Keywords

1 Introduction

With the series of measures taken by Beijing to tap new sources of groundwater and to conserve existing groundwater, as well as the commissioning of the Middle Route of the South-to-North Water Diversion Project in 2014, the groundwater level in Beijing has inevitably rebounded, forming a new urban groundwater environment [1]. Regardless of the structural form of the subway tunnel, the main building material is concrete, and the safety of the subway tunnel depends largely on the mechanical properties of the lining concrete material. The deformation and failure behavior of concrete materials are essentially the result of the evolution of internal micro cracks (micro pores), and understanding the micro structure of micro cracks helps to understand macroscopic behavior. In addition to utilizing micro mechanical methods such as CT scanning and ultrasonic testing to understand the micro structure of micro cracks, historical data on seepage water pressure and flow rate can also be used to speculate to some extent on the development process of micro cracks.

The subway section is built in underground rock and soil mass, and some structures are under the action of water pressure for a long time. When the groundwater level rises, it may lead to cracking, water seepage, floating and structural corrosion of some section structures [2]. However, the subway lining generally bears the load of traffic during the operation stage, and the complex stress state and structural design only consider the mechanical properties of concrete under unidirectional stress state, which varies greatly [3]. Due to insufficient understanding of the influence of pressure water on the performance of subway concrete materials [4,5,6,7], the current subway structural design specifications do not take pressure water into consideration, and only rely on artificially increasing the design strength of the lining. This not only lacks scientific basis, but also is not conducive to reducing construction costs. At present, the mechanical property tests and theoretical research of concrete under water pressure stress need to be further explored, and it is urgent to strengthen research to further reveal the influence of seepage water pressure on the fracture process of concrete.

The deformation and failure of concrete materials are essentially the result of internal micro cracks (micro-pores) under external load. Research on micro crack structures is helpful for studying the failure behavior of concrete. Currently, there are many studies on micro crack structures using CT scanning, ultrasonic detection, and other methods [8,9,10,11,12,13]. This article reveals the development process of concrete micro cracks through the study of the process of seepage pressure loading and the flow rate in cracks.

2 Experimental Design

2.1 Experimental Method and Sample Preparation

The triaxial-seepage coupling experiments are completed on the TAW-3000 electro-hydraulic servo rock triaxial testing machine. The parameters of the testing machine are shown in the literature 1 [14], the experiment was conducted with axial loading at a strain rate of 10–4/s.

The sampling size on the standard concrete test block is ϕ 49 × 98 mm, and the time for the 4Mpa permeating water pressure to act on the concrete test piece is 48 h. After the pressure is applied, the test piece is soaked in non-pressure water for more than 6 h, and after the internal pressure gradient dissipates, the coupling test is performed (Fig. 1).

Fig. 1
A photograph of the triaxial compressive testing machine that is connected to a computer is displayed.

TAW-3000 electro-7hydraulic servo rock triaxial testing machine

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2.2 Results of the Experiment

The test results are shown in the Table 1. The failure state of the concrete specimen after the test is shown in Fig. 2.

Table 1 Experimental results under triaxial-seepage coupling conditions
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Fig. 2
A photograph of three cylindrical-shaped concrete samples after testing with surface cracks.

Failure model of concrete samples subjected to triaxial-seepage coupling conditions

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3 Analysis Method and Principle of Historical Data of Seepage Water Pressure and Flow

The impermeability of concrete is very strong, and external water can only move through the cracks that have formed inside the specimen under the action of water pressure. Assuming that the water transport process in concrete follows the law of fracture seepage, the following relationship exists between flow rate, water pressure, and crack parameters:

$$\mathop q\limits^{ \bullet } \propto \frac{{Nd^{m} }}{L}\left( {\sigma_{w}{\prime} { - }\sigma_{w} } \right)$$
(1)

q、\(\mathop q\limits^{ \bullet }\)-total water injection quantity, volume flow;

σw、\(\sigma_{w}{\prime}\)-Pore water pressure (water pressure inside the test piece), seepage water pressure (pump pressure at the end of the test piece);

L.d and N -the effective length, width, and number of dynamic hydraulic cracks;

m- Experience index (generally > 1).

The ‘effective’ crack size refers to the portion of the crack that can be in contact with water and allow water to flow through it. For example, if the width of a water-containing crack is too small for water to flow through it, then the crack width d = 0 and does not contribute to the total number of cracks N.

As crack growth inevitably increases with crack length, width, and number, it will inevitably be reflected in changes in flow rate and water pressure according to the above formula. Conversely, the crack growth can also be inferred by the flow rate and water pressure.

It should be noted that the axial equal strain rate loading method was used in this experiment, and the derivative of the cumulative water injection rate q with respect to axial strain measured in the experiment is equivalent to the flow rate in the formula. In addition, during the crack propagation process, the length L, width d, and even the number N of cracks will increase, but the rates of increase are different. The length L usually increases much faster than the width d, while the rate of increase of the number N of cracks varies at different stages of crack propagation.

4 Analysis Results of Historical Data of Seepage Water Pressure and Flow

Taking the typical test of concrete under the conditions of confining pressure of 5 Mpa and seepage pressure of 4 Mpa as an example, the change curves of relevant physical quantities are plotted in Fig. 3. As the external load increases, the length, width, and number of cracks in the concrete increase, and the amount of water pumped in also increases with the increase in the number of cracks and the expansion of cracks. However, the growth of each physical quantity exhibits the following stage characteristics as the cracks expand:

Fig. 3
A line graph plots sigma and q versus epsilon 1. The line for sigma has fluctuating decreasing trends. The line for sigma w and q has fluctuating increasing trends.

History curves of water volume and pressure (confining pressure equals to 5 MPa, Axial loading rate equals to 10–4/s)

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① Stage 1: As shown in the q-ε curve in Fig. 3, the slope (volume flow \(\mathop q\limits^{ \bullet }\)) of the curve in this stage is negative, and according to formula (1), the pore pressure σw > pump pressure \(\sigma_{w}{\prime}\). . This indicates that the axial load level at the beginning of loading is not high (the axial pressure is set to 1 kN at the beginning of the test), the Poisson effect is not obvious, and the constraint of confining pressure (5 MPa) leads to the compaction of internal pores. The pore water generates high pressure (σw > \(\sigma_{w}{\prime}\)) due to compression, and finally flows \(\sigma_{w}{\prime}\) out under the action of pressure difference. At the beginning of the pump pressure adjustment process, the water squeezed into the interior of the test piece was gradually compressed and discharged back, resulting in pump body backflow.

Further analysis of the shape of the q-ε curve during this stage reveals that the concave shape indicates a rapid \(\mathop q\limits^{ \bullet }\) decrease in flow velocity, while the water pressure \(\sigma_{w}{\prime}\) gradually decreases during this stage. According to the formula, the pore pressure σw must decrease at a faster rate. The most likely cause of the rapid decrease in σw is the increase in pore volume, indicating that the pores (microcracks) have begun to expand during this stage.

The end point of this stage is the lowest point of water injection on the q-ε curve (the point corresponding to \(\mathop q\limits^{ \bullet }\) = 0), which is also the critical point of hydraulic crack propagation. Before this point, the crack hardly propagates (mainly due to dilatancy), and after this point, the crack enters the propagation stage. Therefore, this critical point of crack propagation is close to the damage point on the stress–strain curve (the q-ε curve shown in Fig. 3).

② Stage 3: This phase \(\mathop q\limits^{ \bullet }\) rapidly rises as the deformation increases, and simultaneously \(\sigma_{w}{\prime}\) rapidly decreases (Fig. 1). According to the above formula, Ndm/L is bound to increase rapidly. Further analysis reveals that due to the fact that cracks have just initiated in this phase, the crack propagation rate should not be very high, meaning that the increase rates of L and d are not significant. As a result, the sharp increase in water injection in this phase is mainly due to the rapid increase in the number of cracks N. In other words, this phase is mainly a stage of rapid initiation of hydraulic cracks.

③ Stage 3: The starting point of this stage is the turning point of the water pressure curve from a decreasing trend to an increasing trend, which basically corresponds to the inflection point of the water injection curve. From Fig. 1, it can be seen that the q-ε curve in this stage is convex upward, with the slope gradually decreasing and tending to a stable value. At the same time, the water pressure increases rapidly, and eventually also tends to a stable value. According to the formula, \(\mathop q\limits^{ \bullet }\) rapid decrease and \(\sigma_{w}{\prime}\) rapid increase inevitably lead to a decrease in Ndm/L at a faster rate. However, in this stage, N has basically increased to its maximum value, and d will only increase and cannot decrease, so the crack length L will inevitably extend at an unprecedented speed until the test piece is completely penetrated to form a macroscopic fracture crack. When the penetrated macroscopic crack appears, L, d, and N all stop growing (in fact, the stability of d also requires a certain residual strength as a guarantee), the crack stops expanding, and the flow rate \(\mathop q\limits^{ \bullet }\) is also stable under constant pump \(\sigma_{w}{\prime}\) pressure, maintaining a stable seepage state.

5 Conclusions

In summary, through the analysis of the flow and water pressure history curves in the concrete triaxial-seepage coupling test, some information about crack propagation can be obtained qualitatively or even quantitatively (with the help of appropriate fluid–solid coupling models). If combined with stress–strain curve collaborative analysis, more information can be obtained. However, it should be noted that the crack belongs to hydraulic crack (crack in which water can seep), so the obtained results can only reflect the microcrack structure changes in the area where the flowing water touches.