The loess samples used in the study were Q₃ Malan loess collected from the Loess Plateau in the central-eastern part of Gansu Province (Figure 1). The samples were collected at 5 m in the Late Pleistocene strata, were undisturbed by engineering activity, showed a homogeneous distribution, and demonstrated few plant roots and wormholes.

The intact loess was cut into rectangles measuring approximately 25 cm × 25 cm× 15 cm. The samples were wrapped in many layers of cling film and shockproof film immediately after collection to preserve them without interference, with markings to indicate intact orientation. Table 1 shows the basic physical parameters of the collected loess. The particle size distribution of the intact loess is shown in Figure 2.

These tests were performed utilizing the British GDS dynamic triaxial system to investigate the dynamic characteristics of the intact loess. Using a soil chipper and a cutter, samples of intact loess were produced in a standard size of φ50 mm×h100 mm.

The seismic load, as a random vibratory load, was reduced to an equal-amplitude sine wave load with cyclic loading in the analysis of the dynamic stress-strain relationship characteristics of loess, the frequency of which was set to 1 Hz. Before shearing, the intact loess samples were consolidated in the triaxial chamber until the changes in sample total volume remained stable (Nan, et al., 2021). This experiment addressed the effect of different cyclic vibrations of dynamic load on the dynamic properties of loess based on consolidation without drainage conditions. The consolidation ratio was K _C =1.0, the cell pressure was σ ₃ =100 kPa, and the dynamic load was σ _d =45 kPa. Considering a seismic fortification intensity in Lanzhou is 8°, the corresponding cyclic vibration times of the equivalent sine wave load were 20 times, and the cyclic vibration times of the dynamic load are set to 20, 150, and 300 times (or while the axial strain ε was >5%) (Figure 3).

After dynamic triaxial tests under default cyclic times (Figure 3), samples were collected from the center of the samples and scanned using an X-ray micro-CT scanner (Xradia 520 Versa, Zeiss) at the State Key Laboratory of Continental Dynamics (Figure 4). Five triaxial samples were cut from a single large block, and the microstructure scanning samples were collected from the center of the samples. The scanning samples were cylinders approximately 4 mm in diameter. During scanning, the voltage and current were set to 50 kV and 81 μA, respectively. The scanning range was 2000 × 2000 ×2000 voxels and the resolution was 1 μm for each pixel in this study. After scanning, 2000 16-bit images in the XY plane for each sample were obtained at 1-μm spacing between adjacent images.

The serial images obtained by micro-CT scanning were imported into Avizo software (FEI Company, France) to reconstruct the 3D microstructure. First, the images were preprocessed using the non-local means filter to eliminate noise and smooth the images (Wei et al., 2019a) (Figure 5A). Then, an appropriate threshold was selected to segment the pores and particles. The blue areas are pores in Figures 5B–E. Small holes in pores often lead to excessive separation during pore segmentation. Thus, the holes were filled with the appropriate values (Wei et al., 2020). Next, a watershed algorithm was used to split the pores into a set of connected and individually numbered pore bodies (Figure 5F). The watershed algorithm assumed the color value of the image as the elevation, simulated the flooding process, and segmented the region according to the watershed lines. Figure 6 shows the segmented results of four randomly selected slices from the intact loess. Finally, the pore network model (PNM) was generated based on the separated pores. The pore structure was characterized using a ball-stick model in which the balls represented pores bodies and the sticks represented the throats between two adjacent pores (Wei et al., 2019a) (Figures 5G, H).

A cubic region of interest of 700×700×700 voxels was selected to calculate the pore microstructure parameters (Wei et al., 2019a). 3D porosity (n) was defined as the total number of pore voxels within the volume of interest divided by the total number of voxels of the volume. The equivalent radius (r _n ) was defined as the radius of a sphere with a volume equal to the pore volume. The equivalent pore-throat area (A _b ) was the radius of the thinnest contact position between two connected pore bodies. The channel length (CL) was defined as the length of the bond between two connected node centers, indicating the distance between two pore bodies. The orientation (O) was the angle between the short axis of the pore body and the horizontal plane. Pore elongation (EL) referred to the ratio of the short axis to the long axis of a pore body, ranging from 0 to 1. The smaller the value, the more elongated the pore. The coordination number (CN) was used to describe the connectivity of the pore structure, which was defined as the number of pores surrounding and connecting to one pore.

The ability of loess soil to resist deformation and damage depends on its microstructure characteristics. The pore size distribution can indicate the complex pore structure in far more detail than porosity alone, and is one of the main factors to influence the microstructure.

The average equivalent pore radius (r _n ) gradually decreased from 13 μm to 10.15 μm with increasing vibration times and decreased by 21.92% when destruction occurred. The significant variations in pore size distribution are shown in Figure 7. For intact loess (N=0), 75.1% of pores had radii of 4–16 μm (Figure 8A), while 87.1% had diameters of 8–44 μm (Figure 8B). These pores included spaced pores and some relatively large inter-particle pores (Wei et al., 2020). The peaks of pore number distribution for N=0, N=20, N=150, and N=300 were 17.1%, 17.7%, 21.1%, and 23.5% corresponding to pore equivalent radii of approximately 8 μm, 8 μm, 8 μm, and 6 μm, respectively. The larger the peak amplitude, the more concentrated the pore size distribution, indicating that the pore size distribution gradually concentrated with increasing vibration times (Figure 8A). The peaks of the pore volume distribution for N=0, N=20, N=150, and N=300 were 7.8%, 9.2%, 9.9%, and 5.2% corresponding to pore equivalent radii of approximately 22 μm, 18 μm, 12 μm, and 24 μm, respectively. From N=0 to N=150, the pore volume distribution gradually concentrated and shifted to smaller radii. However, N=300 showed the opposite trend (Figure 8B).

The differences in pore number and volume proportion among the four samples are plotted in Figures 8A, B. Overall, large pores showed decreased numbers and volumes, while small pores showed increases. The proportions of pores <14 μm increased by 13.6% and 17.9% in the samples after 150 and 300 vibration cycles, respectively. When N=20, the pore number change range was not obvious. Regarding pore volume change, the proportion of pores with radii <28 μm increased by 11.6% for N=20 and by 19.0% for N=150. However, pores with radii <28 μm decreased in volume by 32% for 300 cyclic loads.

The pore distributions and variations under cyclic loading reflect the process of loess subsidence. Spaced pores and some of the relatively large inter-particle pores decreased in number and volume and shifted to small inter-particle pores or intra-aggregate pores. However, after destruction, although the number of small pores increased, loose fracture zones were generated, resulting in an increased proportion of large pore volume (Figure 8B).

The pore throat is the thinnest part connecting two pore bodies, with the throat the channel connecting two pores. In the intact loess, the pore throat number was 8388 in the area of interest, the average pore-throat area was 132.21 μm², and the average channel length was 44.28 μm. For N=20, N=150, and N=300, the pore throat numbers were 8738, 9875, and 11,085; the average pore-throat areas were 49.06 μm², 42.11 μm², and 39.53 μm²; and the average channel lengths were 43.74 μm, 39.30 μm, and 40.26 μm, respectively (Figure 7). Figure 9 depicts the percentage distributions of pore throats for different throat areas and the difference among the four samples under different vibration times. For vibration times from 20 to 300, the number of pores with throat area >50 μm² decreased by 6%, 11%, and 13%, respectively, compared to the intact loess. Moreover, the proportion of those <50 μm² increased (Figure 9A). The number of pores with throat channel lengths >50 μm decreased by 9.6% when the loess was vibrated 20 times. When the loess was subjected to 150 and 300 cyclic vibrations, the number of pores >40 μm decreased by 13.7% and 18.0%, respectively (Figure 9B).

The results indicated that the loess structure is compressed during cyclic vibration loads and that large pores are transformed into many small pores, forming more pores and throats with smaller areas and channels. The effect was especially strong after 150 cyclic vibrations, in which the number of pores and throats was the largest, but the size was the smallest.

Variation in pore elongation can reflect the microscopic deformation characteristics of the loess structure. The average pore elongation values of the four samples were 0.50, 0.49, 0.47, and 0.45, respectively (Figure 7). More than 98% of the pores showed elongation values between 0.1 and 0.9 in intact loess. The difference among the four samples is shown in Figure 10A. The turning point of elongation variation in the samples before and after loading was about 0.45. The number of pores smaller than this value increased by 3%, 6%, and 10%, respectively, while the number of pores above this value decreased correspondingly. These results indicated that the loess structure was compressed and that the pores gradually flattened under the action of cyclic load.

Figure 10B shows the average elongation of the pores according to the radius. For pores <28 μm in the four samples, the average elongation increased gradually with increasing pore radius. For pores >28 μm, the average elongation in the N=0, N=20, and N=150 samples showed varying elongation increases; however, the curve showed no obvious linear trend. In the N=300 sample, the average elongation decreased significantly with the pore increase to >28 μm. These results indicated that the pores with a radius >28 μm are seriously deformed after being loaded and are pressed into a flat elongated shape. This result is consistent with the change in pore volume.

The average CN values were 8.18, 7.06, 5.77, and 3.66 for the N=0, N=20, N=150, and N=300 samples, respectively. CN can roughly reflect the weakening of pore connectivity in loess after loading. Figures 11A–D show the relationships between CN distributions and the equivalent pore radius of the four loess samples. With increased vibration times, the number of pores with CN >10 decreased significantly, especially when the vibration reached 300. Meanwhile, the fitting curve of CN distribution gradually deviated from the 1:1 curve, indicating that with increased vibration times, the CN of the same radius pore decreased. These findings demonstrated that although these pores were large, including those created after destruction, their connectivity was worse than that of pores of the same size in intact loess.

Regarding loess seismic subsidence, a critical challenge is associated with the transition from spaced and loosely packed to compacted and more stable structures. The Malan loess in the present study had a loose microstructure, with pores diameters of 8–44 μm predominating in the total volume at a proportion of 87.1% (Figure 8). These widely distributed spaced, inter-particle, and inter-aggregate pores are the main contributors to loess structural collapse (Lei Wang, 1987; Osipov and Sokolov, 1995). The spaced pores are formed by the stacking of particles, and their size is much larger compared to the surrounding particles (Figure 12). Clay particles <5 μm accounted for only 10% of the studied loess and acted as the main the cement, formed clay bridges and aggregates, and attached to the surface of the silt and sand (Wei et al., 2019b). These characteristics determined the weak cementation in the studied loess and the contact between particles was mainly point contact (Figure 12). The cohesion and internal friction under low water content supported the stability of the structural system, keeping the loess relatively stable in its intact state.

However, when subjected to cyclic loading, the weak cementation and direct point contact no longer function effectively and consistently. When the external load exceeds the bond yield strength, the surrounding particles will break off at weak cementation points. The exfoliated particles will fall into the pore space, forming a new rearrangement structure (Nan et al., 2021). During this process, in terms of pore volume distribution, the collapse of pores >28 μm resulted in an increased number of small-sized pores and a decreased number of large-size pores (Figures 8–10). After the structure collapse, the loess was compressed, resulting in decreased pore-throat channel length and elongation, in addition to flat pore development (Figures 8–10). Under low confining pressure, cyclic loading disintegrated the local microstructure, resulting in structural loss and the generation of large pore cracks (Figure 8). Thus, the microstructural characteristics of loess, including pore types, contact relationship, and cementation degree, are internal factors related to its resistance to external loads.

Loess soil stability challenges exist in underground engineering, slope engineering, and foundations in loess regions (Liu et al., 2018; Juang et al., 2019; Liu et al., 2020). The process of loess deformation and instability is gradual, beginning with local microstructural changes that progressively produce microcracks, which then gradually expand into through-cracks, and finally, slope sliding. Alternatively, microstructure collapse may lead to a large area of uneven settlement, resulting in the instability of the foundation and surrounding tunnel rock. The results of this study showed that multiple dynamic loads can lead to significant changes in soil pore microstructure. The change in pore structure from loose to compact occurs mainly due to microstructure collapse and rearrangement. In some filling and tunnel projects, we can pre-treat the soil in advance to produce subsidence. Regarding earthquakes, the amount of seismic subsidence will be little or even none, thus reducing the amount and speed of deformation. The microstructure evolution can be applied to numerical simulations to simulate variations in local microstructure when combining finite and discrete elements. This new method more accurately simulates soil stability.