Abstract
With the increasing demand for filling engineering construction in the Loess Plateau, the engineering problems related to saturated loess caused by rainfall and irrigation are also increasingly prominent. This work studied the shear characteristics of saturated compacted loess by experiments, and qualitatively and quantitatively explained the mesomechanism of the effect of compaction degree on the shear characteristics combined with the mesopore characteristic parameters. The study shows that the stress–strain curve of saturated loess under 80 and 85% compaction degree is strain softening, it is strain weak softening under 90% compaction degree, and strain hardening under 95% compaction degree. The failure strength and pore water pressure have a good fitting linear relationship with compaction degree, and the fitting correlation coefficients are more than 0.97. Under 95% compaction degree, the pore water pressure increases with the development of axial strain, then decreases after the peak, and may appear negative. With the increase in compaction degree, the micro and small pore content of the saturated loess soil increases, the medium, large and super large pore content decreases, the proportion of pore area decreases, the pore shape becomes uniform and smooth, the complexity of pore shape decreases, the pore arrangement tends to be regular and neat, and the directionality increases. The research results can provide references for engineering design, construction, and numerical calculation of filling engineering in loess area.
1 Introduction
The remolding and compaction of natural loess has been used as a method to improve the mechanical properties of foundation in the Loess Plateau for a long time. The original special structure of the filled loess compacted manually or mechanically is changed or damaged, and the mechanical properties are different from those of the undisturbed loess [1,2]. The unsaturated undisturbed loess has high shear strength under the dry condition due to matric suction and natural cementation between soil particles [3,4,5]. The research shows that the shear strength of unsaturated loess increases with the increase in matric suction, and the increase in matric suction on the shear strength of unsaturated loess is mainly realized by improving its cohesion [6,7,8]. However, saturated loess exists in a stage with an extreme moisture, its strength and stiffness are weakened in the saturated or high moisture due to its special water rationality and strong water sensitivity, and the ability of soil to resist shear failure is reduced. The weakening of shear strength of saturated loess will cause engineering disasters such as foundation settlement deformation, slope, and retaining wall foundation instability. At the same time, loess landslides induced by rainfall and irrigation are common in the Loess Plateau, of which the most typical is Heifangtai landslide in Gansu Province. The cognition on the causes of Heifangtai landslide is basically unified to be related to the saturation of the loess layer [9,10,11].
Loess is the aeolian Quaternary sediment in arid and semiarid areas. The world’s loess covers an area of 13 million square kilometers, including about 640,000 km^{2} in China and forming the famous Loess Plateau [12]. The Loess Plateau has thick soil deposits, complex terrain and landform, fragile ecological environment, and a lot of geological disasters such as loess landslide and soil erosion. It is one of the areas with the most serious geological natural disasters and soil erosion in China and even the world [13]. As “the Belt and Road” initiative and the “transportation power” strategy have been pushed forward, the complex terrain of the Loess Plateau has seriously restricted the development space of the Loess Plateau. Filling land has become an effective way to alleviate the tension of the construction land in this area. Using loess for filling in building sites, road subgrade, airport runway, and embankment slope has become popular [14,15].
Considering the increasing demands for filling engineering construction in the Loess Plateau, saturated loess will inevitably cause engineering harm. The experimental study on the shear characteristic of saturated compacted loess can lay a theoretical foundation for clarifying the various landslide mechanism in saturated loess layers. At the same time, the research results can also provide references for the engineering design, construction and numerical calculation of filling engineering in the Loess Plateau. Therefore, it is necessary to carry out experimental research on the shear properties of saturated compacted loess.
At present, the research on the stress–strain relationship, pore water pressure, and shear strength parameters of saturated loess by means of indoor triaxial shear test shows that the stress–strain curve of saturated loess has softening type and hardening type, and the shear failure forms include shear shrinkage and shear expansion [16,17]. The pore water pressure of saturated loess develops in three stages with axial strain, namely, rapid growth stage, slow growth stage, and stable development stage, and samples deformation and failure are related to the critical pore water pressure [17,18,19]. The shear strength parameters of saturated loess are closely related to loess type, distribution area, dry density of prepared samples, and so on, and have two typical undrained shear characteristics: steady state characteristics and quasi steady state characteristics [16,17,20,21]. Combined with its shear properties, the liquefaction criteria and methods of saturated loess can be put forward, which lays a theoretical foundation for loess liquefaction landslide [22,23,24].
Simultaneously, there are many studies on the shear strength, deformation, and water holding characteristics of unsaturated compacted loess. The research on the shear strength characteristics of unsaturated compacted loess is mainly carried out by considering the influence factors such as moisture and compaction degree. It is found that the shear strength parameters of compacted loess increase with the increase in the compaction degree and decrease with the increase in moisture, and the influence of moisture on the shear strength is greater than compaction degree [25,26,27]. The deformation characteristics of unsaturated loess are related to the settlement of filling engineering. Ma et al. [14], Hu et al. [28], and Jia et al. [29] established the expression model between the modulus and compaction degree through indoor experiments or theoretical derivation. The water holding characteristics can indirectly reflect the soil’s ability to resist damage and deformation. Wang et al. [30,31] proposed a prediction model of the water holding curve considering the effect of compaction degree. At the same time, Wang et al. [30] also clarified the relationship between the soil water characteristic curve and the micropores in combination with the analysis of the soil’s micropore characteristics.
In the above research on the shear characteristic of undisturbed or remolded saturated loess, the dry density is generally small. Although Jiang et al. [16] and Xu et al. [17] involved larger dry density in their research, the research on the relationship between the dry density (compaction degree) and shear characteristic needs to be further combined with the mesocharacteristic. At present, there are many research works on the unsaturated loess, but only few research works on saturated compacted loess. At the same time, few studies have analyzed the internal mechanism of the compaction degree affecting its shear strength in combination with the mesopore characteristics of compacted loess. Therefore, taking the saturated compacted loess as the research object and the compaction degree as the control variable, this work studied the stress–strain relationship, pore water pressure, stress path curve, shear strength parameters, and mesopore characteristics of the saturated loess under different compaction degrees based on experiments. The mesomechanism, in which the compaction degree affects the shear strength of saturated loess was discussed and interpreted.
2 Samples preparation and test methods
2.1 Samples preparation
The soil used for samples preparation is taken from the Linxia, Gansu Province. The loess in this area belongs to typical Q _{3} loess. The properties of loess samples are measured in the laboratory according to ⟪Standard for geotechnical testing method⟫ (GB/T 501232019) [32]. The soil physical properties are shown in Table 1, the particle size distribution of natural undisturbed loess is shown in Figure 1.
Parameter  Value 

Maximum density  1.74 g/cm^{3} 
Optimum moisture  17.2% 
Specific gravity  2.65 
Plastic limit  19.4% 
Liquid limit  28.6% 
Plastic index  9.2 
Samples preparation is to crush the undisturbed soil, pass through a 2 mm sieve after natural air drying, then configure 5% initial moisture, and finally control the error of moisture within 1% [32,33]. Seal the prepared soil with plastic freshkeeping bag for 24 h. After the moisture of the soil sample is uniform, the sample is prepared by applying static pressure at both ends of the jack to ensure that the density of the prepared sample is relatively uniform. The compaction degree of the samples is controlled to be 80, 85, 90, and 95%, respectively according to k = ρ _{d}/ρ _{d max}. The size of the prepared samples is the cylinder with a height of 100 mm and diameter of 50 mm, as shown in Figure 2(a).
Considering that the dry density (1.65 g/cm^{3}) of the sample prepared with 95% compaction is high, the sample is saturated by vacuum saturation to achieve better saturation effect, the saturated samples are shown in Figure 2(b). Vacuumizing saturation is to put the prepared samples into the saturator, then place saturator in a clean and anhydrous sealing cylinder, and vacuumize the sealing cylinder with an air pump to make the air pressure in the sealing cylinder lower than the negative atmospheric pressure. Refer to ⟪Standard for geotechnical testing method⟫ (GB/T 501232019) [32], the vacuumizing time is controlled to 4 h. After the completion of vacuum pumping, slowly inject distilled water into the vacuum pumping cylinder until the water completely submerges the saturator, and keep the vacuum stable. In this process, the sample shall remain stationary in the water for no less than 10 h. Because this work studied the mesopore characteristics of saturated compacted loess, one group of parallel samples is prepared. After saturation, the mass of the sample is weighed and its saturation is calculated. It is found that the saturation degree of the five groups of samples is more than 98%.
2.2 Test methods
The triaxial shear test is completed by WF12440 dynamic triaxial hollow cylinder torsional shear test system, as shown in Figure 2(c). The main technical parameters of this apparatus are: the maximum axial load is 20 kPa, the maximum pressure of triaxial pressure chamber is 3Mpa, axial load and deformation are divided into three levels: 20, 50, and 100%. The load and deformation accuracy are ±1% and the pore pressure accuracy is ±2%.
Considering the different depth of filling, the confining pressure is set as 80, 140, and 200 kPa, respectively. Because the failure of saturated soil is closely related to pore water pressure, consolidated undrained (CU) shear is selected and the shear rate is 0.24 mm/min. Considering the test research objectives and the maximum strain range of the test apparatus, the test shall be stopped when the axial strain reaches ε _{a} = 16%. In the test, if the stress–strain curve has a peak value, the peak value of the deviator stress is taken as the failure point. If there is no peak, the deviator stress at 15% axial strain is taken as the failure point [34].
Before the Scanning electron microscope (SEM) analysis, the saturated compacted loess samples were freezedried, as shown in Figure 3(a). The freezedrying procedure is as follows: (1) prefreezing the instrument for 2 h at a prefreezing temperature of −60°C; (2) the freezing temperature shall not be higher than −40°C, and the freezing time shall be 4 h; (3) After 4 h, turn off freezing and dry for 72 h. After the sample temperature is constant, select the fresh section at the cross section in the middle of the sample, and prepare the sample into a 2 mm thick square sheet, as shown in Figure 3(b). Then, the sample is fixed on the sample holder with conductive adhesive and gold is sprayed on its surface. KYKY2800B SEM was used to take images with magnification of 500 times. The main technical parameters of this apparatus are: resolution is 4.5 nm (tungsten wire cathode), the range of magnification is 15–250,000×, and the acceleration voltage is 0.1–30 kV. In order to ensure that the microstructure images have sufficient information and accuracy of extracted data, 5–8 images are taken in each group [35,36].
The soil mesostructure parameters were obtained by the particles (pores) and crack analysis system developed by Liu Chun of Nanjing University [37]. First, the obtained SEM image is binarized as shown in Figure 3(c). The photos threshold value in the binarization process is a value that can correctly reflect the pore particle profile of the SEM photos. The range of the photos threshold value in this work is 50–60. Second, the SEM image after binarization is vectorized, as shown in Figure 3(d). In the Figure 3(d), the black area represents particles and other color areas represent pores. In this study, the basic mesocharacteristic parameters of loess under different compaction degrees, such as pore distribution content, average pore area, probability entropy, and form factor, are extracted to analyze the mesomechanism of compaction degree affecting the shear strength of loess.
3 Results
3.1 CU test
3.1.1 Stress–strain curve
The ratio (σ _{1} − σ _{3})/(σ _{1} − σ _{3})_{max} is defined as the deviator stress ratio to better analyze the type of stress–strain curves of the saturated compacted loess. According to Figure 4, under different compaction degrees, the stress–strain curves of saturated compacted loess can be divided into strain softening type, strain weak softening type, and strain hardening type. At 80 and 85% compaction degrees, the deviator stress ratio of saturated compacted loess decreased significantly after the peak value of 1.0, the stress–strain curve belongs to strain softening type. When the compaction degree is 90%, the soil deviator stress ratio shows a slight downward trend and the stress–strain curve belongs to strain weak softening type. At 95% compaction degree, the deviator stress ratio of soil increases, until the axial strain is 15%, and reaches the peak value of 1.0, the stress–strain relationship curve is strain hardening.
From Figure 4, the development of deviator stress in the shear process can be divided into two stages. (1) Rapid growth stage: when the axial strain is less than 2%, the deviator stress of saturated compacted loess increases sharply, the deviator stress then increases slowly when the axial strain is within the range of 2–4%. (2) Stable development stage: when the axial strain exceeds 4%, the deviator stress increases to the peak then decreases at 80 and 85% compaction degrees, and the deviator stress increases slowly and becomes stable at 90 and 95% compaction degrees.
Comparing deviator stress of saturated loess under different compaction degrees, the deviator stress of saturated loess increases significantly with the increase in compaction degree under the same confining pressure and strain. Combining with Figure 4, under different compaction degrees, the axial strain corresponding to the failure strength of saturated compacted loess varies greatly. Taking 200 kPa confining pressure as an example, the axial strain is within the range of 8–6% at 80 and 85% compaction degrees, 90% compaction degree is within 10% axial strain, and 95% compaction degree reaches the maximum axial strain of 15%. Under the three confining pressures, the failure strength of saturated compacted loess also shows an obvious growth with the increase in compaction degree. Taking 200 kPa confining pressure as an example, the failure strength of saturated loess under four compaction degrees is 101.9, 134.4, 171.0, and 211.3 kPa, respectively.
From the above, with the increase in the compaction degree, the type of stress–strain curve gradually changes from strain softening to strain hardening, and the corresponding axial deformation increases, that is, the ability of the sample to resist failure and deformation increases. The main reason for this phenomenon is that the high compaction degree makes the soil denser, the connection and friction between soil particles is enhanced.
From Figure 5, the failure strength and compaction degree k of saturated loess under different confining pressures can be fitted linear. The fitting correlation coefficient R ^{2} is more than 0.99.
3.1.2 Pore water pressure–strain
u/u _{max} as pore water pressure ratio. It can be seen from Figure 6 that the laws of pore water pressure u of the saturated loess with axial strain ε under the conditions of 80, 85, and 90% compaction degree are similar. The pore water pressure ratio u/u _{max} increases gradually with the increase in axial strain and reaches the peak value of 1.0, the pore water pressure u increases during the shearing, and the axial strain corresponding to the peak point is 15%. Under the condition of 95% compaction degree, the pore water pressure ratio u/u _{max} begins to decrease after reaching the peak value of 1.0, and the axial strain corresponding to the peak point is related to the confining pressure, the axial strain corresponding to peak point is 2.02, 4.32, and 11.3%, respectively, under 80, 140, and 200 kPa confining pressure. Figure 6 shows that under 95% compaction degree, the pore water pressure u slowly increases to the maximum value with the increase in axial strain and begins to decrease, especially under the confining pressure of 80 and 140 kPa, the decreasing trend of pore water pressure is more obvious, and it may attain a negative value. According to the relevant papers available at present, the variation mode of pore water pressure of saturated compacted loess under triaxial undrained shear test generally tends to be stable with the increase in axial strain to the peak, but there is also a phenomenon similar to that in this study [16,17].
In this work, repeated tests are carried out under the conditions of 95% compaction degree and confining pressure of 80 and 140 kPa, the variation law of pore water pressure is similar. Considering the dry density of sample preparation in this work, and combined with the study of Jiang et al. [16] and Xu et al. [17], it is found that under the conditions of higher dry density and lower confining pressure, the variation law of pore water pressure of compacted saturated loess is similar to that of overconsolidated clay [38]. Under the condition of low confining pressure, the pore water pressure at 95% compaction is similar to that of overconsolidated clay, mainly because the pore content in the soil at 95% compaction is low, and the moisture in the saturated soil sample is relatively small. At the initial stage of triaxial shear, the soil is further compacted, resulting in the increase in pore water pressure. With the development of shear deformation, the soil produces new pores due to dilatancy, and the redistribution of water in the soil leads to the dissipation of pore water pressure, the pore water pressure decreases. The variation law of pore water pressure under lower dry density and higher confining pressure conforms to the general variation mode.
Comparing the law of soil pore water pressure with the increase in axial strain under different compaction degrees, the pore water pressure decreases significantly with the increase in compaction degree under the same confining pressure and lager axial strain. Taking the pore water pressure of the saturated sample with axial strain of 11% under the confining pressure of 200 kPa as an example, the pore water pressure of the sample under four compaction degrees are 111.8, 91, 56, and 41 kPa, respectively.
Figure 7(a) is the relationship curves between maximum pore pressure u _{max} and compaction degree of saturated compacted loess, Figure 7(b) is the relationship curves between failure strength (σ _{1} − σ _{3})_{max} and maximum pore water pressure u _{max}. As shown in Figure 7, the maximum pore water pressure u _{max} and the compaction degree k, the failure strength (σ _{1} − σ _{3})_{max}, and the maximum pore water pressure u _{max} of saturated compacted loess all meet the linear negative correlation. The fitting correlation coefficient R ^{2} is more than 0.95.
3.1.3 Stress path and shear strength parameters
Because the deformation and strength of soil are not only related to the stress, but also related to the stress history of soil, the stress path of soil can simulate the actual stress history of soil and comprehensively reflect the influence of stress change process on soil mechanical properties. Combined with the test results, the stress path curves and stress failure principal lines of saturated loess are obtained, as shown in Figure 8. The values of p, q, p', and q' are shown in formula (1), K _{f} is the total stress failure principal line, K _{f}′ is effective stress failure principal line, ψ and ψ′ are the included angles between the total stress failure principal line and effective stress failure principal line with the abscissa, respectively, and a and a′ are the intercept of the total stress failure principal line and the effective stress failure principal line on the ordinate axis, respectively. The relationship between the marked parameters in the figure and the shear strength parameters c and φ are in agreement with equation (2) [17,38].
It can be seen from Figure 8 that under different confining pressures, the total stress path curves of saturated loess are parallel oblique straight line at an angle with the horizontal standard axis, and the compaction degree does not affect the form of total stress path, but only the value of deviator stress. The effective stress path curves of saturated loess show the phenomenon of deflection to the left due to the positive growth of pore water pressure u. Under the confining pressure of 80 and 140 kPa for 95% compaction degree, the effective stress path curves deflect to the right in form due to the negative increase in pore pressure u during shearing [16,17,38].
The total shear strength parameters c and φ, and effective shear strength parameters c′, and φ′++ of saturated loess under different compaction degrees are obtained in combination with equation (2), as shown in Figure 9. The total shear strength parameters and effective shear strength parameters of saturated compacted loess increase with the rise of compaction degree, and the increase amplitude of cohesion is greater than that of internal friction angle. The cohesion increases more significantly at 90% compaction degree, indicating that higher compaction degree plays a significant role in improving the cohesion of saturated loess. With the increase in compaction degree, the value gap between effective shear strength parameters and total shear strength parameters decreases, which is due to the gradual decrease in pore water pressure and the increase in the proportion of effective stress in total stress. The relationship between the shear strength parameters and the compaction degree of saturated loess can also be expressed linearly, and the correlation coefficients R ^{2} is more than 0.96.
3.2 SEM test
The shear characteristics of saturated loess have great differences in type of stress–strain curve, failure strength, pore water pressure, p–q curve, and shear strength parameters due to the different compaction degrees. It is found that higher compaction degree can improve the shear strength of saturated loess combined with the above analysis. The mesopore characteristics can indirectly reflect the spatial distribution of granular aggregate, in order to clarify the mesomechanism that higher compaction degree can effectively improve the shear strength of saturated loess, the SEM tests of the compaction samples were completed. As shown in Figure 10, the SEM images with magnification of 500 times are selected to qualitatively and quantitatively analyze mesopore characteristics of compacted loess.
As shown in Figure 10, the particles of the soil under the compaction are uniform, and the contact form between particles are mainly angular contact, edge contact, and surface contact, overlapping or overhead, forming pores between particles. With the increase in compaction degree, the contact between particles gradually changes from angular or edge contact to surface contact, and the number of aggregates attached to large particles increases as shown in Figure 10(b). Simultaneously, With the increase in compaction, the number of coarse particles in soil decreases, and the size of particles gradually decreases, resulting in the increase in contact area between the particles.
Due to different particle sizes and contact forms under different compaction degrees, the internal pore morphology is also different. According to the pore distributed state, it can be divided into interaggregate pores and intraaggregate pores [39,40]. Interaggregate pore is the pore between particles formed by angular or edge contact between soil particles. According to the extent to which the pore is surrounded by particles and aggregates, it is divided into “space pores” and “intergranular pores” [40,41,42]. Because space pore is formed in the form of angular or edge contact, it has large size and poor stability. The interaggregate pores are surrounded by soil particles crossing in the plane, with small size and relatively better stability [43]. “Intraaggregate pores” are formed by overlapping between the occurrence and the fine aggregate on the particles, and the size is 1–3 orders of magnitude smaller than that of intergranular pores [18,44]. From Figure 10(a), it can be seen that most of them are “space pores” under lower compaction degree. With the increase in compaction degree, the number of space pores decreases relatively, and the pore form gradually changes from “space pores” to “intergranular pores.” From Figure 10(c), it can be seen that with the increase in compaction degree, the proportion of connection pores in compacted loess decreases, that is, the connectivity of mesopores decreases gradually. At 95% compaction degree, as shown in Figure 10(d), there are basically no connection pores.
3.2.1 Pore content and facial porosity
At present, the pores of loess are mainly classified according to the size of mesopore diameter [40,45]. However, considering the irregular pore shape of soil, it is more reasonable to divide pore types according to pore area. Therefore, based on the pore area, it is divided into five types: micro pore (pore pixel area less than 50), small pore (pore pixel area 50–200), medium pore (pore pixel area 200–800), large pore (pore pixel area 800–3,200), and super large pore (pore pixel area greater than 3,200) [46].
The content of different types of pores refers to the proportion of the number of each type in the total number of pores in the SEM image. It can be expressed by formula (3), where C _{ i } is the content of various types of pores, Q _{ i } is the distribution number of various types of pores in the SEM image, Q _{ t } is the total number of pores in the SEM image, and i represents the pore type.
The average pore content of various types of saturated compacted loess is shown in Figure 11(a). It can be found that the percentage of small pores in compacted loess is the highest, and the content of small pores under each compaction degree is 62.85, 63.48, 65.82, and 66.52%, respectively. The second is medium pore, and the content of medium pore under each compaction degree is 16.76, 16.51, 16.12, and 15.67%, respectively. Then there is micro pore, and the micro pore content under each compaction degree is 8.62, 9.39, 10.28, and 12.17%, respectively. The next is large pore, and the large pore content of each degree compaction is 7.54, 6.92, 5.68, and 4.43%, respectively. The content of super large pore is the smallest, and the content under each compaction degree is 4.23, 3.7, 2.1, and 1.21%, respectively. Under each compaction degree, there is little difference in the content of medium pores, and the difference between large pores and super large pores is obvious. The increase in micro pore content is more obvious at 95% compaction degree, and the increase in small pores is more significant at 90% compaction degree.
Facial porosity is the ratio of pore area to particle area on SEM image, which can indirectly reflect the change in threedimensional void ratio [47], which can be expressed as equation (4).
where P _{p} – area of pores on SEM images; P _{s} – area of soil particles on SEM images.
From Figure 11(b), with the increase in compaction degree, the facial porosity basically shows a linear decreasing trend, the proportion of pore area in particle area in soil gradually decreases, indicating that higher compaction degree can significantly reduce the proportion of pore area in soil.
3.2.2 Pore form factor and fractal dimension
The pore form factor is the ratio of the circumference of the equal area of the pore to the actual circumference of the pore [48]. Its value can show the shape characteristics of the pore, which can be expressed as equation (5).
where S _{a} – actual perimeter of pores; C _{c} – circumference of a circle equal to the area of a pore. The error of calculating the form factor of a single pore is large and meaningless. Therefore, the average form factor is used to statistically analyze the pore shape characteristics. The larger the average form factor is, the smoother the pore shape is, the smoother the particle shape is, and the closer the spatial arrangement of particles is. The value of F is between 0 and 1. The smaller the value, the narrower the pore shape.
From Figure 12(a), the form factor of loess under each compaction degree are 0.4668, 0.4773, 0.4837, and 0.4857, respectively. The smoothness of compacted loess pores is moderate. With the increase in compaction degree, the pore form factor of saturated compacted loess shows a slowly increasing trend, indicating that with the increase in compaction degree, the pore shape tends to be smooth and the overlap between particles tends to be close.
Pore fractal dimension reflects the complexity of pore structure [49,50]. Equation (6) reflects the relationship between the equivalent area and perimeter of pores in SEM images.
where A – equivalent area of any polygon; L – equivalent perimeter of polygon; C – constant; D – pore fractal dimension. The value of D is between 1 and 2. The larger the D is, the more complex the pore structure is, and the farther the spatial morphological characteristics of pores deviate from the smooth surface [46].
From Figure 12(b), it can be seen that the pore fractal dimension of compacted loess is generally low, indicating that the complexity of pore structure of compacted loess is lower. With the increase in compaction degree, the pore fractal dimension decreases, that is, the complexity of pore structure decreases, and the degree of deviation of pore spatial morphology from smooth surface is smaller.
3.2.3 Pore probability entropy
Probability entropy is a parameter describing the overall arrangement of pores, it can be expressed in equation (7). Its value represents the arrangement characteristics of pores [51,52]. The smaller its value, the more regular the arrangement of pores, the stronger its order and orientation, and the more stable the structure.
where n – number of equal intervals of interval length α divided into 0° to 180°; m _{ i } – number of pores in the ith interval along the major axis; the value of H _{m} is 0–1. The smaller the value, the more regular the pore arrangement and the higher the order.
As shown in Figure 13, the pore probability entropy value of compacted loess is between 0.96 and 0.98, which is generally high, indicating that the arrangement regularity of pores in compacted loess is relatively weaker. However, the probability entropy decreases with the increase in compaction degree, which shows that the arrangement of soil mesopores is slightly improved in regularity, order, and orientation under condition of high compaction degree.
4 Discussion
It can be found from the analysis of CU test results that high compaction degree can improve the shear resistance of saturated loess, it is worth noting that the shear strength characteristic parameters and compaction degree can be expressed by linear fitting. From the analysis of SEM test results, it can be found that the parameters such as pore content, facial porosity, form factor, fractal dimension, and probability entropy of saturated loess under different compaction degrees also show obvious differences, and with the increase in compaction degree, each parameter develops in the direction of benefiting the soil to enhance the shear strength. In order to more intuitively analyze the relationship between the shear strength of saturated loess and the pore characteristic parameters, combined with the analysis results of CU and SEM test, this study establishes the relationship curve between the failure strength of saturated loess and the small pore content, facial porosity, form factor, fractal dimension, and probability entropy, as shown in Figure 14. The reason why the content of small pores is selected as the analysis factor is that the content of small pores is the highest, accounting for more than 60% of the total number of pores.
It can be found from Figure 14 that under the confining pressure of 140 kPa, the failure strength of saturated loess can be linearly fitted with mesopore characteristic parameters, and the highest fitting coefficient is 0.9974, the lowest is 0.8309. The failure strength of saturated loess increases with the increase in small pore content and form factor, and decreases with the increase in apparent porosity, pore fractal dimension, and probability entropy. It indicates that the change in mesopore characteristics of compacted loess is the reason for the change in its shear strength. The mesomechanism of compaction degree changing shear strength of saturated loess can be summarized in the following three aspects: (1) The pore distribution area decreases. With the increase in compaction degree, the larger pores in the soil are gradually filled by the soil particles, so that the medium, large, and super large pores gradually transition into small pores and micro pores. Combined with the facial porosity, the pore distribution area in the soil is significantly reduced under high compaction degree. (2) The pore morphology becomes regular with the increase in compaction degree. With the increase in the compaction degree, the overlapping area between soil particles gradually increases, and the pore shape formed by different overlaps also changes. From the value of form factor and fractal dimension, the pore shape becomes relatively regular, and the complexity of pore structure is also relatively reduced under high compaction degree. (3) The spatial arrangement of pores becomes better with the increase in compaction degree. The compaction is a process of rearrangement and recombination of soil particles, which also makes the spatial distribution of pores in the soil change greatly. From the value of probability entropy, the spatial arrangement of pores becomes more orderly and the directionality becomes better. These changes in micro pore characteristics effectively improve the contact connection between soil particles, enhance the adhesion and friction between particles, and thus show better shear strength.
In this study, the pore pressure of saturated loess increases and then decreases with the development of axial strain under the condition of 95% compaction degree, which is similar to the pore pressure growth mode of overconsolidated clay under low confining pressure, and which is different from the general pore pressure growth mode in the shear undrained test [23,53]. Combined with the undrained shear test of saturated loess and undisturbed Q2 loess by Jiang et al. [16] and Xu et al. [17], the saturated remolded loess has similar phenomena in the pore pressure when the dry density is 1.70 g/cm^{3} and the confining pressure is below or equal to 200 kPa. The undisturbed Q2 loess with natural density of 2.01–2.04 g/cm^{3} has similar phenomena under the confining pressure of 100 kPa. Based on the research of Jiang et al. [16] and Xu et al. [17], and considering the test conditions in this study, it can be inferred that during the undrained shear test, the pore water pressure growth mode similar to overconsolidated clay in saturated loess needs to meet the requirements of higher dry density and lower confining pressure. Further research is needed to define the specific scope of higher dry density and lower confining pressure.
This phenomenon can be explained as follows: from Figure 11(b), the proportion of soil micro pore area in soil particle area decreases under higher compaction degree, especially when the compaction degree is 95%, facial porosity is only about 12%. With the increase in compaction degree, the connectivity between soil mesopores decreases. Under the same saturation condition, the moisture of higher compaction degree soil is much lower (as shown in Figure 15). Because the CU shear is strain controlled and the soil volume remains basically unchanged during the shearing, the lateral constraint of the soil is weak under the condition of lower confining pressure. Under the same axial deformation, the lateral deformation of the soil with higher compaction degree is relatively larger. The lateral deformation caused by shear will make the soil produce new pores, resulting in the diffusion and redistribution of water in the soil, which shows the phenomenon of dissipation and reduction in pore water pressure.
In this study, the shear properties of saturated loess under different compaction degrees are discussed, and the mesomechanism of compaction improving the shear strength of loess is analyzed in combination with the mesopore characteristics of soil. However, the influence of confining pressure of triaxial shear test is not considered in the analysis of mesopore characteristics, and the selection of compaction degree can be expanded upward and downward. Therefore, further research is needed on the basis of this study.
5 Conclusion
Based on the systematic study of the shear characteristics of saturated loess under four groups of compaction degree, combined with the qualitative and quantitative analysis of its mesopore characteristics, this study explains the mesomechanism of the influence of compaction degree on the shear characteristics of saturated loess. The following conclusions are drawn:
The stress–strain relationship curves of saturated loess show different forms with the degree of compaction. It is strain softening type under 80 and 85% compaction degree, strain weak softening type under 90% compaction degree, and strain hardening under 95% compaction degree. The failure strengths and shear strength parameters increased significantly with the increase in compaction degree, and the pore water pressure decreased significantly with the increase in compaction degree. There is a good linear fitting relationship among failure strengths, shear strength parameters, maximum pore water pressure, and compaction degree, and the fitting correlation is more than 0.97.
The pore water pressure of 95% compacted saturated loess under confining pressures of 80 kPa and 140 kPa appears the phenomenon of “quasi overconsolidated clay”. That is, the pore water pressure first reaches the peak with the increase of axial strain, then decrease with the increase of axial strain, and may become a negative value. The reason for this phenomenon can be summarized as follows: saturated loess samples have higher dry density and smaller axial confining pressure in shear testing.
The mesomechanism that higher compaction degree can effectively improve the shear resistance of saturated loess are as follows: with the increase in compaction degree, the content of micro and small pores increases, the content of medium, large, and super large pores decreases, and the proportion of pore area in soil decreases significantly. The mesopore shape of soil becomes uniform and smooth, the complexity of pore shape is reduced, and the spatial arrangement of soil particles is denser. The arrangement of pores is more regular, orderly, and directional. These changes make better the shear strength of saturated loess under higher compaction degree.

Funding information: This work is supported by the grants from the Gansu science and technology program of Gansu Province (Grant No. 21JR7RA792), Basic Scientific Research Fund, Science and Technology Innovation Base of Lanzhou, Institute of Earthquake Forecasting, China Earthquake Administration (Grant No. 2017IESLZ04), the Funding of Science for Earthquake Resilience (Grant Nos. XH20057 and XH21034), and the National Natural Science Foundation of China (Grant Nos. 51778590 and 51408567). Scientific Research Fund of Institute of Engineering Mechanics, China Earthquake Administration （Grant No. 2020D17).

Conflict of interest: The authors declare that they have no conflict of interest regarding the publication of this article.
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