Introduction

The resilient modulus is not only a mechanical index reflecting the deformation resistance of the roadbed but is also a key parameter in the design of road structure1,2,3. The resilient modulus is the ratio of stress to the corresponding strain of road materials under load and is an effective index for characterizing the elastic deformation characteristics of subgrade soil, which has been widely used in road design4,5,6. Based on an in-depth analysis of the subgrade resilient modulus (E0), many scholars and research institutions worldwide have found that the dynamic resilient modulus (MR) is more consistent with the actual mechanical characteristics of roads7,8,9,10,11,12. Simultaneously, the current Chinese subgrade design code clearly indicates that the subgrade filler should take the dynamic resilient modulus of the top surface of the road bed as the design index on the basis of meeting the CBR and provides the test method and evaluation standard of the dynamic resilient modulus of subgrade soil13. However, owing to the expensive equipment, complex operation, and high cost of dynamic resilient modulus testing, there are some limitations in specific engineering applications. Therefore, if a simple, reliable, and popular CBR test method can be used to establish a prediction model for the dynamic resilient modulus based on the CBR value14, the CBR value can be used to accurately predict the dynamic resilient modulus of the subgrade soil, which has important engineering application value.

In view of the correlation between the resilient modulus of subgrade soil and the CBR value, researchers at home and abroad have obtained relevant research results. Heukelom and Klomp15 obtained a linear relation of CBR, E = αCBR, through a regression analysis based on the field resilient modulus test results of the Shell Company and several other public data. The regression coefficient α varied between 5 and 20, generally taking 10 and a safety factor of 2. This relationship has been adopted in several fine-grained soil subgrade design methods16,17,18,19. Zhao et al.20 conducted a large number of field tests on a test road section of silt-medium liquid-limited clay in the Xinyang area, Henan Province, China, and proposed that the relationship between the resilient modulus of the soil foundation and the bearing ratio in this area was E0 = 3.192CBR0.555, and the correlation coefficient R = 0.9404, indicating a very good correlation between the two. Xiao et al.21 took silty clay and silty soil in Jilin Province as research objects, and based on the data of indoor resilient modulus (E0) test and CBR test, obtained the values of resilient modulus of silty clay E0 ≈ 2.4CBR and that of silty soil E0 ≈ 4.5CBR through statistical analysis. These differences were caused by the different properties of silty clay and silty soil. Zhang22 used improved silty clay from oil shale waste residue of Jilin Province as the subgrade filler and proposed a dynamic resilient modulus prediction model based on CBR value through the CBR test and dynamic triaxial test. The model had a high correlation coefficient and strong applicability. Cheng et al.23 selected two types of subgrade soil in a seasonally frozen region, such as clay soil and silty soil, to conduct an indoor resilient modulus (E0) test and CBR test and obtained the specific relationship between the resilient modulus of subgrade soil in the seasonal freezing region and CBR through linear regression (i.e., low liquid limit clay E0 = 6.73CBR0.73, correlation coefficient R2 = 0.829; low liquid limit silt E0 = 7.40CBR0.70, and correlation coefficient R2 = 0.899). Wu et al.24 selected four expressways in Shanxi Province to conduct field tests on the resilient modulus E0 and the CBR. By collating and analyzing the test data, the relationship between the resilient modulus of loess in northern Shanxi and CBR was in line with a power exponential relationship, and the expression was E0 = 5.04CBR0.6–5.15. The relationship between the loess resilient modulus and CBR in northern Shanxi is exponential, and its expression is E0 = 9.737e0.032CBR. Cheng25 selected the subgrade of typical sections of the Shanping, Guangyuan, and Heyun expressways under construction in the Loess region to conduct in situ resilient modulus and CBR tests. Through a linear regression analysis of the measured data, a power function relationship between the subgrade resilient modulus (E0) and CBR was obtained (i.e., the Shanping loess subgrade E0 = 0.70CBR0.96, correlation coefficient R2 = 0.726; Guangyuan loess subgrade E0 = 6.46CBR0.48, correlation coefficient R2 = 0.674; Heyun loess subgrade E0 = 0.07CBR1.66, and correlation coefficient R2 = 0.708). Fang et al.26 used unmodified fine-grained sulfate soil (clay and silt) in the Qinghai region as the raw material to perform laboratory tests on the resilient modulus and CBR. By analyzing and fitting a large amount of test data, it was found that there was a good fitting relationship between the resilient modulus (E0) and CBR2.5 under different test conditions (i.e., E0 = aCBRb). The correlation coefficient between E0 and non-flooded CBR2.5 is above 0.9, which is better than that between E0 and flooded CBR2.5. Deng et al.27 conducted an indoor repeated loading triaxial test and CBR test on the road performance index (dynamic resilient modulus and CBR) of coarse-grained chlorine saline soil, focusing on the influence of water and salt on the two design indices, and evaluated the feasibility of this type of saline soil as a subgrade filler. However, this study did not analyze the correlation between the two design indicators in detail.

These results have shown that the correlation studies of the subgrade resilient modulus and CBR mainly focus on the static resilient modulus (E0) and CBR of fine soil (such as loess, clay, and silt), and the relationship between them. However, there is little research on the dynamic resilient modulus of widely distributed four-phase saline soil, which has led to the abandonment of large areas of natural coarse-grained saline soil, especially coarse-grained chlorine saline soil, with good strength and stability. Considering the differences in particle composition, history, origin, scale, stable state, and degree of damage to highways in different regions, there are certain differences in engineering mechanical properties, resulting in different relationship models between the dynamic resilient modulus (MR) and CBR of the subgrade soil in different regions. Therefore, it is necessary to study the correlation between the dynamic resilient modulus and CBR of coarse saline soil to provide a simple and practical method for obtaining subgrade design parameters in saline soil areas.

Considering this, this study uses coarse-grained chlorine saline soil as the research object (coarse-grained saline soil in the following expression refers to chloride saline soil) and conducts experimental studies on the dynamic resilient modulus (MR) and CBR values of coarse-grained saline soil under different stress levels, water contents, and salt contents through repeated loading triaxial tests and CBR tests. The change law and correlation between the dynamic resilient modulus and load-bearing ratio under different test conditions were analyzed. Through statistical analysis of the test data, a prediction model for the dynamic resilient modulus concerning CBR was developed to accurately estimate the dynamic resilient modulus of coarse-grained chlorine saline soil. This model offers a simple and re-liable method for obtaining design parameters of saline soil subgrade in a reasonable manner. It holds significant reference value and importance in guiding the design and construction of saline soil subgrade.

Materials and methods

Test materials

Owing to regional differences in the original state, historical origin, abundance scale, and environmental conditions of the saline soil samples on site, it was impossible to accurately control its physical property indices, such as salt content, water content, and particle composition, by artificial means. The test material used in this study was coarse-grained chlorine saline soil artificially configured in the laboratory to reduce the influencing factors of the test and more accurately and comprehensively study the correlation between the dynamic resilient modulus of coarse-grained saline soil and its CBR.

The original soil sample was determined to be plain soil (salt content less than 0.1%) by soluble salt content. Its particle size composition and basic physical property indices are shown in Tables 1 and 2. According to the relevant norms13, the saline soil was classified according to the degree of salinization, and the salt content limit of NaCl was 0% (coarse-grained soil), 2% (weakly saline), 5% (medium-saline), and 8% (strongly saline). Coarse-grained chloride saline soil with the prescribed salt content was obtained by blending NaCl with well-graded coarse-grained soil using the mass method.

Table 1 Particle size composition of soil sample.
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Table 2 Basic physical properties of soil sample.
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Sample preparation

The sample was controlled with a unified compaction degree of 96% (the ratio of field density to indoor density) and prepared under different salt and water contents to study the evolution law of the dynamic resilient modulus and CBR value of coarse-grained chloride saline soil affected by water content and salt content. Samples with the same salt content were prepared with moisture contents of 4%, 5.1%, and 6%, with three parallel samples in each group. The test conditions are listed in Table 3.

Table 3 Test conditions.
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Triaxial test sample

The sample size for the standard triaxial test has a height of 200 mm and a diameter of 100 mm. The samples were prepared in strict accordance with the relevant provisions for the dynamic resilient modulus test of subgrade soil in the Specifications for Design of Highway Subgrades (JTG D30-2015, China) and the Test Methods of Soils for Highway Engineering (JTG 3430-2020, China) (Fig. 1). To ensure a uniform degree of compaction for the entire sample, it was divided into eight layers in a split die. The soil sample quality was used to control the loose layup thickness of each layer to ensure that the compaction of each layer reached the target value. Hair drawing between the layers was simultaneously performed to ensure the integrity of the specimen.

Figure 1
Figure 1
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Triaxial specimen.

CBR test sample

The sample for the CBR test was obtained using a heavy compaction test, and the sample size, compaction times, and number of layers were determined in accordance with the relevant provisions of the Test Methods of Soils for Highway Engineering (JTG 3430-2020, China). In this study, a compaction cylinder, with a height of 170 mm and a diameter of 150 mm, was used to prepare the samples. The test soil sample was prepared under optimal water content conditions, and the target compaction degree was controlled by the mass and volume. Comparison test groups with moisture content of ωopt ± 1% were set to analyze the effect of humidity on the CBR of coarse-grained chlorine saline soil.

Test methods

Dynamic resilient modulus test

A British GDSLAB dynamic triaxial test system (5 Hz/60 kN MinDyn) was used for the dynamic resilient modulus tests in this study. The triaxial pressure chamber has a height of 300 ± 2 mm and an inner diameter of 170 ± 2 mm (Fig. 2). This test adopted half-sine wave loading with a load frequency of 1 Hz, load holding time of 0.2 s, intermittent time of 0.8 s, and confining pressure of pneumatic loading.

Figure 2
Figure 2
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Dynamic triaxial test system.

Based on the structural characteristics of China's typical asphalt pavement and the stress state of the subgrade, Luo and Chen et al.28,29 proposed a dynamic triaxial stress loading sequence for subgrade coarse-grained soil with reference to the NCHRP 1–2830 test method (as shown in Table 4). The above stress-loading sequence was adopted to perform repeated loading triaxial tests in this study, and the operational procedures were strictly in accordance with the Chinese standard test methods stipulated in the Specifications for Design of Highway Subgrades and Test Methods of Soils for Highway Engineering. The dynamic resilient modulus of the coarse-grained chlorine saline soil was calculated according to Eq. (1).

$$M_{{\text{R}}} = \frac{{\sigma _{\text{d}} }}{{\varepsilon _{{\text{R}}} }},$$
(1)

where MR is the dynamic resilient modulus (MPa), σd is the deviator stress (kPa), σd = σ1 − σ3, σ1 is the vertical stress, σ3 is the confining stress (generally σ2 = σ3), and εR is the mean axial rebound strain (0.001 mm).

Table 4 Triaxial loading sequence of coarse-grained soil (Unit: kPa).
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California bearing ratio (CBR) test

The CBR test in this study adopted the CBR-1 bearing ratio tester produced by the Chinese Nanjing Ningxi Soil Instrument Co., Ltd. (Fig. 3). Its penetration rod has a standard size H × D = 100 × 50 mm, the maximum load was 30 kN, and the lifting speed was 1 mm/min. In addition, it was necessary to use three dial indicators and their supporting shelves, four load plates (1.25 kg each), perforated plates, and other supporting-measuring equipment.

Figure 3
Figure 3
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CBR-1 bearing ratio tester.

Considering the decrease in subgrade strength caused by rain and groundwater immersion, the CBR after 96 h of immersion is often used as the most unfavorable standard for subgrade filling in subgrade design. For the specific operating procedures of the sample immersion test (Fig. 4) and penetration test (Fig. 3), please refer to the T0134-2019 Bearing ratio (CBR) test in the Test Methods of Soils for Highway Engineering (JTG 3430-2020, China).

Figure 4
Figure 4
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CBR sample in saturated water.

In this study, the dial meter readings were recorded at penetration depths of 30, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, and 600 m (units = 0.01 mm). The stress-penetration curves of the samples under different test conditions were plotted using the penetration quantity and unit compressive stress as the transverse and longitudinal coordinates, respectively (Fig. 7). Based on the calculation and value regulation of the CBR issued by the latest Test Methods of Soils for Highway Engineering (JTG 3430-2020) of China, the ratios of unit pressure and standard pressure corresponding to 2.5 and 5.0 mm penetration were calculated, respectively (as percentages). The larger value of the two was considered as the CBR of the coarse-grained chlorine saline soil, and the specific calculation method is shown in Eqs. (2) and (3).

$$CBR_{{2.5}} = \frac{{P_{{2.5}} }}{{7000}} \times 100,$$
(2)
$$CBR_{{5.0}} = \frac{{P_{{5.0}} }}{{10500}} \times 100,$$
(3)

where CBR2.5 and CBR5.0 are the bearing ratio (%) when the penetration depth is 2.5 and 5.0 mm, respectively, and P2.5 and P5.0 are the corresponding unit pressure values (kPa) when the penetration volume is 2.5 and 5.0 mm, respectively.

In addition to the determination of CBR for coarse-grained chloride saline soil with optimal moisture content, this study also tested the CBR for ωopt ± 1% moisture content to compare the influence of humidity on CBR value of coarse-grained chloride saline soil.

Results and discussion

To analyze the evolution law of the dynamic resilient modulus and CBR value of coarse-grained chloride saline soil affected by stress conditions, water content, and salt content, the compaction degree of the selected test samples was 96%, and the test results are shown in Figs. 5, 6, 7, 8, 9, 10 and 11. To facilitate expression and interpretation, the water content, salt content, confining stress, deviator stress, bulk stress, and dynamic resilient modulus were expressed by ω, Z, σ3, σd, θ, and MR in this study, respectively. In addition, there was a multiple relationship between the deviator stress and the confining stress (σd = 0.5σ3, 1.0σ3, 2.0σ3) and θ = σ1 + σ2 + σ3.

Figure 5
Figure 5
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Relationship between MR and σd under different confining pressures at 5.1% water content: (a) Z = 0%; (b) Z = 2%; (c) Z = 5%; (d) Z = 8%.

Figure 6
Figure 6
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Relationship between MR and θ under different partial stresses at 5.1% water content: (a) Z = 0%; (b) Z = 2%; (c) Z = 5%; (d) Z = 8%.

Figure 7
Figure 7
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Relationship between unit pressure and penetration quantity under different salt contents at degree of compaction k = 96%: (a) ω = 4%; (b) ω = 5.1%; (c) ω = 6%.

Figure 8
Figure 8
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Relationship between MR and ω under different salt contents at confining pressure 45 kPa: (a) σd = 23 kPa; (b) σd = 45 kPa; (c) σd = 90 kPa.

Figure 9
Figure 9
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Relationship between CBR and ω under different penetrations at degree of compaction k = 96%: (a) Z = 0%; (b) Z = 2%; (c) Z = 5%; (d) Z = 8%.

Figure 10
Figure 10
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Relationship between MR and Z under different water contents at confining pressure 45 kPa: (a) σd = 0.5σ3 = 23 kPa; (b) σd = 1.0σ3 = 45 kPa; (c) σd = 2.0σ3 = 90 kPa.

Figure 11
Figure 11
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Relationship between CBR and Z under different penetrations at degree of compaction k = 96%: (a) ω = 4%; (b) ω = 5.1%; (c) ω = 6%.

Influence of stress conditions on dynamic resilient modulus and penetration quantity

As shown in Fig. 5, when the optimal moisture content was 5.1%, under different salt conditions, the dynamic resilient modulus of the coarse saline soil with different confining pressures decreased with an increase in the deviator stress. With an increase in deviator stress, when Z = 0, the decreases in the dynamic resilient modulus MR under various confining pressures were 2.3%, 5.6%, 7.2%, 9.9%, and 12.7% (Fig. 5a). When Z = 2%, the decrease in MR increased to 8.2%, 11.5%, 17.4%, 22.8%, and 28.6% (Fig. 5b). When Z = 5%, the reduction in MR ranged from 11.7 to 26.7% (Fig. 5c). When Z = 8%, the reduction of MR Increases to 15.4–33.3% (Fig. 5d). The greater the deviator stress, the greater the reduction in the dynamic resilient modulus, and the higher the salt content in the coarse saline soil, the more obvious the influence of the deviator stress on the dynamic resilient modulus. The microscopic mechanism of this phenomenon can be explained as follows. When the salt content Z in the soil is less than the limit salt content (i.e., corresponding to the saturated state of the salt solution, the limit salt content is approximately 10%)31,32, the ion concentration after dissolution increases with increasing salt content, the thickness of the double electric layer increases, the lubrication effect of sodium ions gradually strengthens, and the shear strength of the chloride saline soil gradually decreases. The shear effect caused by the increase in the deviator stress was greater than the lateral effect caused by the shear strength and confining pressure of the soil in the late loading period, leading to dislocation movement and rearrangement of the soil particles, and the dynamic resilient modulus gradually decreased.

As shown in Fig. 6, when the humidity is the optimal moisture content of 5.1%, under different salt content conditions, the dynamic resilient modulus of coarse-grained saline soil with different deviator stresses increases as the bulk stress increases. As the bulk stress increases, when Z = 0, as shown in Fig. 6a, the dynamic resilient modulus MR under different deviator stresses increases by 40.3%, 32.8%, and 25.4%. As shown in Fig. 6b, when Z = 2%, MR increased by 59.1%, 40.0%, and 28.9%, respectively. As shown in Fig. 6c, when Z = 5%, MR increased by 76.5%, 62.5%, and 46.7%, respectively. As shown in Fig. 6d, when Z = 8%, MR increased by 107.7%, 91.7%, and 63.6%, respectively. The experimental observation shows that the smaller the deviator stress, the larger the increase in the dynamic resilient modulus caused by the increase in bulk stress. The higher the salt content of the coarse saline soil, the more evident the influence of bulk stress on its dynamic resilient modulus. Based on the analysis, when the deviator stress is constant, the increase in bulk stress is due to the strengthening of the confining pressure σ3 on the transverse deformation of the sample, the increase in soil stiffness, and the gradual increase in the dynamic resilient modulus.

As shown in Fig. 7, the amount of penetration with different salt contents increased with an increase in the unit compressive stress when the degree of compaction was 96% under various humidity conditions. Moreover, the penetration quantity of the low-salt content (Z ≤ 2%) increases nonlinearly, whereas that of the high-salt content (Z > 2%) increases approximately linearly. When the unit compressive stress was constant, the penetration quantity of the sample with the same humidity increased with increasing salt content. When Z increases from 2 to 8%, the vertical local compressive stress of the coarse saline soil with different humidities gradually decreases, and the decreasing range increases from 13.89%, 16.39%, and 21.43% to 45.83%, 54.10%, and 66.07%, respectively. This indicates that the penetration quantity with a smaller salt content is more weakly affected by unit pressure, and the influence of unit compressive stress on the penetration quantity becomes gradually obvious with an increase in salt content, especially for samples with high salt content. This shows that the unit compressive stress has a significant influence on the penetration of a sample with a high salt concentration. In other words, the higher the salt content, the smaller is the resistance of the coarse saline soil to local loading deformation. The test law can be analyzed as follows: after the coarse saline soil is immersed in water, the salt in the soil is easily dissolved in water and loses water, and the soil void increases further. Consequently, the compactness of the sample decreased, the compressibility increased, and the deformation resistance decreased, which is consistent with the above law that the dynamic resilient modulus is affected by the vertical deviator stress.

Influence of water content on dynamic resilient modulus and CBR value

As shown in Fig. 8, when the confining pressure was 45 kPa, the dynamic resilient modulus of coarse saline soil with different salt contents gradually decreased with increasing water content under various deviator stress conditions. When the water content increases from 4 to 6% and σd = 23 kPa, the dynamic resilient modulus MR with different salt content decreases by 6.4%, 7.5%, 8.6%, and 9.3%, respectively (Fig. 8a). When σd = 45 kPa, MR decreases by 9.7%, 10.1%, 13.3%, and 12.0%, respectively (Fig. 8b). When σd = 90 kPa, MR decreases by 12.6%, 12.2%, 13.5%, and 12.8%, respectively (Fig. 8c). The analysis of the test data shows that when the salt content is constant, the decrease of the dynamic resilient modulus increases with the increase of the deviator stress, and the maximum difference of the reduction is in the range of 3.5–6.2%. This is because an increase in water causes the water film between the soil particles to thicken and the salt dissolved in the water destroys the salt skeleton in the soil. In particular, under the condition of high salt content, with an increase in water content, the lubrication effect of the salt solution was enhanced, and the friction strength between coarse particles of soil was weakened, resulting in a gradual decrease in the dynamic resilient modulus.

As shown in Fig. 9, when the degree of compaction is 96%, the CBR value of coarse-grained chlorine saline soil with different penetration quantities decreases with an increase in water content under different salt concentration conditions, and the CBR value of the 5 mm penetration quantity is greater than that of the 2.5 mm (i.e., the CBR value corresponding to a 5 mm penetration quantity is the bearing ratio of the soil sample tested in this study). With an increase in the water content in the molded sample, the CBR value under each salt concentration condition decreased by 10.09%, 11.15%, 11.98%, and 12.61%. When the salt content increases from 2 to 8% (as shown in Fig. 9b,c, and d), the difference between the CBR value of the 2.5 mm penetration quantity and the CBR value of 5 mm tends to shrink with the increase in water content, and both gradually decrease. This test rule shows that the CBR value of coarse-grained chlorine saline soil is significantly affected by the humidity before sample molding. The higher the moisture content in the coarse chlorine saline soil, the smaller the CBR value measured after immersion. The reasons for this test phenomenon are derived from the water film theory33. The thickening of the water-film diffusion layer weakened the suction and effective connection between the soil particles, and the shear strength of the soil decreased, resulting in the failure of the sample to achieve the expected compactness after compaction. However, this is mainly because, after the sample is immersed in water, the particle framework of the soil is damaged again by water and salt migration, and the plasticity is further enhanced. Therefore, the strength attenuation value of the coarse-grained saline soil with a greater moisture content is more significant after soaking in water.

Influence of salt content on dynamic resilient modulus and CBR value

As shown in Fig. 10, when the confining pressure was 45 kPa, the dynamic resilient modulus MR of coarse saline soil with different water contents gradually decreased as the salt content increased under various deviator stress conditions. When the salt content Z increases from 0 to 8%, and σd = 23 kPa (Fig. 10a), the dynamic resilient modulus MR of different water content decreases by 31.2%, 32.2%, and 33.3%, respectively. As shown in Fig. 10b, when σd = 45 kPa, MR decreases by 35.5%, 37.2%, and 37.1%, respectively. As shown in Fig. 10c, when σd = 90 kPa, MR decreases by 43.0%, 43.3%, and 41.9%, respectively. The results indicate that as the salt content increases, the decline in dynamic resilient modulus of coarse-grained saline soils with varying water content tends to rise, and the maximum difference is in the range of 1.4–2.1%. When the deviator stress increases from 23 to 90 kPa, the decrease in the dynamic resilient modulus gradually increased with the increase in salt content, and the maximum difference in the decrease range was 8.6–11.8% under different humidity conditions. The primary reason is that the rise in sodium chloride causes expansion of the salt skeleton within the soil. Upon contact with water, more salt skeletons dissolve, thereby increasing the space between soil particles and consequently enhancing soil compressibility. Simultaneously, the increase in salt solution concentration promotes lubrication among soil particles, making it easier for soil particles to slip or rearrange under cyclic loading, resulting in plastic deformation, which results in the decline of the soil resilient deformation ability, consistent with existing research conclusions34,35,36.

As shown in Fig. 11, when the degree of compaction was 96%, the CBR value of the coarse saline soil samples formed under various humidity conditions decreased with an increase in salt content after water immersion. With the increasing salt content of the samples, the CBR values under different humidity conditions decreased from 45.40%, 38.46%, and 35.31% to 24.59%, 17.66%, and 11.98%, respectively. In addition, with the increase of salt content, the difference between CBR value of 5.0 mm penetration and CBR value of 2.5 mm penetration increased first and then decreased, and the maximum difference between the two was 5.04%, 3.78%, and 3.15%, respectively. With an increase in salt content, the decrease in the CBR value of coarse saline soil with different moisture contents tends to increase, with a maximum decrease of 23.33% (corresponding to the condition of 6% moisture content). This test phenomenon verified that the dynamic resilient modulus was affected by the chloride content. That is, with the increase of salt content (Z ≥ 2%)36,37, when the soil is immersed in water for a short time and there is not much water, part or all of the chlorine salts in the soil are dissolved in water, and the salt skeleton is destroyed, which increases the space between the soil particles and gradually increases the dissolution deformation rate under the soil body weight and load. However, when the coarse saline soil is immersed for a long time (4 days and nights) and the amount of water immersed is large, resulting in seepage, the chlorine salt is fully dissolved with the water loss but also removes part of the soil particles in the soil, resulting in latent erosion and a further increase in the void in the soil. As a result, additional deformation (i.e., latent erosion deformation, which is the main component of solution subsidence deformation of coarse-grained saline soil) is generated in the soil, resulting in a gradual decrease in the strength of the chlorinated saline soil, which is more consistent with the existing research results of chloride salt solution subsidence38,39,40.

In summary, the dynamic resilient modulus (MR) and CBR values of the coarse-grained chloride saline soil were similar under the influences of stress, water, and salt, and there was a good mechanical correlation between them. The measured values under different test conditions were sorted and statistically analyzed, as shown in Table 5, to further clarify the specific relationship between the dynamic resilient modulus and CBR.

Table 5 Dynamic resilient modulus and CBR test values at the compaction degree of 96%.
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According to the test results in Table 5, the average dynamic resilient modulus under each test condition ranges from 85.42 to 153.73 MPa, with the minimum value recorded at 51.05 MPa. These values comply with the minimum resilient modulus requirements for saline soil subgrade specified in the Guidelines for Highway Design and Construction in the Saline Soil Area of China41. Thus, it is necessary to build high-grade and first-class highways in areas with strongly saline soil and over saline land, and the subgrade resilient modulus cannot be less than 35 MPa. It also meets the requirements of the minimum resilient modulus of the top surface of the road bed in the light traffic load class stipulated in the current Chinese road design codes (JTG D50 and D40). The test results showed that the saturated-water CBR value under different working conditions was greater than 11.98%, exceeding the minimum value of 8% required by the current subgrade design code and subgrade Construction Technical Code. The roadworthiness requirements of the current subgrade design and construction codes are consistent with respect to the strength of the fillers and analysis based on the deformation resistance of the subgrade. Therefore, a certain mechanical correlation exists between the dynamic resilient modulus of coarse chloride saline soil and its CBR value.

Prediction model of dynamic resilient modulus based on CBR value

Determination of the prediction model of dynamic resilient modulus

According to the analysis of the above test results, the evolution law of the dynamic resilient modulus and CBR value of the coarse-grained chloride saline soil under the influence of stress, water, and salt was the same, which is consistent with the theoretical conclusion that the tangent modulus of the penetration curve was approximately the elastic modulus in the CBR test1. Therefore, the form of the model formula should first be determined when determining a prediction model for the dynamic resilient modulus to accurately reflect the internal relationship between them.

The relationship between the soil resilient modulus and CBR value has always been a concern for highway builders worldwide. Initially, researchers in the Netherlands, the United States, France, the United Kingdom, and other European and American countries conducted a large number of tests and studies on the relationship between the soil resilient modulus and the CBR value and obtained an approximate relationship between the subgrade soil CBR and the resilient modulus in different countries25. The specific model formulae are listed in Table 6.

Table 6 Relationship between foreign soil resilient modulus and CBR value.
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Many Chinese researchers have conducted numerous tests and studies on the relationship between the resilient modulus and CBR of eight representative subgrade soils in Xinjiang, expansive soil and clay in Guangxi, loess in Shanxi and Shaanxi, red clay in Guizhou, clay in Inner Mongolia, and clay in Heilongjiang. A method for calculating the resilient modulus based on the CBR value was proposed, and prediction models25,42 were obtained. The model forms are presented in Table 7.

Table 7 Relationship between Chinese soil resilient modulus and CBR value.
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The relevant domestic and foreign investigations in Tables 6 and 7 show that the relationship between the soil resilient modulus and its CBR value is E0 = k1CBRk2. The current Specifications for Design of Highway Subgrades (JTG D30-2015) in China clearly provides a prediction model for estimating the resilient modulus of subgrade soil based on the CBR of the subgrade soil, as shown in Eqs. (4) and (5).

$$M_{R} = 17.6CBR^{{0.64}} \left( {2\% < CBR \le 12\% } \right)$$
(4)
$$M_{R} = 22.1CBR^{{0.55}} \left( {12\% < CBR < 80\% } \right)$$
(5)

This can provide an effective basis and scientific reference for the preliminary road design to be consistent with the mechanical state of the road subgrade. Based on previous studies’ results and the test data in this study, the prediction model of the dynamic resilient modulus of coarse-grained chloride saline soil established based on the CBR value is shown in Eq. (6).

$$M_{{\text{R}}} = {k_{1}}CBR^{{k_{2}}},$$
(6)

where MR is the dynamic resilient modulus (MPa) and CBR is the CBR value (%) after 96 h of immersion. k1 and k2 are model parameters greater than zero.

Regression analysis of model parameters

To accurately determine the relevant parameters of the prediction model, regression analysis was performed on the average dynamic resilient modulus of the coarse-grained chloride saline soil compacted to a degree of 96% (Table 5) (That is, the average value under the 15 stress conditions in Table 4), along with the CBR value after 96 h of water saturation. The resulting model parameters k1 and k2, as well as the error results, are presented in Table 8.

Table 8 Results for parameter regression analysis of dynamic resilient modulus prediction model.
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The results of the regression analysis in Table 8 show that the model parameters k1 = 21.063 and k2 = 0.516 are consistent with the formula parameters recommended in the current subgrade design code in China (Eq. (5)), and most of the CBR values measured in the test fall within the range of 12–80%. There was a high correlation coefficient (R2 = 0.893) between the established prediction model and the test results. The predicted value was in good agreement with the measured value, with an overall error within 10% and a maximum error of no more than 15%, as shown in Fig. 12.

Figure 12
Figure 12
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Relationship between average dynamic resilient modulus and CBR value: (a) Average MR and CBR; (b) Measured MR and predicted MR.

Model accuracy verification

To verify the accuracy of the prediction model, another soil sample with a salt content Z = 10% (oversaline soil) was prepared, and the compaction degree was kept constant. Dynamic triaxial and CBR tests were conducted under three humidity conditions with water contents of 4.0%, 5.1%, and 6.0%. Average dynamic resilient modulus values measured were 80.47, 71.60, and 63.07 MPa, and the average CBR values measured were 8.83%, 5.67%, and 5.04%. The measured results were compared with the predicted values of the model (Fig. 13).

Figure 13
Figure 13
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Correlation between predicted and measured values based on CBR value.

As shown in Fig. 13, the measured dynamic resilient modulus of the coarse-grained chloride saline soil with a salt content of 10% had a good correlation with the predicted value based on the CBR. The accuracy of the prediction model based on the CBR value formed using Eq. (6) was above 0.891, and the error between the measured and predicted values was small. The prediction model of the dynamic resilient modulus based on the CBR value is highly reliable and can effectively predict the dynamic resilient modulus of chloride saline soil under other environmental conditions in the prediction area.

Conclusions

Repeated loading triaxial tests and CBR tests were carried out to study the correlation between the dynamic resilient modulus (MR) and CBR values of coarse-grained chloride saline soil, and the development law of the two mechanical indices under the influence of stress, water content, and salt content were discussed. Based on the correlation between the two revealed by experimental observations, a simple and reliable prediction model for the dynamic resilient modulus was proposed. The main conclusions of this study are as follows:

  1. (1)

    The MR and CBR values of coarse-grained chloride saline soil were significantly dependent on stress. MR gradually increased as the confining pressure and bulk stress increased, but significantly decreased with an increase in the deviating stress when the confining pressure was constant. The CBR value increased with an increase in the unit compressive stress, corresponding to a penetration quantity of 5.0 mm. An increase in the bulk stress caused an increase in the dynamic resilient modulus, which was caused by the lateral constraint of the confining pressure. Coarse-grained saline soil with high salt content has less resistance to local compressive stress after being saturated with water because chlorine salts are easily dissolved in water and are lost with water, resulting in insufficiently compacted soil samples and increased compressibility. The effect of stress on the two mechanical indices is the same, which is consistent with the conclusion that the tangent modulus of the penetration curve is approximately equal to the elastic modulus in the theoretical CBR test.

  2. (2)

    The dynamic resilient modulus (MR) and CBR values of the coarse-grained chloride saline soil were significantly affected by water and salt, and the influence of salt was more significant than that of water. Under the same stress, with an increase in water and salt content, the dynamic resilient modulus and CBR value after water saturation gradually decrease. With the increase of water content and salt content, the dynamic resilient modulus respectively decreases in the range of 6.4–13.5% and 31.2–43.3% (σ3 = 45 kPa), while the maximum decrease of CBR value is 12.61% and 23.33% (i.e., when the corresponding test conditions are Z = 8%, the water content is increased by 2%; salt content increases by 8% when ω = 6%). Analysis of the test data showed that the evolution laws of MR and CBR were similar under the influence of water and salt, which further revealed a good mechanical correlation between them.

  3. (3)

    By investigating and analyzing the existing prediction models, it was determined that the typical model form between the dynamic resilient modulus and the CBR value is E0 = k1CBRk2. Based on this model, a regression analysis was performed on the test data, and the obtained model parameters (parameters k1 = 21.063 and k2 = 0.516) were consistent with the recommended formula parameters in the current subgrade design code in China. The error analysis showed that the predicted value was in good agreement with the measured value, and the error was generally less than 10%. The prediction model had high accuracy (MR = 21.06CBR0.52 and correlation coefficient R2 = 0.893).

The study results accurately and comprehensively reflected the evolution law of the dynamic resilient modulus and CBR of coarse-grained chloride saline soil under the influence of load, moisture, and salt, and revealed a good correlation between them. The prediction model based on CBR is convenient for accurately predicting the dynamic resilient modulus of coarse chloride saline soils. The prediction model can provide a simple and reliable method for the reasonable selection of design parameters in the design process of roadbeds in saline soil areas. Because the prediction model of the dynamic resilient modulus established in this study was only obtained based on the test data of a graded coarse chloride saline soil, conducting testing research on the dynamic resilient modulus and CBR of coarse saline soil with multiple gradations in the future to verify and revising the prediction model in this study to improve its reliability and practical engineering application value are necessary.