Keywords

1 Introduction

Immersed tunnels have been widely used as river-crossing channels for urban public transportation in major cities in China. However, the immersed tube tunnels are usually buried in soft grounds, which do not meet the requirements of foundation bearing capacity or settlement of the submerged tunnels. One of the solutions is to use a composite foundation, such as by applying deep mixing piles or jet grouting piles. Even so, fatigue damages and uneven settlements of the immersed tunnel are commonly seen owing to the long-term effects of traffic loadings, which significantly affect the waterproofing at the tunnel joints. Therefore, it is crucial to investigate the fatigue damage characteristics of cement-stabilized soils under such circumstances.

At present, a number of studies have been carried out on the fatigue damage characteristics of cement-stabilized soils. Jian Wenbin et al. [1] have studied the fatigue life of the cement reinforced soil using fatigue tests with asymmetric sine wave. Zhang Minxia et al. [2] have established the evolution equation for fatigue cumulative damage of cement soil based on uniaxial compression fatigue tests. Th. Tika [3] and Jiang Guolong et al. [4] have established the regression equation for the relationship between the tensile strength of cementitious soil and the frequency, amplitude and accumulated vibration times using cyclic loading tests. Chen and Tong [5] have analyzed the fatigue damage characteristics and fatigue life of the basalt fiber-cemented soil using uniaxial compression fatigue tests. Guo et al. [6] have studied the effect of freeze-thaw cycles on the fatigue resistance of cemented soil with and without fibers by performing unconfined fatigue tests. Zhao et al. [7] have analyzed the evolution rules of the compressive strength of cemented soil with freeze-thaw time, fatigue time, and loading amplitude through unconfined compression tests. Zhang zhen, Qinyong Ma, et al. [8,9,10] have analyzed the influences of confining pressure, static deviator stress, and replacement rate on the cumulative plastic strain of the cemented soil unit of a composite pile by conducting large-scale dynamic triaxial tests.

In conclusion, the majority of previous research on the fatigue damage properties of cement-stabilized soil was based on the results of unconfined uniaxial cyclic loading tests; little research was published using data from dynamic triaxial tests. Furthermore, the majority of previous studies concentrated on cemented soils for subgrades in highways, which may not be the same as those for immersed tunnel composite foundations. It is crucial to use a dynamic triaxial apparatus to expose the fatigue damage features of such cement-stabilized soil.

2 Dynamic Triaxial Fatigue Damage Tests of Cement-Stabilized Soil

2.1 Specimen Preparation

The cement-stabilized soil of the composite foundation of an immersed tunnel in the Pearl River Delta was taken as the research object. The testing material was prepared using three components: fine sand, silt, and cement. The particle size of the fine sand is not larger than 0.075 mm, and 325 ordinary Portland cement was used. The amount of silt was kept at 5% for all the tests, while the mixing ratio of cement varies from 10% to 25%, as seen in Table 1. A constant water-cement ratio of 0.5 was used when mixing the sample material. The specimen is cylindrical in shape, with a diameter of 39.1 mm and a height of 80 mm. The standard curing procedure was adopted for all the specimens.

Table 1. Mechanical and physical properties of the cement-stabilized soil
Full size table

2.2 Fatigue Damage Tests

The fatigue damage tests of cement-reinforced soil were carried out using a dynamic triaxial test system with an electro-hydraulic servo. A dynamic load of the asymmetric sine-wave was adopted to simulate the effect of traffic loads. In each test set, four maximum amplitudes of the dynamic stress \(\sigma_{\max }\), namely 0.85 \(f_{cm}\), 0.8 \(f_{cm}\), 0.7 \(f_{cm}\), and 0.6 \(f_{cm}\), , were adopted to consider the effect of stress level, corresponding to the stress level (S = \(\sigma_{\max }\)/\(f_{cm}\)) of 0.85, 0.8, 0.7, and 0.6, respectively (Table 2). The minimum stress amplitude was taken as 0.05 \(f_{cm}\), and the loading frequency was 2 Hz. Three repetitions were made for each test condition, i.e., there are 12 tests in each test set.

Table 2. Test configurations
Full size table
Fig. 1.
figure 1

Results of a fatigue test in CM3

Full size image

The results of a typical test in CM3 are plotted in Fig. 1, showing the evolution of strain with vibration number, and the hysteretic stress-strain curve.

In the fatigue tests, mainly two typical specimen failure modes were observed, namely the combined tension-shear failure at the specimen ends and the combined compression-shear failure in the middle. The specific failure mode mainly depends on the initial damage state inside the specimen. When the initial damage of the specimen occurs at the ends, under the action of the axial dynamic load, cracks are first seen at the ends of the specimen along the axial direction. With the increase in load cycles, the axial cracks continue to accumulate and expand, resulting in a combined axial shear and tensile failure of the specimen. When the initial damage of the specimen is not obvious or the initial damage crack exists only in the middle zone of the specimen, under the axial dynamic load, an “X” type shear crack first appears in the middle zone, where the dynamic compressive stress also concentrates. With the increase in the number of load cycles, the damage in the middle zone continues to accumulate, finally giving rise to a combined compression-shear failure in the middle zone.

3 Analysis of the Fatigue Characteristics

Using the test results under different stress levels, the fatigue life (N) - stress level (S) relationship can be obtained for each test set, some of which are shown in Fig. 2. A certain dispersion can also be seen for some repeated test results; however, the general tendency is not affected. Overall, the lower the dynamic stress level, the longer the fatigue life. Similar S-lgN curves were obtained for cemented soil with different compressive strengths. They are fitted by a second-degree polynomial, as shown in Table 3.

Fig. 2.
figure 2

S-lgN fatigue curves of the cemented soil

Full size image
Table 3. Fitted results of the fatigue curves
Full size table

4 Analysis of Fatigue Damage Characteristics

In order to obtain the relationship between the number of load cycles and the damage parameter, according to the results of initial ultrasonic sound velocity tests, specimens with similar wave velocity were selected to perform acoustic damage tests. Based on the damage theory of elastic body, the damage parameter D can be calculated using measured elastic wave velocity as follows:

$$ D = 1 - \frac{{\hat{E}}}{E_0 } = 1 - \frac{{\hat{v}^2 }}{v_0^2 } $$
(1)

Where \(E_0\) and \(\hat{E}\) respectively represent the elastic modulus of the specimen before and after the damage, \(v_0^{\,}\) and \(\hat{v}\) respectively represent the elastic wave velocity before and after the damage. According to Miner's linear fatigue cumulative damage theory, if the fatigue life of the material under a cyclic load with a stress level of \(S_i\) is \(N_{fi}\), then the material damage caused by a load cycle is 1/\(N_{fi}\).

For a multi-stage fatigue test with varying stress amplitude, the cumulative damage of the material can be calculated as follows:

$$ D = D_1 + D_2 + ... + D_n = \sum_{n = i} {D_i } = \frac{n_1 }{{N_{f1} }} + \frac{n_2 }{{N_{f2} }} + ... + \frac{n_i }{{N_{fi} }} = \sum_{n = i} {\frac{n_i }{{N_{fi} }}} $$
(2)

where \(D_i\) represents the part of cumulative damage when the loading stress level is \(S_i\); \(n_i\) represents the cumulative vibration number under the stress level of \(S_i\), \(N_{fi}\) is the ultimate cumulative vibration number when the stress level is kept constant at \(S_i\).

Fig. 3.
figure 3

Damage evolution curves of cemented soil with different compressive strengths

Full size image

Applying the above definition of cumulative damage parameter D, the relationship of \(D - N/N_f\) is obtained as shown in Fig. 3, where N is the cumulative vibration number. A similar dynamic cumulative damage process can be seen for the cement-stabilized soil with different compressive strengths. When N is low, the cumulative damage parameter D of the specimen increases with N due to the influence of initial damage. Afterwards, a relatively stable stage is reached, where D remains almost unchanged. As N increases further to exceed a critical value, due to the continuous expansion of the initial damage and the generation and development of new cracks, the cumulative damage parameter accelerates significantly with N, resulting in the macro-damage of the specimen and the ultimate life of Nf. At the same dynamic stress level, the cumulative ultimate vibration number Nf increases linearly with the uniaxial compressive strength fcm.

5 Conclusions

  1. (1)

    Under the long-term action of traffic loads, the cement-stabilized soil of the composite foundation for immersed tunnels has shown evident fatigue damage characteristics. Mainly, two typical modes of fatigue damage were observed: the combined tension-shear failure at the specimen ends and the combined compression-shear failure in the middle zone, depending on the initial damage location and damage degree of the cement-stabilized soil.

  2. (2)

    A similar relationship between the cumulative damage parameter and the cumulative vibration number was obtained for cement-stabilized soil with different compressive strengths. It is characterized into three stages: when the cumulative vibration number N is low, the damage parameter D increases with N, which is followed by a relatively stable stage where D remains almost unchanged; at last, when N exceeds a certain critical value, the growth rate of damage parameter D accelerates significantly and eventually leads to the macroscopic failure.