Keywords

1 Introduction

Due to the high porosity, high water content, high clay content, low permeability, and rheological properties of soft soil, the strength of soft soil is related to deformation and time, exhibiting certain mechanical effects of loading rate under the action of loads [1, 2]. As early as the 1930s, Buisman [3] pointed out that the influence of loading rate cannot be ignored in the study of constitutive relationships and strength characteristics of soft soil. However, there is usually a significant difference between the loading rate in practical engineering applications and the loading rate in indoor tests. If the influence of loading rate is not considered, it may lead to instability or excessive settlement of certain saturated soft soil foundations during construction or after construction. [4, 5].

Domestic and foreign scholars have conducted a series of exploratory studies on loading rate and its impact on soil mechanical response characteristics [5,6,7,8,9,10,11,12,13]. Diaz Rodrigues et al. studied the relationship between strength and strain rate of Mexico cohesive soil, indicating that the peak value of the stress-strain curve increases with the increase of strain rate, and found the phenomenon of “strain rate softening” [6]. Cai Yu, Kong Lingwei, and others [7] confirmed the influence of soil structure on soil mechanical properties by studying the strain rate of Zhanjiang clay. Zhu Qiyin et al. conducted a systematic study on the normalization of the loading rate effect of soft soil under uniaxial and triaxial stress conditions. Graham [11] summarized 15 types of clay and found that the average increase rate of undrained shear strength is 10%; Gao Yanbin [4] used an anisotropic elastic-plastic constitutive model to calculate the strain rate parameter ρ Between 7.2% and 12.2%, while foreign test results ρ ranges from 5% to 23% [12,13,14,15,16,17,18,19,20,21], with an average of 12%. The above literature mostly studies the loading rate under certain specific conditions (certain consolidation state, stress history, and test methods); studying soil properties involves structural clay, structural loess, soft clay with general moisture content, and remolded soil; in terms of experimental methods, conventional triaxial apparatus, direct shear apparatus, and ring shear apparatus are mainly used for testing; sowever, there are still few reports on the research of true triaxial tests, and there are few research results on the strain rate of saturated soft soil [22,23,24,25,26,27]. Previous studies have shown that strain rate has an impact on the undrained strength, pre consolidation pressure, pore water pressure, yield pressure, and shear dilation (shear dilation) characteristics of soil. The strain rate effect of clay with different characteristics varies greatly. Therefore, in-depth research is still needed for soft soil in different regions.

This article takes common saturated soft soil in the Nansha area of Guangzhou as the research object, and conducts true triaxial consolidated undrained shear tests with different confining pressure and strain rates. Based on the comparison of other cohesive soils in the literature, the variation law of undrained shear strength and pore water pressure with strain rate is analyzed, aiming to provide a certain basis for the engineering characteristics of saturated soft soil and the study of elastic-plastic constitutive models of saturated soft soil.

2 Test Soil Samples and Test Plan

2.1 Test Instruments

The SPAX-2000 improved true triaxial testing instrument produced by GCTS company in the United States was used to conduct triaxial consolidated undrained shear tests on saturated soft soil. The main functions and parameters of the testing system are shown in Table 1. This experiment used the SPAX-2000 static and dynamic true triaxial tester from GCTS company in the United States. The testing system consists of six major components: pressure chamber, rigid loading actuator, SCON digital servo controller and acquisition system, confining/back pressure volume controller, advanced servo software, and variant constant pressure hydraulic source. The testing system can simulate the real triaxial stress state. This means that the stress conditions experienced by the soil sample during the experiment are closer to the actual engineering conditions. In addition, the system can provide more accurate test results, which is crucial for capturing the subtle changes in saturated soft soil under different strain rates.

Table 1. Main functions and indicators of SPAX-2000
Full size table

2.2 Test Soil Sample

Nansha District of Guangzhou City is located at the southernmost end of Guangzhou City, on the west bank of Humen Waterway of the Pearl River, where Xijiang River, Beijiang River and Dongjiang River converge. The test soil sample was taken from a soft soil foundation treatment project site in Nansha District, Guangzhou City, and was a high water content marine saturated soft soil. As Nansha is located at the mouth of the the Pearl River, due to its unique geographical environment and geological conditions, it forms a deep soft soil sedimentary layer. The burial depth of this batch of soil samples is about 6.0–8.0 m, with a soft soil porosity ratio of 1.94, a natural moisture content of 74.72%, a weight of 15.61 kN/m3, a liquid limit of 67.23%, a plastic limit of 37.98%, and a clay content of 41.0% less than 0.005mm. Sampling and wax sealing were carried out in situ according to the requirements of geotechnical tests.

2.3 Test Scheme

In this experiment, three types of confining pressures (100 kPa, 150 kPa, 300 kPa) were applied to the undisturbed saturated soft soil samples; three types of intermediate principle stresses (120 kPa, 175 kPa, and 230 kPa); three types of pore water pressures (30 kPa, 60 kPa, and 90 kPa); under the same consolidation stress ratio \({\text{K}}_{\text{c}}\)= 1.28, triaxial consolidated undrained shear tests were conducted at five shear rates (10–6/s, 0.8 × 10–5/s, 10–4/s, 0.5 × 10–3/s, 10–2/s). Based on the second set of test conditions (confining pressure σ3 of 150 kPa, intermediate principle stress σ2 of 175 kPa, and axial strain of 10%), the true triaxial consolidated undrained shear tests with different strain rates were mainly conducted, supplemented by the comparison of results from other test conditions. A total of 38 specimens were subjected to CU tests to obtain the influence of strain rate on the mechanical properties of high moisture content marine saturated soft soil.

Test steps: Preparation of specimens (rectangular specimens with dimensions of 50 mm × 50 mm × 120 mm) → Vacuum saturation → Backpressure saturation (pore water pressure coefficient B ≥ 0.95) → Sample consolidation (set consolidation program by GCTS-CATS software: through isobaric consolidation and eccentric consolidation) → Conduct CU tests at the set strain rate until the soil sample reaches the set axial strain value or the specimen fails.

3 Testing Results and Analysis

3.1 Characteristics of Stress-Strain Relationship Curves Under Different Strain Rates

Due to the structural and rheological properties of saturated soft soil, there is a significant correlation between the stress-strain strength relationship of the soil and the loading rate. To study the effect of shear strain rate on the stress-strain relationship curve, the specimens were vertically sheared at the same consolidation ratio (\({\text{K}}_{\text{c}}\)= 1.28), different confining pressures (100 kPa, 150 kPa, and 200 kP), and different intermediate principle stresses (120 kPa, 175 kPa, and 230 kPa) under three consolidation pressure conditions. The stress-strain relationship curves were obtained by dividing them into different shear strain rates (10–6/s, 0.8 × 10–5/s, 10–4/s, 0.5 × 10–3/s, and 10–2/s) until the axial strain reached 10%, as shown in Figs. 1 and 2.

Fig. 1.
figure 1

Comparison curves of deviation stress - strain rate - axial strain

Full size image
Fig. 2.
figure 2

Comparison curves of deviation stress - intermediate principle stress - axial strain

Full size image

Figure 1 shows the stress-strain relationship curves of specimens under three different strain rates: the first group (σ2 = 100 kPa, σ2 = 120 kPa), the second group (σ3 = 150 kPa, σ2 = 175 kPa), and the third group (σ3 A = 200 kPa, σ2 = 230 kPa). Figure 2 shows the stress-strain relationship curves under different vertical strain rates. From the graph, it can be seen that when the strain is less than 1%, the deviatoric stress of each specimen during the CU test increases sharply, and the faster the strain rate, the faster its growth rate; when the axial strain is between 1% and 8%, the deviatoric stress still increases rapidly; when the strain is greater than 8%, there are differences in the trend of deviatoric stress changes among various soil samples, with some samples maintaining a continuous growth trend and some samples experiencing strain softening phenomenon; the peak stress increases with the increase of strain rate. The shear strength of soil increases with the increase of shear strain rate under the same confining pressure; strain softening has a strain rate effect; the faster the shear rate under the same confining pressure, the more obvious the strain softening phenomenon. The strain softening phenomenon under lower intermediate principle stress is more obvious than that under higher intermediate principle stress.

Compared with reference [7], the stress-strain relationship curve of Zhanjiang strongly structured clay (with a water content of 48.6% and sensitivity of 5–7) in conventional triaxial CU tests has two significant characteristics: (1) the phenomenon of strain rate softening in strongly structured soil is significant; (2) under the same confining pressure, the peak shear stress of CU decreases first and then increases with the increase of shear strain rate, and there is a clear critical rate turning point. Reference [10] found through conventional triaxial CU and UU tests that Dalian saturated remolded soil (with a moisture content of 29%) undergoes strain strengthening at low shear rates and strain softening at high shear rates. The soft soil in Tianjin Binhai New Area (with a water content of 50.6%) [24] has a critical shear rate under low confining pressure conditions, and the critical shear rate disappears under high confining pressure conditions. The experimental results show that the saturated soft soil in Nansha has the basic characteristics of general clay, but its strain rate effect is different from that of strong structured soil and remolded soil. Strong structured soft soil has obvious critical rate turning points [7, 8], and the strength of saturated soft soil gradually changes with shear strain rate, without any obvious critical rate turning points. The differences in strain rate effects are related to factors such as the genesis, high moisture content, low permeability, and structural characteristics of saturated soft soil [23, 26].

In summary, “strain softening” in indoor tests refers to the phenomenon where the stress of a soil sample decreases as the strain increases after reaching its peak strength; during the process of strain softening, the rate of strain growth accelerates with the increase of stress. Through the comparison of this experiment and soil properties, it is shown that there are three main reasons for the above phenomenon: (1) the hardening or softening phenomenon during the experiment depends first on the physical properties of the soil, such as the obvious softening phenomenon of saturated soft soil at a certain moisture content, internal structure, and physical state; (2) secondly, it is closely related to the stress state and test conditions of the soil sample. When the confining pressure and intermediate principle stress are small, due to small lateral constraints and large vertical deformation, the strain growth rate accelerates, the load growth rate relatively decreases, and the softening phenomenon becomes more obvious; (3) the strain softening of saturated soft soil has a strain rate effect. When the strain rate is high, due to the poor permeability of saturated soft soil, stress superposition occurs in the sample, and the softening phenomenon becomes more obvious.

3.2 The Effect of Shear Strain Rate on Undrained Strength

The undrained shear strength is an important indicator in engineering design. The method for determining the undrained strength Su of saturated soft soil in this article takes 10% axial strain when the stress-strain curve of the soil sample shows strain hardening, i.e. no peak value appears \({\upvarepsilon}_{1}\) corresponds to the difference in principal stress (\({\upsigma}_{1}\)– \({\upsigma}_{3}\)) Half of it; when the stress-strain curve shows a softening form, take half of the peak principal stress difference \({\text{q}}_{\text{k}}\).

Fig. 3.
figure 3

The peak shear stress -strain curves

Full size image

In order to quantitatively analyze the effect of strain rate on undrained shear strength, three sets of relationship curves between peak (or maximum) shear stress \({\text{q}}_{\text{k}}\) and strain rate \(\dot{\upvarepsilon}\) under test conditions were plotted in semi logarithmic coordinates, as shown in Fig. 3. It can be seen that \({\text{q}}_{\text{k}}\)– \(\dot{\upvarepsilon}\) shows a linear distribution in semi logarithmic coordinates, and the regression equations of strength strain rate under the three test conditions are (1), (2), and (3), respectively. (The three experimental conditions include: the first group (σ3 = 100 kPa, σ2 = 120 kPa), second group (σ3 = 150 kPa, σ2 = 175 kPa) and the third group (σ3 = 200 kPa, σ2 = 230 kPa)

$${\text{q}}_{\text{k}} = 3.390 {\text{ln}}\left(\dot{\upvarepsilon}\right) + 94.101$$
(1)
$${\text{q}}_{\text{k}} = 3.062{\text{ln}}\left(\dot{\upvarepsilon}\right) + 96.476$$
(2)
$${\text{q}}_{\text{k}} = 2.236{\text{ln}}\left(\dot{\upvarepsilon}\right) + 90.825$$
(3)

The slope of the regression line can reflect the rate of change of shear strength with strain rate; when the slope of the straight line is larger, the undrained shear strength increases faster with the rate. As shown in Fig. 3, the undrained shear strength of soil is a monotonic increasing function of strain rate. At the same consolidation ratio, the slope of the first group (confining pressure 120 kPa) is the highest (k = 3.390), and the strength increases the fastest with strain rate. The growth rate of strength in the three experimental groups is in the following order: the first group > the second group > the third group, indicating that the strain rate has a more significant impact on strength under low confining pressure.

The degree of influence of shear strain rate on undrained strength is represented by the strain rate parameter \({\upeta}\). When the strain rate is increased by 10 times (one order of magnitude), the growth rate of undrained shear strength [4] is defined as follows:

$${\upeta}=[\Delta{\text{S}}_{\text{u}}/{\text{S}}_{\text{u0}}]/\Delta {\text{lg}} \dot{\upvarepsilon}$$
(4)

In the formula: \({\Delta}{S}_{u}\) represents the strength increment; \({S}_{u0}\) is a reference undrained strength under the same consolidation conditions, and the sample with the smallest strain rate in each group of this test is used as the reference strength value; \(\Delta {\text{lg}}\dot{\varepsilon }\) is the axial strain rate.

To analyze the variation characteristics of shear strength with loading rate, Fodil [12] proposed an exponential strain rate equation based on Graham, and some scholars proposed a logarithmic equation [4, 7, 15]. Using the second set of experiments as an example, analyze the adaptability of exponential and logarithmic rate equations to saturated soft soil in Nansha.

Exponential rate equation:

(5)
(6)

Logarithmic rate equation:

(7)
(8)

In the formula, \({\upeta}_{\text{e1}}\) and \({\upeta}_{\text{e2}}\) are exponential rate equation parameters, \({\upeta}_{\text{L1}}\) and \({\upeta}_{\text{L2}}\) are logarithmic rate equation parameters, \({\dot{\upvarepsilon }}_{\text{i}}\) and \({\dot{\upvarepsilon }}_{{0}}\) are strain rate and strain rate of the reference sample group, respectively; \({\text{q }}_{\text{ik}}\) and \({\text{q }}_{0}\) are the peak shear stress and reference peak shear stress of a certain sample, respectively.

The occupation fitting in semi logarithmic coordinates is good, and the regression coefficients \({\text{R}}^{2}\) of the regression equation are all high. Among them, the fitting degree between the two logarithmic equations and the distance between points is slightly poor, with \({\text{R}}^{2}\) below 0.920; the regression coefficients \({\text{R}}^{2}\) of the two exponential rate equations are both greater than 0.956, indicating that the exponential equation can better reflect the characteristics of the undrained strength of saturated soft soil changing with shear strain rate, and Eq. (5) is more concise in expression. As shown in Fig. 4, when the rate parameters of saturated soft soil in Nansha are \({\upeta}_{\text{e1}}\)= 0.1305 and \({\upeta}_{\text{e2}}\)= 0.1319, and the strain rate increases by 10 times, the undrained shear strength growth rate is 13.12%.

Fig. 4.
figure 4

Comparison curves of rate formulation for undrained shear strength of saturated soft soil

Full size image

Research has shown that under the same consolidation conditions, the relative growth rate of shear strength is a monotonic increasing function of the logarithm of shear strain rate, and the smaller the intermediate principle stress, the more significant the effect of shear strain rate on shear strength. In addition, due to the structural strength of undisturbed saturated soft soil, there is a slight dispersion in the test results near the yield stress level. The magnitude of the rate parameter is closely related to the internal factors of soil formation, material composition, structure, and physical properties, as well as factors such as consolidation state, stress history, and testing methods.

3.3 The Effect of Shear Strain Rate on Pore Water Pressure

As shown in Fig. 5, the relationship curves of ultra static pore water pressure \({\text{u}}\), strain rate \(\dot{\upvarepsilon}\), and axial strain \({\upvarepsilon}_{1}\) under three consolidation conditions and different shear rates show that the strain rate has a significant impact in the initial loading stage, but has no significant impact on pore water pressure in the later stage. In the early stage of shearing, the strain rate is low (10–6/s and 0.8 × 10–5/s), and the sample has a higher rate of pore water pressure growth. The excess pore water pressure rises rapidly, and this trend gradually disappears with increasing strain; after reaching a certain axial strain (about 3% to 7%), the pore water pressure of samples with high shear rates gradually increases compared to samples with low shear rates. Under the conditions of this experiment (axial strain \({\upvarepsilon}_{1}\) ≤ 10% at the end of the experiment), the final excess pore water pressure stabilized at a certain value. In addition, the influence of intermediate principle stress on soil strength is significant, while its effect on pore water pressure is not significant.

Fig. 5.
figure 5

Comparison curve of pore pressure-axial strain

Full size image

Another noteworthy phenomenon is the fluctuation and hysteresis of pore water pressure. This is because the saturated soft soil has a flocculent structure, with particles mostly in the form of flakes or columns. Under the action of loads, the soil properties and structure are adjusted, causing the clay particles in the soil to transition from “edge-edge” contact and “edge-surface” contact to “surface-surface” contact form. The structure tends to homogenize, and the soil structure gradually transitions to reshaped soil properties. In the initial stage of applying load, the internal stress of the soil is concentrated, and the non-uniform distribution of stress causes the pore water in the sample to flow from the middle to both ends; in addition, the bonding effect of clay particles and poor vertical permeability have a certain inhibitory effect on pore water flow, and the pore water pressure measured by the pore pressure sensor at the bottom of the specimen is low, with a time lag. In addition, due to the influence of multiple factors, the variation of pore water pressure is not an increasing function of strain rate, resulting in slight fluctuations.

According to reference [7], the peak pore water pressure of Zhanjiang strongly structured clay obtained at different shear rates under low confining pressure is basically equal; under high confining pressure, the effect of shear rate on pore water pressure gradually becomes apparent. Crawford [15] found in his study on Leda clay that shear rate has a significant impact on pore water pressure, while Guy Lefebvre's study on Quebec clay found that pore water pressure is independent of shear rate during triaxial testing. The comparison results show that the properties and test conditions of cohesive soil are different, and the influence of shear rate on pore water pressure during the triaxial consolidated undrained shear test process varies greatly.

In summary, we have obtained similar conclusions as previous studies on the mechanical effects of shear strain rate in saturated soft soil through true triaxial tests, but there are also new insights. There are still significant differences in the characteristics and rate parameters of undrained shear strength of high moisture saturated soft soil with increasing shear strain rate, as well as the variation law of pore water pressure compared to soil types such as strong structured clay, remolded soil, and general low moisture clay in literature. This is related to the causes of saturated soft soil, high water content, high clay content, high liquid limit, medium sensitivity, flocculation structure, rheological properties, and true triaxial test conditions, which are different from previous research results and have certain representativeness.

4 Conclusion

  1. (1)

    Under the conditions of this experiment, the undrained shear strength of saturated soft soil in Nansha follows an exponential equation with strain rate. The exponential rate parameters \({\upeta}_{\text{e1}}\) are 0.1305 and \({\upeta}_{\text{e2}}\) are 0.1319. When the strain rate increases by 10 times, the undrained shear strength growth rate is 13.12%.

  2. (2)

    Under the same consolidation conditions, in the early stage of shear, the excess pore water pressure of samples with lower strain rates increases rapidly, and this trend gradually disappears with increasing strain; the ultra static pore water pressure is influenced by multiple factors and is not an increasing function of strain rate.

  3. (3)

    High moisture content soft soil has the basic characteristics of general clay, but it is different from strong structured clay and remolded soil. The strength of saturated soft soil gradually changes with strain rate, and there is no obvious critical rate turning point. The difference in strain rate effect is related to factors such as high moisture content, low permeability, and structural characteristics of soft soil.

  4. (4)

    The strain softening of saturated soft soil has a strain rate effect; the faster the shear rate under the same confining pressure, the more obvious the strain softening phenomenon. As the consolidation pressure increases, the influence of strain rate on the undrained shear strength of soil gradually weakens. The strain softening phenomenon under lower intermediate principle stress is more obvious than that under higher intermediate principle stress.

  5. (5)

    The conclusion of this article is suitable for saturated soft soil with similar physical properties and the same test conditions (load conditions and shear strain rate) as the soil used in this experiment. For other soils with a natural moisture content far greater than or less than 74.72%, if the moisture content of the soil sample decreases significantly after exposure to sunlight, the significant changes in soil physical properties will inevitably cause corresponding changes in the mechanical properties (shear characteristics) of the soil. Therefore, in the construction of soft soil engineering, it is necessary to reasonably control the loading rate and closely pay attention to the mechanical effects of shear strain rate to ensure the safety, stability, and economic rationality of engineering buildings.

  6. (6)

    This article investigates the mechanical response of saturated soft soil under different shear strain rates, but the limited number of samples may affect the universality of the results. Future research can further validate these findings by increasing sample size and considering saturated soft soil types in different regions.