Introduction

Loess is a kind of sediment formed in the Quaternary period. It was formed under arid and semi-arid conditions. Due to its specific formation and depositional environment, a special structure of loess is created. Hence, loess is rich in pores, its structure is loose, vertical joints are developed, and generally, it is easy to collapse. The structure of loess is the result of various factors in the formation of the geological history of the soil. The engineering nature of the soil is related to its structure. Terzaghi (1943) first described the concept of loess structure and studied its physical properties. In actual engineering, the strength and stability problems of loess, such as seepage deformation, cracking and collapse foundation settlement, and slope instability, are all related to the special structural properties of loess (Suebsuk et al. 2010; Zhong et al. 2015; Wen 2013; Chen 2014; She et al. 2013; Yao et al. 2020; Panjaitan et al. 2021; Mihajlović 2020). Academician Zhujiang Shen (1996) declared that the core and one of the hottest issues in the field of soil mechanics in the twenty-first century will be the structural research of loess. At present, the research on loess structure is mainly focused on three methods: microscopy, solid mechanics, and soil mechanics. The soil mechanics method also includes two quantitative research methods of structural parameter and structural strength: the structural strength is obtained by using the difference between undisturbed and remolded loess regarding the inflection point of their stress–strain curves (Dang and Li 2001; Yuan et al. 2017); the principle of the structural parameter is to release the structural potential of the loess, that is to say, the structure of the undisturbed loess can be completely destroyed by disturbance, loading, and flooding to achieve the purpose of measuring the strength of the loess structure (Xie et al. 1999). Many scholars have conducted a lot of research in this scientific area and put forward many representative structural parameters based on different mechanical parameters (Shao et al. 2004; Luo et al. 2004; Chen et al. 2006a, b; Deng et al. 2012; Hao et al. 2019).

In northwestern China, the climate is cyclically changing. Loess has been in a state of alternating wetting–drying cycles for a long time. The structure of loess will inevitably change and will be destroyed, affecting also its physical and mechanical properties. Pires et al. (2005) used GCT scans results to show that the wetting–drying cycles can change the structure of loess, and the porosity of the soil increases with the increase of the number of wetting–drying cycles. Oliveira et al. (2021) also concluded that the wetting–drying cycles change the pores distribution in the clay, which affects the retention and movement of water. Yan et al. (2021) took reinforced soil as the research object and showed that the cohesive and internal friction angle exhibited a decreasing trend after wetting–drying cycles, while the disintegration rate and permeability coefficient showed an increasing trend. Liu and Zhang (2020) also found that under the periodic action of the wetting–drying cycle, the tested mudstone samples continuously disintegrate, with bigger pieces with various sizes broken down into smaller fragments of different sizes. Esfandiari et al. (2021) performed several groups of parallel tests and demonstrated that under large vertical stress, the compressibility and expansion coefficients of the soil can be significantly improved by wetting–drying cycles, but this does occur at lower vertical stress levels. Wang et al. (2016), through micro-permeameter tests, proved that the shear strength of silty clay decreases with the increase of the number of wetting–drying cycles. Kholghifard et al. (2014) verified that the wetting–drying cycles have a significant impact on the collapse potential of the residual red soil, meaning that with the increase of the wetting–drying cycles, the collapse potential decreases and the swelling increases. Aldaood et al. (2014) pointed out that the compressive strength and structure of gypsum soil are affected by the wetting–drying cycles. Kay and Dexter (1992) also concluded that the tensile strength of the soil is significantly reduced due to the wetting–drying cycles. Studies such as Malusis et al. (2011) found that with the increase of the number of wetting–drying cycles, the hydraulic conductivity of the soil gradually increases.

It can be seen from the above research results that many scholars have done some valuable research on the structure and physical and mechanical properties of the soil under the wetting–drying cycle, but there are still some problems. There is no unified quantitative standard for the strength of loess structure, and most studies on loess structure focus on microscopic research. Moreover, the attenuation law of the shear strength and structural strength of loess under the action of wetting–drying cycles has not been systematically described. In view of this, this article takes Malan loess as the research object. Through a series of laboratory tests and conventional triaxial tests, the shear strength of the sample under wetting–drying cycles is obtained, and the calculation method of the structural parameter is proposed. The changes of structural parameter and shear strength of loess subjected to a number of wetting–drying cycles are discussed and the relationship between its shear strength and the structural parameter is studied.

In the remainder of the paper, the experimental methodology is presented in the “material and methods” section. In the “results and analysis” section, the changes in the shear strength and structural parameter of loess under wetting–drying cycles are analyzed. The relationship between the shear strength of loess and the structural parameter is discussed in the “the relationship between loess structural parameter and shear strength” section, followed are the conclusions presented in the “conclusions” section. The flow chart of the research method of this paper is shown in Fig. 1.

Fig. 1
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Flow chart of the research method

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Material and methods

Materials and preparation of sample

Materials

The undisturbed soil sample was taken from Linfen City, China and was obtained in the field by manual sampling (Fig. 2). The sampling depth is about 2.5–4.5 m, the soil samples are Malan loess, which is yellowish-brown, with relatively uniform soil quality, with wormholes, a few plant roots, and no white calcareous nodules. According to the laboratory geotechnical tests, the physical parameters of the test soil sample are shown in Table 1.

Fig. 2
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Location of sampling points

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Table 1 Physical parameter indexes of test soil
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Preparation of samples

The study of loess structure requires three kinds of soil samples: undisturbed, remolded, and saturated. A three-axis sampler can be used indoors to obtain the undisturbed soil sample. The remolded soil sample is prepared by compaction. The remaining soil after cutting the original sample is placed in an oven at 108 °C for 24 h, crushed, and passed through a 2 mm sieve. According to the test moisture content (5%, 10%, 15%, and 20%), the wet soil material is configured, and then the wet soil material is placed in the moisturizing tank for 24 h to keep the moisture fully transported in the wet soil material. Using a static pressure meter, a triaxial specimen is made with a height of 80 mm, a diameter of 39.1 mm, and a dry density of 1.48 g/cm2. The prepared undisturbed and the remolded sample is sealed with plastic wrap and placed in a moisturizing tank to prevent water loss. When the soil sample is saturated, first the sample is vacuumed in the vacuum cylinder for at least 1 h, and then distilled water is sucked into the vacuum cylinder while maintaining the vacuum. The water level is at least below the sample, and the soil sample saturation time is not less than 24 h.

Experimental program

Wetting–drying cycle tests

According to actual field survey data, the water content of loess in the area from where it was extracted varies between 5–20% under natural conditions. Therefore, in order to be as close to the actual situation as possible, the amplitude of wetting–drying cycles is 5–20% and the cycle number is set as 0, 1, and 3.

Taking the test water content of 10% as an example, the wetting–drying cycle test plan is shown in Fig. 3. The sample is humidified by the water film migration; while natural air drying is used for the drying. The target water content is controlled by sample quality. From the batch of samples that need to be air dried, one is selected for observation. When the sample quality is close to the target one, the other soil samples are weighed, and then air drying is stopped when the target water content is reached. After each humidification or air drying to the target water content, the soil sample is sealed with plastic wrap, and cured in a moisturizing tank for at least 24 h to ensure the full migration of water molecules in the soil sample.

Fig. 3
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Schematic diagram of wetting–drying cycle experiment

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Triaxial shear test

In this paper, the conventional triaxial test adopts a strain-controlled triaxial compression apparatus to carry out a triaxial consolidation undrained shear test, and the shear rate is 0.08 r/min. The sample height is 80 mm, the diameter is 39.1 mm, each group has 3 samples, and the confining pressure is 50 kPa, 100 kPa, and 200 kPa. The test water content varies with values of 5%, 10%, 15%, and 20%. According to the experimental settings, 36 undisturbed samples, 36 remolded samples, and 3 saturated samples are required, for a total of 75 soil samples (Table 2).

Table 2 Experimental program of conventional triaxial test
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Results and analysis

Analysis of shear strength of loess under wetting–drying cycles

According to the stress–strain curve \(\left(\left({\sigma }_{1}-{\sigma }_{3}\right)\backsim \varepsilon \right)\), obtained by the triaxial test, the peak stress is taken as the failure stress. When there is no peak in the curve, the failure stress is assumed to be the principal stress that corresponds to an axial strain (ε) equal to 15%. The stress Mohr circle is used to obtain the shear strength parameter values of the undisturbed and remolded soil samples in different states as shown in Tables 3 and 4, respectively. The shear strength parameter is expressed in terms of cohesion and internal friction angle.

Table 3 Shear strength parameters of undisturbed loess
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Table 4 Shear strength parameters of remolded loess
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Figure 4 shows the relationship between the number of wetting–drying cycles and the shear strength parameters of the undisturbed and remolded loess, respectively. In the figure, c represents cohesion and φ represents internal friction angle.

Fig. 4
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The relationship between the cycle number and shear strength parameters

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It can be seen in Fig. 4 that the wetting–drying cycle can reduce the shear strength of the loess, which is manifested by the decrease of the cohesion and internal friction angle of the sample as the number of the wetting–drying cycles increases. The research of Yan et al. (2021) also showed that repeated wetting–drying cycles can significantly reduce the erosion resistance of soil samples, and the shear strength and permeability of the soil sample are significantly decreased. Aldaood et al. (2014) studied the long-term strength of gypsum soil in wetting–drying cycles and found that the strength of gypsum soil is closely related to the number of wetting–drying cycles.

The decreasing trend of cohesion and internal friction angle is different with the increase of wetting–drying cycles. According to Table 3, it can be seen that when the moisture content of the undisturbed loess is 5%, the cohesive force is reduced by 11.6 kPa after 1 cycle and by 8.6 kPa after 3 cycles. It can also be seen from the cohesion change curve, the slope of the curve is steeper before the first wetting–drying cycle and then becomes smoother indicating that the first wetting–drying cycle has the most significant impact on cohesion. Comparing the curves under different water content, it is found that when the water content is larger than 15%, the slope of the curve is obviously slower, indicating that the influence of the wetting–drying cycle on the cohesion of the loess is more intense at small water content.

The curve change law of the internal friction angle under the wetting–drying cycle is similar to the one of the cohesions. As the number of cycles increases, the internal friction angle decreases, but in general, it remains small in value compared to cohesion. when the moisture content is 5%, the internal friction angle of the undisturbed loess is reduced by only about 2.7° after 3 cycles. Unlike the cohesion curve, the response of internal friction angle to changes in water content is different. It can also be seen from Fig. 4 that in the process of increasing the water content from 5 to 20% step by step, the attenuation value of cohesion is gradually reduced, presenting the maximum attenuation value when the water content increases from 5 to 10%. Taking the undisturbed loess after 3 cycles as an example, it can be concluded from Table 3 that the water content ranges from 5 to 20%, and the cohesion reduction values are 26.7, 15, and 6.4, respectively. Instead, the attenuation value of the internal friction angle is smaller when the water content increases from 5 to 10% and for water content larger than 10% it gradually increases, The reduction values of the internal friction angle of the undisturbed loess after 3 cycles are 1.42, 2.68, and 2.47, respectively.

Analysis of structural parameter of loess under wetting–drying cycles

Structural parameter of loess

The structure of undisturbed loess can be destroyed by disturbance, loading, and water immersion. Disturbance destroys the connection between the loess particles, loading changes their spatial arrangement and connection characteristics of the particles in the soil, and water immersion causes the cement in the soil to dissolve and the connecting forces to disappear (Xie et al. 1999). In the process of triaxial shearing, the primary structure of the soil is gradually destroyed, and the secondary structure (referring to the re-arrangement of soil particles) is gradually formed. The shear resistance of the undisturbed soil sample during the shearing process mainly includes cohesion and friction, and its essence is the arrangement and connection characteristics of soil particles. The structural potential caused by the arrangement and connection characteristics of the soil particles can be released by disturbing, loading, and saturation of the undisturbed soil. Therefore, the structural changes of undisturbed loess are comprehensively reflected by analyzing the changes in shear stress of undisturbed soil, remolded soil, and saturated soil during the shearing process. Based on this and on the reference stress structural parameter (Shao et al. 2004), this paper studies the influence of wetting–drying cycles on the structure of loess. The defined structural parameter is shown in Eq. 1.

$${m}_{\sigma }=\frac{{\left({\sigma }_{1}-{\sigma }_{3}\right)}_{y}}{{\left({\sigma }_{1}-{\sigma }_{3}\right)}_{r}}\bullet \frac{{\left({\sigma }_{1}-{\sigma }_{3}\right)}_{y}}{{\left({\sigma }_{1}-{\sigma }_{3}\right)}_{s}}$$
(1)

Here, \({m}_{\sigma }\) is the structural parameter of undisturbed loess; \({\left({\sigma }_{1}-{\sigma }_{3}\right)}_{y}\) is the deviator stress of undisturbed loess under wetting–drying cycles, kPa; \({\left({\sigma }_{1}-{\sigma }_{3}\right)}_{r}\) is the deviator stress of remolded loess under wetting–drying cycles, kPa; \({\left({\sigma }_{1}-{\sigma }_{3}\right)}_{s}\) is the deviator stress of saturated loess, kPa.

It can be seen from Eq. 1 that the ratio of \({\left({\sigma }_{1}-{\sigma }_{3}\right)}_{y}\) to \({\left({\sigma }_{1}-{\sigma }_{3}\right)}_{r}\) reflects the structural change of the undisturbed loess after being disturbed. The larger the ratio, the greater the connection strength between the undisturbed soil particles; The ratio of \({\left({\sigma }_{1}-{\sigma }_{3}\right)}_{y}\) to \({\left({\sigma }_{1}-{\sigma }_{3}\right)}_{s}\) reflects the structural change of the undisturbed loess after being saturated with water. The larger the ratio, the greater the chemical bonding force between the undisturbed loess particles. Therefore, the two ratios in Formula 1 can be used to comprehensively reflect the structural changes of undisturbed loess during the wetting–drying cycles. The greater the value of \({m}_{\sigma }\), the greater the structural strength of the undisturbed loess.

Variation laws of structural parameters of loess under wetting–drying cycles

Based on the results of the triaxial tests, the structural parameter values of the loess are calculated according to Eq. 1. The results under 50 kPa are shown in Fig. 5, and ω on the figure represents the water content, ε represents the axial strain.

Fig. 5
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The relationship between structural parameter and strain at different water content (σ3 = 50 kPa)

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It can be seen in Fig. 5 that the relationship curves between the structural parameter and strain of loess have all a softening type. As the shearing process evolves, the following three stages are identified: In the first stage, the shearing has just started, and the structural parameter rapidly increases and reaches the peak value under a small strain. At this stage, as the shear strain increases, the soil particles in the soil are gradually compacted, and the loess structure appears to resist structural failure. In the second stage, as the shearing progresses, the structural parameter is reduced rapidly. This is because the loess structure plays its role in resisting loess damage, which leads to the loosening of the internal connections between the soil particles, the interference of the spatial arrangement among them, the destruction of loess structure, and the formation of secondary structure. In the third stage, as the shearing continues to the later stage, the structural parameter slightly changes. At this time, the structure of the undisturbed loess is close to remolded loess and saturated loess, the structural parameter is close to 1, and the structure of the undisturbed loess is basically completely destroyed.

In order to better analyze the change law of the structural parameter under wetting–drying cycles, the peak value of the structural parameter of loess is considered the research object. According to the results, the peak structural parameters of each curve are extracted from the relationship between structural parameters and strain. That is, the structural parameter peaks of the samples under different confining pressures, different moisture contents, and different cycles are obtained, and the results are shown in Table 5. The relationship between the number of wetting–drying cycles and the structural parameter of loess is also drawn in Fig. 6, and ω on the figure represents the water content.

Table 5 Structural parameter values of loess under different water content and confining pressure
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Fig. 6
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The relationship curve between the cycle number and the structural parameter of loess

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It can be seen in Fig. 6 that the peak values of the structural parameter of loess are significantly affected by the number of wetting–drying cycles. Under certain confining pressure and water content, the maximum values of the structural parameter tend to decrease with the increase of the number of cycles. As the number of cycles increases, the curve gradually slows down, indicating that the influence of the first wetting–drying cycle on the structural parameter of loess is more intense than that of the third cycle.

The confining pressure and water content of the sample also determine the degree of influence of the wetting–drying cycles on the structural parameter. In Table 5, it can be noted that when the water content is 5% and the confining pressure is 50 kPa, the structural parameter decreases by 6.1 after one wetting–drying cycle, and decreases by 2.2 after three wetting–drying cycles. When the water content is 20% and the confining pressure is 200 kPa, the structural parameter decreases by 0.9 after one wetting–drying cycle and decreases by 0.5 after three wetting–drying cycles. It can also be seen from Fig. 6 that the change curve of the structural parameter is relatively steep when the confining pressure or the water content are both small, indicating that the wetting–drying cycle has the most significant influence on the structure for small values of these two magnitudes.

The structure of loess includes the arrangement and connection characteristics of loess soil particles. During the humidification process of the sample, due to the loose and porous characteristics of loess, water molecules penetrate into the sample through the pores of the sample and dissolve the chemical cement and soluble substances between the soil particles. Hence, the cementation between the soil particles is reduced. Large soil particles are decomposed into smaller clusters, and the dissolved substances are dispersed into the pores and soil skeletons in the soil sample to form secondary pores, leading to the destruction of the original stable spatial arrangement of the soil sample. When the sample is air-dried, water molecules migrate to the outside of the sample, and the water content decreases. At this time, the pores in the soil sample change from the original state of stable large pores to secondary small pores, causing the spatial rearrangement of the soil particles. After many wetting–drying cycles, the cement in the soil is repeatedly dissolved, forming more unstable secondary pores. This is indicated that the structural parameter of loess is significantly affected by the number of wetting–drying cycles.

The content of cement in the loess varies according to the water content. At low water content, the cement content in the soil is larger, and the spatial arrangement is relatively stable. Confining pressure can destroy the structure of loess in the consolidation stage. As the confining pressure increases, the damage to the loess structure becomes more severe. Therefore, the structure of loess is stronger for small water content and confining pressure.

Analysis of loess microstructure under wetting–drying cycles

Scanning electron microscopy (SEM) is used to study the changes of loess microstructure under the wetting–drying cycles. The sample adopts the same undisturbed soil sample as the above-mentioned triaxial test, and the undisturbed soil sample after 0, 1, and 3 wetting–drying cycles are selected accordingly. Figure 7 shows the scanning electron micrographs of the samples under different wetting–drying cycles, and the magnification of the photos is 500 times.

Fig. 7
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Scanning electron micrograph of undisturbed loess

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It can be seen from Fig. 7 that the loess particles with 0 cycle are closely arranged, and the soil skeleton particles are mostly aggregates and agglomerates, which have a honeycomb structure. The connection methods are mostly surface-surface contact and point-surface contact. The pores of the sample are relatively developed, and the pores are filled with cementing materials (powder particles, clay particles, etc.), which connect the large particles and present obvious cemented contact. With the increase of the wetting–drying cycles, it can be clearly seen that the small particulate matter that originally played the role of cementing between the particles is significantly reduced, and the dissolved substances are dispersed into the pores and soil skeletons in the soil sample to form secondary pores. It shows that the wetting–drying cycles destroy the connection between soil particles, and the spatial arrangement of soil particles undergoes irreversible changes. The final manifestation is that the loess structure is damaged and the shear strength is reduced.

The relationship between loess structural parameter and shear strength

The above analysis shows that under the influence of wetting–drying cycles, the changes in the shear strength and structural parameter of loess are very similar. Therefore, there should be a close relationship between these two characteristics of the loess. The structure of loess is affected by many factors. The undisturbed loess may have the same or similar structural parameter under different water contents, confining pressures, and numbers of wetting–drying cycles. Therefore, the undisturbed loess under different conditions is regarded as loess in different structural states. On this basis, the relationship between the structural parameter and the shear strength is determined and discussed.

The ratio of structural parameter and the ratio of shear strength indexes are proposed to explore the relationship between the structural parameter and the shear strength of loess. According to the results of the triaxial test, the ratio of the structural parameter is calculated, and the results are shown in Table 6. The structural parameter \(\left({m}_{\sigma 0}\right)\) of the soil with a water content of 5% and 0 wetting–drying cycles is denoted as the “benchmark.” For a specific value of the confining pressure, the ratio of the structural parameter is the ratio of the above-mentioned “benchmark” over the ones under different water content and the number of wetting–drying cycles. That is, the ratio of the structural parameter under the confining pressure of 50 kPa, 100 kPa, and 200 kPa under different structural conditions can be obtained. The ratio of the average structural parameter \(\left({m}_{\sigma }^{^{\prime}}\right)\) is the average value of the ratios of the structural parameter under different confining pressures for the same water content and number of wetting–drying cycles, which can relatively represent the strength of the loess structure. Similarly, the undisturbed loess shear strength indexes \(\left({c}_{0},{\varphi }_{0}\right)\) with a water content of 5% and 0 wetting–drying cycles are considered the “benchmarks.” The ratio of shear strength indexes is defined as the “benchmark” over the ones under different structural states, this ratio can relatively represent the shear strength of loess. Based on Tables 3 and 4, the ratios of cohesion and internal friction angle are calculated, and the results are shown in Table 7.

Table 6 The ratio of structural parameter of undisturbed sample.
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Table 7 The ratio of cohesion and ratio of internal friction angle under different structural states
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The relationship curve between the ratio of average structural parameter and the ratio of shear strength indexes are plotted in Fig. 8.

Fig. 8
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The relationship between the ratio of average structural parameter and the ratio of shear strength indexes

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By definition, the larger the ratio of the loess structural parameter is, the smaller the structural parameter of the undisturbed loess. Similarly, the larger the ratio of shear strength indexes, the smaller the cohesion and internal friction angle of the undisturbed loess and thus the smaller the shear strength. In Fig. 8 it can be noted that there is a linear correlation between the shear strength indexes c, φ, and the structural parameter, that is, the larger the structural parameter of the undisturbed loess, the larger the corresponding c and φ values and consequently the shear strength value. Hence, as the structural parameter of undisturbed loess increases, the structure of the undisturbed loess becomes stronger to resist external deformation. The linear fitting can be performed to obtain the following relationships:

$$\frac{{c}_{0}}{c}={1.4188m}_{\sigma }^{^{\prime}}-0.5551$$
(2)
$${\varphi }_{0}/\varphi ={0.3183m}_{\sigma }^{^{\prime}}-0.6304$$
(3)

where \({m}_{\sigma }^{^{\prime}}\) is the average value of \({m}_{\sigma 0}/{m}_{\sigma }\), and \({c}_{0}\) \({\varphi }_{0}\), and \({m}_{\sigma 0}\) can all be regarded as certain values. The correlation of the above semi-empirical formulae is satisfactory, as shown in Fig. 8.

Conclusions

In view of the changes in the structure of loess under wetting–drying cycles, the structural parameter is introduced to characterize the strength of the loess structure after the wetting–drying cycles. This structural parameter has a good linear correlation with the shear strength and has good adaptability to reflect the changes of the loess structure. The main conclusions are as follows:

(1) During the wetting–drying cycles, the shear strength and structural parameter of the loess samples have a significant decreasing trend. Among them, compared with the third cycle, the decreasing trend is faster during the first wetting–drying cycles. Although the third wetting–drying cycle has not reached stability, it can also be seen that as the number of wetting–drying cycles increases, its decreasing trend becomes slower.

(2) During the wetting–drying cycles, the water content and confining pressure of the loess sample affect the degree of the wetting–drying cycles on the structural parameter. When the water content and the confining pressure have a small value, the structural parameter of the loess is degraded more intensely by the wetting–drying cycles.

(3) The wetting–drying cycle eventually decreases the strength and damages the structure of the undisturbed loess. The strength of the undisturbed loess gradually approaches the remolded loess under the repeated wetting–drying cycles. In order to have a more comprehensive and in-depth understanding of the changes in the structure of loess under the wetting–drying cycles, it is necessary to study the structure change by using both quantitative parameters and microscopic methods.