A Study on the Dynamic Strength and Index Model of Artificial Structural Loess

Abstract

Loess is a distinctly structured soil. Undisturbed loess is prone to geological hazards, such as liquefaction and landslides under dynamic loads. There are also problems such as the inhomogeneity, anisotropy, and disturbance of in situ sampling. An artificial structural loess is prepared to accurately display the dynamic characteristics of undisturbed loess. This study took artificial structural loess as the study object, through dynamic triaxial tests, analyzed the effects of the confining pressure (σ₃), dry density (ρ_d), and cement content (D) on its dynamic strength. Then, a dynamic strength index model of artificial structural loess was established. Our results show that the dynamic strength of artificial structural loess rises with enhanced σ₃, ρ_d, and D. The dynamic cohesion (c_d) and dynamic friction angle (φ_d) increased with the rise of ρ_d, and D. The dynamic strength of artificial structured loess is closer to that of undisturbed loess when the ρ_d is 1.60 g/cm³ and D is 2%. The R² values of the φ_d and the c_d model were 0.97 and 0.98, respectively, fitting the dynamic strength index of artificial structural loess with different D, ρ_d, and σ₃. Our study outcomes can serve as references and guides for engineering construction in loess areas.

1. Introduction

Undisturbed soil has structural properties in nature. Soil structure is defined by the size, shape, and distribution of soil particles, as well as the connections between soil particles. It affects the physical and mechanical properties of soil [1,2]. Loess is a distinctly structured soil. It has a high porosity, low density, and high soluble salt content [2,3]. It is prone to geological disasters such as landslides and liquefaction under dynamic loads [4,5,6]. This poses a serious threat to the safety of lives and property. The structural properties of loess are intrinsically manifested as having different microstructures and extrinsically manifested as different microstructures corresponding to different physico-mechanical properties. So the intrinsic microstructures and extrinsic physico-mechanical properties of loess are highly connected [7]. Some scholars have studied the relationship between the microstructure and seismic subsidence of loess [8], the relationship between its structure and strength criterion [9,10], and the anisotropic characteristics exhibited by its structure [11], achieving fruitful results. At present, research on the structural properties of loess mainly focuses on undisturbed loess. However, undisturbed loess has problems, such as inhomogeneity, anisotropy, and in situ sampling disturbance [3], which affects experimental results. In the background, experts are exploring the feasibleness and effectiveness of producing artificial structural soil [3]. Studies have shown that artificial structural soil has a more uniform structure and a higher strength [12,13]. It is clear that this is the better option for studying soil structure. For example, Rao et al. [14] used remolded loess, kaolin, and iron oxide as raw materials, and prepared a clayey silt with collapsible characteristics after multiple dry–wet cycles. Diambra et al. [15] and Yao et al. [16] added cement to remolded soil to prepare structured soil. Bharati and Chew [17] developed an artificial structured soil by “restructuring” loose marine soil, copper slag, and cement.

Loess has unique structural characteristics that make it prone to geological disasters under dynamic loads, seriously threatening the safety of lives and property [18]. Consequently, scholars explored the dynamic property of loess. There are two categories of effect factors: the initial condition of the soil and the dynamic load characteristics [19,20]. Mosallamy et al. [21] found that confining pressure and water content affected the dynamic shear modulus of loess. Chen et al. [22] thought that the dynamic shear modulus of loess increased notably with fly confining pressure after cyclic freezing–thawing. Researchers [23,24] showed that the dynamic strength of compacted loess decreased with decreasing dry density and decreasing loading frequency. Sun et al. [25] believed the stronger structural properties of undisturbed loess make its dynamic strength higher than that of remolded loess. Jiang et al. [26] studied the effects of loading frequency and amplitude on the dynamic behavior of saturated loess in Xianyang. Then the relationship between soil microstructure and dynamic elastic modulus using SEM was summarized. Wang et al. [27] obtained a complete dynamic constitutive relationship between loess. Wu et al. [28] predicted the dynamic stress–strain relationship of undisturbed loess by introducing structural parameters into the Hardin–Drnevich model. Qiao et al. [29] studied the dynamic characteristics of Haiyuan loess; the recommended model of shear wave velocity and burial depth of loess in the study area is given. Shi and Zhang [30] established a hyperbolic model to model the accumulation characteristics of the dynamic strain of loess, and the model parameters are calculated with the differential evolution method.

The above research indicates that studies on the dynamic characteristics of loess are mainly limited to undisturbed soil [31]. Further research is needed on the dynamic characteristics and models of artificial structural loess. Based on triaxial consolidation drainage shear tests, the influence of confining pressure (σ₃), dry density (ρ_d), and cement content (D) on the dynamic strength of artificial structural loess was analyzed. Artificial structural loess with a structure similar to the undisturbed loess in the sampling area was obtained according to the dynamic strength of artificial structural loess, confirming the feasibility and effectiveness of artificial soil. A dynamic strength index model applicable to artificial structural loess was established and validated. These research results have a certain guiding significance for studying the property of the structure of loess in different regions.

2. Materials and Methods

2.1. Test Materials

The loess was taken from Xi’an, China. The physical property of the loess is shown in

Table 1. Physical property of loess.

Specific Gravity Gs	Dry Density ρd (g/cm3)	Water Content w (%)	Density ρ (g/cm3)	Liquid Limit wL (%)	Plastic Limit wp (%)	Porosity Ratio e
2.71	1.52	19.41	1.62	35.78	20.54	0.97

. The artificial structural material consists of salt (NaCl, produced by China Na-tional Salt Industry Group Co., Ltd., Beijing, China) and PO52.5 cement (produced by Yangchun Cement Co., Ltd., Zhucheng, China), as shown in Figure 1. In terms of characteristics, the PO52.5 cement has a high compressive strength, an early setting time, and good plasticity.

2.2. Sample Preparation

In the test, the diameter of the specimen was 39.1 mm and the height was 80 mm. Based on the Standard for Geotechnical Test Methods (GB/T 50123-2019) [32], the speci-men was made as follows: (a) dried loess was passed through a 2 mm sieve; (b) a certain mass of loess, cement, salt, and ice particles was weighed and mixed; (c) water was added and stirred evenly; (d) the mixed soil was placed for 12 h; (e) the mixed soil was poured into the specimen maker and compacted it into 5 layers with scraping treatment between layers; and (f) the specimen was placed into a moisturizing tank to cure for 14 d. Figure 2 shows the specimen production process.

2.3. Test Methods

Based on the Standard for Geotechnical Test Methods (GB/T 50123-2019) [32], the triaxial consolidation drainage shear test was carried out on the specimen using a DYNTTS-type soil dynamic triaxial testing machine (produced by Global Digital Systems Ltd., London, UK). To analyze the dynamic strength characteristics of artificial structural loess under dynamic loads, confining pressure (σ₃), dry density (ρ_d), and cement content (D) were considered in the test. The salt content was 2% and the water content was 12.64%. Based on the Standard for Geotechnical Test Methods (GB/T 50123-2019) [32] and relevant research [3,7,23,33], the design of our experimental plan is shown in

Table 2. Experimental plan.

Cement Content D (%)	Dry Density ρd (g/cm3)	Confining Pressure σ3 (kPa)
0	1.52	100, 150, 200
1	1.20	100, 150, 200
	1.40	100, 150, 200
	1.60	100, 150, 200
2	1.20	100, 150, 200
	1.40	100, 150, 200
	1.60	100, 150, 200
4	1.20	100, 150, 200
	1.40	100, 150, 200
	1.60	100, 150, 200

. The specimens were saturated by a combination of vacuum saturation and back pressure saturation. The saturation process was ended when the pore water pressure coefficient value (B) was greater than 0.95 [19]. The specimens were consolidated under equal pressure. Consolidation was completed when the consolidation drainage was lower than 0.1 cm³ per hour. Consolidation was completed when the consolidation drainage was lower than 0.1 cm³ per hour. The test was carried out by stress-controlled loading with a frequency of 1 Hz and a sinusoidal wave. The specimens were loaded step by step [34], with 10 vibrations per step, and the number of cycles (N) was 10,000. The test was completed when the axial dynamic strain was over 5%, i.e., the specimen was damaged.

3. Results and Discussion

3.1. Analysis of the Effect of Dry Density on Dynamic Strength

The ρ_d had a significant impact on the dynamic strength of loess. Figure 3 shows the dynamic strength curves of artificial structural loess under different ρ_d. The figure shows the dynamic strength of the specimen dropped as the vibration number rose at different ρ_d. At a constant vibration number, the dynamic strength improved with the rise of ρ_d [24]. The dynamic strength at ρ_d of 1.60 g/cm³ increased by 8.24% and 14.48%, respectively, compared with a ρ_d of 1.40 g/cm³ and 1.20 g/cm³, when the D was 1% and the σ₃ was 200 kPa. The reason for the above phenomenon is that the specimen structure was relatively loose and the pores were large when the ρ_d was low. This led to a smaller coupling force between the soil particles, and the specimens could be destroyed under a lower dynamic stress. As the ρ_d grew, the number of soil particles per unit volume significantly increased. Specimens tend to become denser. The coupling force between soil particles increases, making it difficult to slip and resulting in enhanced dynamic strength characteristics of specimens [35].

3.2. Analysis of the Effect of Confining Pressure on Dynamic Strength

The effect of the σ₃ on the dynamic strength of artificial structural loess was analyzed. Figure 4 shows the dynamic strength curves of artificial structural loess under different σ₃. The figure shows that the dynamic strength rose significantly as the σ₃ improved. The dynamic strength reduced as the vibration number rose for a certain σ₃ [36,37]. The dynamic strength of artificial structural loess with the σ₃ of 200 kPa was 20.01% and 41.10% higher than that with the σ₃ of 150 kPa and 100 kPa, respectively, when the D was 1% and the ρ_d was 1.60 g/cm³. The dynamic strength of artificial structural loess with the σ₃ of 200 kPa increased by 14.34% and 24.70% compared to the σ₃ of 150 kPa and 100 kPa when the D was 4% and the ρ_d of specimens was 1.60 g/cm³. The reason for the above phenomenon is that the higher the σ₃, the tighter specimens are consolidated. The closer the soil particles, the larger the friction between them. The bonding effect of soil particles in the specimens requires more energy to be destroyed [38,39]. Therefore, the stronger the anti-vibration ability of artificial structural loess, the stronger its dynamic strength.

3.3. Analysis of the Effect of Cement Content on Dynamic Strength

The effect of the D on the dynamic strength of artificial structural loess was analyzed. Figure 5 shows the dynamic strength curves of artificial structural loess under different D. The figure shows that the higher the D, the larger the dynamic strength of artificial structural loess [40]. The higher the D, the higher the dynamic strength when σ₃ and ρ_d were continuous. The higher the required number of destructive vibrations for artificial structural loess. The dynamic strength of artificial structural loess with a D of 4% was 13.28% and 23.80% higher than that with a D of 2% and 1%, respectively, when the σ₃ was 200 kPa and the ρ_d was 1.60 g/cm³. The reason for the above phenomenon is that cement and loess undergo hydration reactions and produce hydration products that link soil particles. The soil particles are enveloped and bonded by the cement as the D increases. The pores of the specimen become progressively smaller, which increases soil cohesion. During the loading process, the capacity of the specimen to tolerate the distortion is enhanced, leading to an increase in dynamic strength and the vibration number of destruction [41]. According to the variation law of dynamic strength, a conclusion can be obtained. The dynamic strength of artificial structural loess is closer to that of undisturbed loess when the ρ_d is 1.60 g/cm³ and the D is 2%. It was found that the D had the most significant impact on the dynamic strength of artificial structural loess through one-way ANOVA analysis of the D, ρ_d, and σ_₃.

3.4. Dynamic Strength Index of Artificial Structural Loess

The dynamic strength index of soil has a dynamic cohesive force (c_d) and a dynamic friction angle (φ_d) [31]. Based on the confining pressure and dynamic strength during testing, the dynamic strength index can be calculated. The test data are listed in

Table 3. Dynamic strength index of artificial structural loess.

Cement Content D (%)	Dry Density ρd (g/cm3)	Confining Pressure σ3 (kPa)	Dynamic Shear Stress τd (kPa)	Dynamic Cohesive Force cd (kPa)	Dynamic Friction Angle φd (°)
0	1.52	100	68.21	37.79	16.92
		150	83.42
		200	98.63
1	1.20	100	48.99	21.19	15.54
		150	62.90
		200	76.81
	1.40	100	53.89	25.27	15.97
		150	68.20
		200	82.51
	1.60	100	59.30	29.75	16.46
		150	74.07
		200	88.84
2	1.20	100	56.94	28.32	15.97
		150	71.24
		200	85.56
	1.40	100	60.34	30.86	16.43
		150	75.09
		200	89.83
	1.60	100	66.13	35.79	16.88
		150	81.31
		200	96.48
4	1.20	100	65.62	36.15	16.42
		150	80.35
		200	95.09
	1.40	100	70.61	40.02	17.01
		150	85.90
		200	101.20
	1.60	100	79.31	47.11	17.85
		150	95.41
		200	111.51

. Figure 6 shows how the dynamic strength index of artificial structural loess is related to D. The values of c_d and φ_d are 37.79 kPa and 16.92°, respectively, when the ρ_d is 1.52 g/cm³. The c_d and φ_d values of artificial structural loess are closest to the undisturbed loess when ρ_d is 1.60 g/cm³ and D is 2%. As ρ_d and D increase, the c_d and φ_d of artificial structural loess rise [42]. The trend of c_d with increasing D is relatively gentle. The reason for the above phenomenon is that a large number of aluminosilicate particles adhere to the soil particles with the increase of D, causing certain bonding and friction effects. In addition, the hydration of soil and cement produces many binders, which enhance the c_d between particles [43]. These limit the displacement of soil particles and soil deformation, and share a certain amount of compressive stress. Thus, the c_d of artificial structural loess was enhanced, and the dynamic strength was increased.

4. Dynamic Strength Model of Artificial Structural Loess

4.1. Model Establishment

To study the relationship between the cement content, dry density, confining pressure, and dynamic strength mechanical indexes of artificial structural loess, the models for dynamic cohesion and dynamic internal friction angle were established. Based on the reference [44], which are respectively Formulas (1) and (2), as follows:

$$c_{\mathrm{d}}=a_{1}D+b_1{\rho }_{\mathrm{d}}-c$$

(1)

$${\phi }_{\mathrm{d}}=a_{2}D+b_2{\rho }_{\mathrm{d}}$$

(2)

where: c_d—dynamic cohesive force, kPa; a₁, a₂, b₁, b₂, and c—model parameters, 1; D—cement content, %; φ_d—dynamic friction angle, °; ρ_d—dry density, g/cm³.

4.2. Parameters Obtaining and Model Validation

Based on Table 3, Formulas (1) and (2), a dynamic strength index model for artificial structural loess was established, reflecting the relationship between D, σ₃, ρ_d, and the index of dynamic strength. To validate the model, it was fitted and analyzed under different working conditions. The fitting model for the dynamic friction angle and dynamic cohesion of artificial structural loess were quantified using Formulas (3) and (4), respectively. The data are presented in

Table 4. Comparison between predicted values and experimental values.

Number	Cement Content D (%)	Dry Density ρd(g/cm3)	Experimental Values	Predicted Values	Experimental Values	Predicted Values
			Friction Angle φd (°)	Friction Angle φd (°)	Dynamic Cohesive Force cd (kPa)	Dynamic Cohesive Force cd (kPa)
1	1	1.20	15.54	15.59	21.19	21.34
2	1	1.40	15.97	15.96	25.27	25.84
3	1	1.60	16.46	16.43	29.75	30.34
4	2	1.20	15.97	15.93	28.32	26.50
5	2	1.40	16.43	16.39	30.86	30.99
6	2	1.60	16.88	16.96	35.79	35.50
7	4	1.20	16.42	16.41	36.15	36.81
8	4	1.40	17.01	17.06	40.02	41.31
9	4	1.60	17.85	17.81	47.11	45.81

. Formulas (3) and (4) can be expressed as follows:

$$c_{\mathrm{d}}=5.1569D+22.4917{\rho }_{\mathrm{d}}-10.8033$$

(3)

$${\phi }_{\mathrm{d}}=0.3629D+2.7167{\rho }_{\mathrm{d}}$$

(4)

where: c_d—dynamic cohesive force, kPa; φ_d—dynamic internal friction angle, °; D—cement content, %; ρ_d—dry density, g/cm³.

Figure 7 shows the fitting of the dynamic strength index model of artificial structural loess under different conditions. As shown in this figure, the models all exhibit a “slope type”. The c_d and φ_d gradually increase as the rise of D and ρ_d. This is because the cement and the water in the soil are hydrolyzed which produces the gel and the agglomeration caused by the ion exchange, which makes the soil particle connection and cohesion increase [42,44]. The compactness of the specimen rises with the enhancement of ρ_d, and the interlocking effect between particles strengthens. During the shearing process, the constraint effect of adjacent particles on relative movement becomes stronger, and the internal friction angle also increases [42,44]. The fitting planes of the artificial structural loess dynamic friction angle model and dynamic cohesion model under different conditions are all planar shapes, with R² values of 0.97 and 0.98, respectively. Overall, the dynamic strength index model proposed provides a good simulation method and theoretical basis for studying the dynamic strength of artificial structural loess.

5. Conclusions

This study examined the effects of confining pressure, dry density, and cement content on the dynamic strength of artificial structural loess through dynamic triaxial tests. Based on our test results, an artificial structural loess dynamic strength index model was established. The results were the following:

• The dynamic strength of the specimen dropped as the vibration number rose at different ρ_d. The dynamic strength reduced as the vibration number rose for certain σ₃.
• The dynamic strength rose significantly as the σ₃ increased. The dynamic strength of artificial structural loess with the σ₃ of 200 kPa was 20.01% and 41.10% higher than that with the σ₃ of 150 kPa and 100 kPa, respectively, when the D was 1% and the ρ_d was 1.60 g/cm³.
• The higher the D, the larger the dynamic strength of artificial structural loess. The dynamic strength of artificial structural loess was closer to that of undisturbed loess when the ρ_d was 1.60 g/cm³ and the D was 2%.
• As ρ_d and D increased, the c_d and φ_d of artificial structural loess rose. The trend of c_d with increasing D was relatively gentle.
• A dynamic strength mechanical index model for artificial structural loess was established, which presents a “slope type”. The R² values of the artificial structural loess c_d model and φ_d model were 0.98 and 0.97, respectively. The model is suitable for the prediction of indexes of dynamic strength.
• This study mainly replicated the structural characteristics of Chang’an loess. Future research will combine numerical methods to explore its micro mechanisms in depth and will expand the study of artificial structural loess to different regions.