completed within one h by the static coMPaction method. Each sample is a cylinder with a height of 50 mm and a diameter of 50 mm. After a sample is prepared, it is cured in a curing box at a temperature of 20 °C ± 2 °C and a relative humidity of more than 95% for 7, 14 or 28 d, and the unconfined compressive strength test is conducted.

4.2 Expansion test

Sample preparation is carried out according to the code for highway geotechnical tests (JTG E40-2020) [23]. The test steps are as follows:

  1. (1)

    Put the permeable stone, collar and filter paper into the expander, put the ring knife into the collar with the blunt end facing down, rotate the ring knife to put the bottom surface of the sample in close contact with the top surface of the permeable stone, install the fixed collar, tighten the fixing screws of the collar, put the filter paper and measuring plate on the top surface of the sample, align the plate with the center, install the dial indicator and record the initial reading.

  2. (2)

    Inject water into the expander to force the water to enter the sample from bottom to keep the water surface 5 mm higher than the sample. Record the start time of water injection. After 24 h measure and read the dial gauge after 5 min, 10 min, 20 min, 30 min, 1 h, 2 h, 3 h and 24 h. Check that the expansion deformation of the sample is less than 0.01 mm after 2 h, which means that the expansion deformation has been modified, and the test can be terminated.

  3. (3)

    According to the reading of the dial indicator, calculate the absolute expansion rate and relative expansion rate during the expansion deformation of the sample. The absolute expansion rate at any time is calculated according to formula (1.1):

    $$ \delta_{{\text{t}}} = \frac{{h_{{\text{t}}} - h_{0} }}{h} $$
    (1.1)

where δt is the absolute expansion rate (%) at time t; h0 – reading of the gauge at the beginning of the test (mm); ht—reading of the gauge at time t (mm); h—initial height of sample (mm).

4.3 Shrinkage test

Sample preparation is carried out according to the code for highway geotechnical tests (JTG E40-2020) [23]. The test steps are as follows:

  1. (1)

    Take the prepared sample, measure the mass, place the sample on the perforated plate, place the measuring plate in the center of the sample, install the dial indicator, align the dial indicator with the center of the measuring plate, measure the mass of the sample plus instrument to an accuracy of 0.01 g, modify the instrument and place it in a controlled environmental chamber, and record the initial reading.

  2. (2)

    The shrinkage tester with the sample installed is placed in a controlled environmental chamber at a constant temperature of 25 °C for the shrinkage test. The dial indicator reading is measured after 1 h, 2 h, 3 h, 4 h, 24 h and every 24 h thereafter, and the mass of the sample plus instrument mass is measured to an accuracy of 0.01 g. When the dial indicator reading remains unchanged for 2 h, shrinkage modification of the sample is complete.

  3. (3)

    The sample is dried at 80 °C, and the dry soil mass was measured.

  4. (4)

    Calculate the linear shrinkage at different times.

The linear shrinkage is calculated as follows:

$$ \mathop \delta \nolimits_{t} = \frac{{\mathop H\nolimits_{t} - \mathop H\nolimits_{0} }}{{\mathop H\nolimits_{{}} }} \times 100 $$
(1.2)

where δt is the linear shrinkage of the sample at a certain time in the shrinkage process (%); Ht—dial indicator reading at a certain time during shrinkage (mm); H0—initial reading of dial indicator (mm); H—initial height of sample (mm).

4.4 Dynamic characteristic test

Samples shall be prepared according to the test code for modified materials of inorganic cementitious materials in Highway Engineering (JTG E51-2009) [22]. During the test, after sieving the red clay and phosphogypsum for 2 mm respectively, weigh the corresponding quality of red clay and phosphogypsum according to the ratio in Table 5 and mix them evenly, then add the predetermined quality of water according to the corresponding moisture content, mix the mixture evenly and stew it overnight. After the stewing is completed, add cement and stir evenly before sample preparation. The sample preparation is completed within one hour by static coMPaction method. The size of the sample is a cylinder with a height of 80 mm and a diameter of 39.1 mm. After the sample is prepared, it shall be placed in a curing box with a temperature of 20℃ ± 2℃ and a relative humidity of more than 95% for curing for 7 days, and the dynamic characteristic test shall be carried out.

4.5 Microstructure test

Before sample preparation, the sample mass is calculated according to the ring knife volume and the corresponding proportion in Table 4. The mixture volume is the same as the unconfined test. Then, the mixture of the predetermined quality is weighed and poured into the sample preparation device for one-time static pressure forming. The sample diameter is 61.8 mm, and the height is 20 mm. After the sample is prepared, it is cured in a constant temperature and humidity box at a temperature of 20 ± 2 °C and humidity of 95%. After 7 d, the sample is removed from the ring knife. XRD composition analysis is carried out between the middle core parts of the sample. In the SEM test, the soil block is broken into 2 approximately cubic specimens by hand because it cannot be cut with a knife. The soil block is polished with coarse sand paper first and then with fine sand paper to make a soil sheet close to 0.5 cm3. The thinner the soil sheet is, the clearer the photographs. During grinding, small powder particles form on the soil block due to grinding. It is necessary to remove the powder from the surface by using sticky transparent tape until the sample surface is clean. The conductivity of phosphogypsum-modified red clay is poor. It is necessary to spray gold on the sample surface before scanning for better observations.

5 Results and analysis

5.1 Analysis of unconfined compressive strength results

Figures 1, 2, 3 show that the unconfined compressive strength of phosphogypsum-modified red clay after 7 d, 14 d and 28 d under each degree of compaction first increases and then decreases with increasing phosphogypsum content. When the cement content is 3, 5, and 7%, the unconfined compressive strength of the mixture is maximum when the phosphogypsum content is 9, 15, and approximately 16%, respectively. That is, when cement:phosphogypsum = 1:2.2–1:3, the unconfined compressive strength of phosphogypsum-modified red clay is the largest. At the same age and the same degree of compaction, the greater the cement content is, the greater the unconfined compressive strength of the mixture.

Fig. 1
figure 1

Relationship between unconfined compressive strength of mixture and phosphogypsum content at different ages (3% cement)

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Fig. 2
figure 2

Relationship curve between unconfined compressive strength and phosphogypsum content of mixture at different ages (5% cement)

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Fig. 3
figure 3

Relationship curve between unconfined compressive strength and phosphogypsum content of mixture at different ages (7% cement)

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This paper shows only the relationship between the unconfined strength and age of the mixture for the 7% cement content group; the trend is basically the same for the other groups.

Figure 4 shows that with increasing age, the unconfined compressive strength of the mixture increases rapidly during the first 14 d and basically tends to be modified in the next 14 d. Taking the 7% cement + 14% phosphogypsum mixture as an example, the unconfined compressive strength at 7, 14, and 28 d is 1.57, 1.72, and 1.78 MPa, respectively. The unconfined compressive strength at 7 and 14 d reaches 88.2 and 96.7%% of the unconfined compressive strength at 28 d.

Fig. 4
figure 4

Relationship curve between unconfined compressive strength and age of mixture (7% cement)

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5.2 Analysis of expansion test results

The trend in the absolute expansion rate of the mixture with time for the 5% cement mixture is analyzed here and shown in Fig. 5. The trends are basically the same for the other mixtures.

Fig. 5
figure 5

Relationship between absolute expansion rate of mixture and time (5% cement)

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Figure 5 shows that the absolute expansion rate of the mixture first increases rapidly with time, then increases slowly, and finally stabilizes. As shown in Fig. 5e, the absolute expansion rate for 95% compactness increases rapidly to 1.3% from 0 to 10 h and then slowly to 2.1% from 10 to 80 h. It basically does not increase after 80 h and tends to be flat. Figure 6 shows that the greater the degree of compaction is, the greater the absolute expansion rate. Additionally, the absolute expansion rate of the mixtures first increases and then decreases rapidly with increasing phosphogypsum content. The maximum absolute expansion rates were obtained for the following values of K and the cement:phosphogympum ratio: 90% and approximately 1:2.4; 92% and approximately 1:2.5; 93% and approximately 1:2.5; 94% and approximately 1:2.1, and 95% and approximately 1:2.5. That is, when cement:phosphogypsum = 1:2.1–1:2.5, the absolute expansion rate of phosphogypsum-modified red clay is the largest.

Fig. 6
figure 6

Relationship between absolute expansion rate of mixture and phosphogypsum content (5% cement)

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5.3 Analysis of shrinkage test results

The variation of linear shrinkage with time for mixtures with 3% cement is analyzed here, and the trends are basically the same for the other mixtures.

Figure 7 shows that the linear shrinkage increases rapidly with time, then increases slowly, and finally tends to be stable. As shown in Fig. 7c, K = 90% increases rapidly from 0 to 1.2% in the first 30 h, then increases slowly, reaching approximately 1.4% at 60 h, and subsequently is flat with time.

Fig. 7
figure 7

Relationship between linear shrinkage of mixture and time (3% cement)

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Figure 8 shows that the final linear shrinkage of the mixture first decreases and then increases with increasing phosphogypsum content. For example, for 90% compactness, the linear shrinkage is minimum (1.04%) when the phosphogypsum content is 24.1%; similar results for compactness, minimum linear shrinkage and phosphogypsum content are 92%, 1.19%, and 24.5%; 93%, 1.19%, and 24.2%; 94%, 1.09%, and 24.3%; and 95%, 1.21%, and 24.3%. That is, when phosphogypsum: soil = 1:3, the linear shrinkage is minimum and then increases gradually with increasing compactness.

Fig. 8
figure 8

relationship between linear shrinkage of mixture and phosphogypsum content (3% cement)

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5.4 Analysis of dynamic characteristic test results

5.4.1 Relationship between dynamic shear modulus and confining pressure, consolidation ratio and frequency

It can be seen from Figs. 9, 10, 11 that the dynamic shear modulus of plain red clay and phosphogypsum stabilized soil decreases with the increase of dynamic shear strain. It increases with the increase of consolidation ratio, confining pressure and frequency. The reason is that with the increase of consolidation ratio and confining pressure, the mixture becomes dense, the pores become smaller, the ability to resist shear deformation is enhanced, and the dynamic shear modulus becomes larger. The increase of frequency reduces the load action time, and the performance of the mixture does not change, so the change of the backbone curve is not obvious.

Fig. 9
figure 9

Relationship between dynamic shear modulus and dynamic shear strain of phosphogypsum stabilized soil under different confining pressures

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Fig. 10
figure 10

Relationship between dynamic shear modulus and dynamic shear strain of phosphogypsum stabilized soil under different consolidation ratios

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Fig. 11
figure 11

Relationship between dynamic shear modulus and dynamic shear strain of phosphogypsum stabilized soil under different vibration frequencies

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5.4.2 Dynamic constitutive model of dynamic shear strain and dynamic shear modulus

Dynamic constitutive relation has always been a hot and difficult point in academic research [25] and davidenkov model of P.P. Martin [26]. By fitting the data from Figs. 9, 10, 11, the results are shown in Tables 7, 8, 9. It is found that the relationship between dynamic shear modulus and dynamic shear strain of phosphogypsum cement stabilized red clay can be modeled by H–D model, and R2 is greater than or equal to 0.99. Namely:

$$ Gd = \frac{Gd\max }{{1 + \frac{{\gamma_{{\text{d}}} }}{\gamma r}}} $$
(4.1)
$$ \gamma_{{\text{r}}} = \frac{{{\uptau }_{{{\text{dmax}}}} }}{{G_{d\max } }} $$
(4.1)

where Gd is the dynamic shear modulus; τdmax is the maximum dynamic shear stress; Gdmax is the maximum dynamic shear modulus; γr is the reference dynamic shear strain; γd is the dynamic shear strain.

Table 7 Fitting parameters and correlation coefficients of dynamic shear modulus under different confining pressures
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Table 8 Fitting parameters and correlation coefficients of dynamic shear modulus under different consolidation ratios
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Table 9 Fitting parameters and correlation coefficients of dynamic shear modulus at different frequencies
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5.4.3 Relationship between maximum dynamic shear modulus and confining pressure, consolidation ratio, vibration frequency and phosphogypsum content

It can be seen from Fig. 12 that the maximum dynamic shear modulus of plain soil and phosphogypsum stabilized soil increases approximately linearly with the increase of confining pressure, consolidation ratio and vibration frequency. The maximum dynamic shear modulus of phosphogypsum cement stabilized red clay is greater than that of plain soil. With the increase of phosphogypsum content, the maximum dynamic shear modulus of phosphogypsum cement stabilized red clay increases first and then decreases. When cement: phosphogypsum = 1:3, the maximum dynamic shear modulus is the largest.

Fig. 12
figure 12

Variation curve of maximum dynamic shear modulus with confining pressure, consolidation ratio, vibration frequency and phosphogypsum content

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5.5 Modification mechanism

We use spectroscopy is used to observe the structure and crystal shape of the particles of the phosphogypsum-modified red clay mixture; we can observe not only the overall structure but also the specific morphology of the particles of the mixture [27]. Therefore, in this test, 10,000 times magnification is selected to conduct SEM scanning of plain red clay and 5% cement phosphogypsum mixture. The results are shown in Fig. 13. XRD quantitative analysis is shown in Fig. 14 and Table 10.

Fig. 13
figure 13

SEM photos of plain red clay and phosphogypsum modified soil

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Fig. 14
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Quantitative analysis of compound composition of mixture

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Table 10 Quantitative analysis of mineral composition of mixture
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Figures 13, 14 and Table 10 show that the plain red clay has a single form and obvious granules. With the addition of cement and phosphogypsum, the surface morphology of the mixture and the granular characteristics of the red clay changes greatly. With increasing phosphogypsum content, the cement hydration reaction and phosphogypsum generate acicular ettringite. When cement:phosphogypsum = 1:2.2–1:3, the most ettringite is generated, and it fills large interstices between particles in the mixture to form a network structure. The interstices become smaller, the structure becomes denser and the strength is maximized. The strength and expansion rate increase gradually, and the linear shrinkage rate decreases gradually. When the content of phosphogypsum further increases, the mixture is acidic, ettringite is dissolved, the ettringite network is damaged, there are many flakes of unreacted phosphogypsum and less cementitious substances, the strength and expansion rate decrease, and the linear shrinkage rate increases. The reaction mechanism is as follows:

Under certain compaction conditions, a series of physical and chemical changes occur in the cement-phosphogypsum mixture. The main chemical reactions are hydration of cement and formation of calcium silicate hydrate (C-S–H gel) and calcium hydroxide:

$$ {\text{3CaO}} \cdot {\text{SiO}}_{{2}} + {\text{nH}}_{{2}} {\text{O}} = {\text{xCaO}} \cdot {\text{SiO}}_{{2}} \cdot \left( {{\text{n}} - {3} + {\text{x}}} \right){\text{H}}_{{2}} {\text{O}} + \left( {{3} - {\text{x}}} \right){\text{Ca}}\left( {{\text{OH}}} \right)_{{2}} $$

Then, calcium hydroxide reacts with SiO2 and Al2O3 in soil:

$$ \begin{gathered} {\text{3Ca}}\left( {{\text{OH}}} \right)_{{2}} + {\text{SiO}}_{{2}} + \left( {{\text{n}} - {3}} \right){\text{H}}_{{2}} {\text{O}} \to {\text{3CaSiO}}_{{2}} \cdot {\text{nH}}_{{2}} {\text{O}}, \hfill \\ {\text{3Ca}}\left( {{\text{OH}}} \right)_{{2}} + {\text{Al}}_{{2}} {\text{O}}_{{3}} + \left( {{\text{n}} - {3}} \right){\text{H}}_{{2}} {\text{O}} \to {\text{3CaAl}}_{{2}} {\text{O}}_{{3}} \cdot {\text{nH}}_{{2}} {\text{O}} \hfill \\ \end{gathered} $$

Hydrated calcium aluminate is not the final product. It continues to react with the main component of phosphogypsum, calcium sulfate dihydrate (CaSO4·2H2O), to form disulfide hydrated calcium aluminate (3CaO·Al2O3·3CaSO4·32H2O), also known as AFT).

$$ {\text{3CaO}} \cdot {\text{Al}}_{{2}} {\text{O}}_{{3}} \cdot {\text{nH}}_{{2}} {\text{O}} + {\text{3CaSO}}_{{4}} \cdot {\text{2H}}_{{2}} {\text{O}} + \left( {{26} - {\text{n}}} \right){\text{H}}_{{2}} {\text{O}} \to {\text{3CaO}} \cdot {\text{Al}}_{{2}} {\text{O}}_{{3}} \cdot {\text{3CaSO}}_{{4}} \cdot {\text{32H}}_{{2}} {\text{O}} $$

Ettringite (AFT) has a cubic crystal system with columnar structure. Its properties have a great influence on the properties of phosphogypsum cement-modified soil. An appropriate amount of phosphogypsum was added to the cement-red clay mixture. Phosphogypsum activates the mixture, accelerates the cement hydration reaction, and participates in the reaction to form a certain amount of fine needles of AFT. In addition, the intersecting needle columnar crystals of ettringite and hydrated calcium silicate form a network structure that not only reduces the average pore size of the reinforced soil but also supports the pores and improves the strength. The volume expansion caused by the formation of AFT can not only compact the internal structure, reduce the pore size and decrease the porosity but also reduce the dry shrinkage of the modified soil mixture and improve its crack resistance. This can be confirmed by physical experiments. When cement:phosphogypsum = approximately 1:3, the most AFT is generated, resulting in the maximum strength and expansion rate of the mixture, while the shrinkage is close to the minimum.

Kaolinite has a two-layer structure composed of a layer of tetrahedral silica and a layer of octahedral alumina. There are strong hydrogen bonds between adjacent crystal cells. There is almost no isomorphic substitution, no residual charge, or structural modification; the crystal plane spacing is not affected by water, and the crystal lattice is firm. Polar water molecules and exchange captions cannot enter the interlayer, so it has little ability to expand. The crystal structure of elite is similar to that of montmorillonite, which is composed of two layers of tetrahedral silica and one layer of octahedral alumina. Unlike montmorillonite, the coupling force between two crystal cells in elite is enhanced by to the adsorption of potassium ions, the activity capacity of the crystal lattice is lower than that of montmorillonite, and some polar water molecules can enter the middle of the crystal layer of elite, which can slightly expand. With the increase in phosphogypsum content in the mixture, the total content of kaolinite and muscovite first increases, reaches a maximum of 34.1% in the cement:phosphogypsum = 1:2–1:3 range, and then decreases gradually. This proves the conclusion that the expansion rate is the largest for mineral compositions in the cement:phosphogypsum = 1:2–1:3 range. The expansion and contraction of red clay are reversible, and the expansion rate increases when the contraction decreases.

In conclusion, when the phosphogypsum content is small, the cement hydration reaction is sufficient, and the enhancement effect of the calcium sulfate dihydrate reaction product is not obvious. In contrast, swelling destroys the gel, leading to decreases in early and late strength. When the phosphogypsum dose is too high, the alkalinity is very low, the gel performance is very poor, the mixture pH decreases rapidly, and the ettringite dissolves. Additionally, the initial support fractures, which decreases expansion and leads to the formation of connections between soil particles and flakes of unreacted phosphogypsum. The result is the formation of a weak sandwich layer that reduces the strength [28,29,30].

It should be indicated that there is an optimal amount of phosphogypsum in the mixture, with the increase of the content of phosphogypsum, the amount of ettringite in the mixture increases, and the strength of the mixture increases. However, if phosphogypsum is continued to be added, the ettringite will dissolve and the strength of the mixture will decrease. Therefore, there is an optimal amount of phosphogypsum in the mixture, and we try to find the corresponding amount of phosphogypsum when the ettringite is generated the most. The amount of phosphogypsum is the optimal amount of phosphogypsum, that is, the optimal amount of phosphogypsum is the goal of our work.

6 Conclusions

  1. (1)

    The unconfined compressive strength of the phosphogypsum stabilized soil in the low content phosphogypsum group is greater than that in the high content phosphogypsum group. When cement:phosphogypsum = 1:2.2–1:3, the unconfined compressive strength of the mixture is maximum.The more cement content, the greater the unconfined compressive strength of the mixture. With increasing time of cure, the unconfined compressive strength of the mixture increases rapidly during the first 14 d and tends to stabilize during the last 14 d.

  2. (2)

    The absolute expansion rate of phosphogypsum stabilized soil in the low content phosphogypsum group is higher than that in the high content phosphogypsum group, which indicates that the more the content of phosphogypsum, the smaller the expansion rate of the mixture. When cement: phosphogypsum = 1:1–1:3, the absolute expansion rate is 6.5–12.3%. Phosphogypsum: red clay = 1:1–1:3, the absolute expansion rate is 0.2–4%.

  3. (3)

    The linear shrinkage rate of phosphogypsum stabilized soil in the low content group is greater than that in the high content phosphogypsum group, which indicates that the more the content of phosphogypsum, the smaller the linear shrinkage rate of the mixture. When cement: phosphogypsum = 1:1–1:3, the linear shrinkage rate is 1.3–2%. Phosphogypsum: red clay = 1:1–1:3, the linear shrinkage rate is 1–1.5%.

  4. (4)

    The relationship between dynamic shear modulus and dynamic shear strain of plain red clay and phosphogypsum stabilized soil can be fitted by H–D model. When cement:phosphogypsum = 1:3, the maximum dynamic shear modulus is the largest

  5. (5)

    The strength of phosphogypsum stabilized soil is derived from the comprehensive effect of cement and phosphogypsum. Calcium silicate hydrate, calcium aluminate hydrate and ettringite are generated to form the skeleton of the mixture, forming a spatial network structure and increasing the strength. When the content of phosphogypsum further increases, the mixture is acidic, the ettringite is dissolved, the skeleton is destroyed, the cementitious substances are less, and the strength is reduced. The proportion of red clay decreases, and the content of hydrophilic minerals decreases, which inhibits the expansion and shrinkage deformation characteristics of red clay.

In this paper, a preliminary exploratory study on the mechanical properties and microscopic mechanism of cement phosphogypsum-stabilized red clay was carried out. The unconfined compressive strength of phosphogypsum stabilized soil in the low content phosphogypsum group is greater than that in the high content phosphogypsum group, but the absolute expansion rate and linear shrinkage of the low content phosphogypsum group phosphogypsum stabilized soil are greater than those in the high content phosphogypsum group. It shows that the more phosphogypsum content, the smaller the expansion deformation and shrinkage deformation of the mixture. In view of the requirements of roadbed strength and water stability, it is recommended that the cement content of 5%, phosphogypsum: red clay = 1:1 be used as the roadbed filler, which can not only make full use of phosphogypsum solid waste, but also improve the engineering properties of red clay.