Introduction

In the past few years, petroleum shortages have become an acute problem all over the world, prompting rapid developments in the petroleum storage industry. Among different kinds of petroleum depots, the underground water-sealed depot has become a favorable choice due to its huge volume and high safety level (Xue et al. 2015). Thanks to their high hydraulic conductivity, deep strata consisting of sandstone are always regarded as ideal project sites. In China, three underground water-sealed storage depots are under construction in Huangdao, Jinzhou, and Zhanjiang. Meanwhile, a number of technical problems still remain to be explored. Among them, a key issue concerns the long-term influences of water and petroleum on the stability of the surrounding sandstone in underground water-sealed storage depots. A large amount of discontinuous structures including flaws, faults and weak intercalated layers are present in natural rock masses, which have a momentous effect on the fracturing behavior and strength of the rock masses (Yang et al. 2008; Park and Bobet 2009; Janeiro and Einstein 2010; Li et al. 2005; Wong and Chao 1998). Therefore, it is highly warranted to investigate the fracture mechanism of sandstone containing pre-existing flaws soaked in water or petroleum. Failures of rock masses are generally caused by the initiation and propagation of micro-cracks. A better understanding of the relationships between failure characteristics, crack propagation features and the forms of pre-existing flaws may provide some practical guidelines for choosing and improving underground petroleum storage depot sites.

Numerous relevant explorations have been conducted previously. Wong and Chau (1998) studied rocklike materials that contain pre-existing flaws under uniaxial compression. They summarized three main modes of crack propagation and coalescence patterns from the experimental results. Vasarhelyi and Bobet (2000) built a model of a gypsum specimen with two pre-existing flaws under uniaxial compression. They simulated the process of crack initiation, propagation and coalescence based on displacement discontinuity theory. Subsequently, Sagong and Bobet (2002) explored crack coalescence types and propagation patterns of pre-cracked gypsum specimens for a number of the pre-existing flaws. Afterwards, with the purpose of investigating the influence of flaw geometry on strength and failure modes of pre-cracked brittle marble, Yang et al. (2009) conducted a series of uniaxial compression tests on cylindrical specimens. Wong and Einstein (2009) illustrated the influence of two artificial flaws of different flaw angles and geometrical sizes on the failure process of artificially molded gypsum and Carrara marble specimens. However, most of these investigations only considered the effects of rock type and flaw geometry on the failure mechanism, while ignoring some occurrence factors in practical engineering.

In recent years, improvements of experimental conditions and numerical analysis methods have enabled researchers to consider various influencing factors on the failure characteristics of pre-cracked rock material (Zhang and Wong 2013). Feng et al. (2009) conducted a series of uniaxial compression tests in limestone to explore the mutual effects of two different flaws under certain chemical solutions. Jiang et al. (2014) intuitively presented the erosion of mudstone caused by water using the X-ray computerized tomographic scanning. An experimental study recently conducted by Zhou et al. (2015) examined the hydro-mechanical-chemical coupling effects on sandstone in the context of CO2 storage in aquifers.

To ensure the long term stability of the engineering of underground petroleum storage depots, it is of great importance to understand the relationships among the immersion of water or petroleum, the forms of pre-existing flaws, and the failure characteristics of the rock material. In order to gain a preliminary understanding of the effects of water and petroleum on the crack coalescence behavior in fractured rock masses, a series of uniaxial compression experiments on pre-cracked sandstone were conducted on a rock mechanics servo-controlled testing system. All the sandstone specimens had been immersed in water to become saturated and some of them had been immersed in petroleum for different durations. Uniaxial compression tests were conducted to study the influence of petroleum on the strength of intact saturated specimens, as well as fracturing and failure pattern in pre-cracked specimens. Three groups of tests were conducted. Group 1 (G1) studied the influence of petroleum on failure patterns of pre-cracked specimens. Group 2 (G2) studied the crack propagation in specimens containing flaws arranged in different geometries. Group 3 (G3) studied the strength variations of intact specimens that had been immersed in petroleum for different durations.

Experiments

Materials

In this research, the tested sandstone was sampled in Chongqing, China. The rock is a kind of medium-grained heterogeneous material with an average density of 2000 kg/m3. Its average porosity ranges from 32% to 37%. Details of the petroleum in which the specimens were immersed are shown in Table 1.

Table 1 Key chemical and physical properties of the petroleum used in the experiment
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Experimental scheme

Rectangular prismatic specimens of sandstone in the dimensions of 80 mm × 150 mm × 17 mm were cut from a big intact rock block. All specimens had a height-to-width ratio of about 2.0. The sandstone specimens were divided into three groups. All of them were immersed in water for 48 h in advance to be totally saturated, simulating natural environmental conditions. Some of the specimens were pre-cracked with four 2 cm long flaws. The flaws were first created by an electric drill, which were then lengthened mechanically by a steel wire saw.

The first group of specimens (G1) consisted of two sub-groups with the same flaw geometries. The flaws were arranged in “rectangular” style as shown in Fig. 1a. The flaw angle α is 45°. One sub-group had been immersed in petroleum for 48 h, while the other sub-group had been immersed in water as described above.

Fig. 1
figure 1

Specimen dimensions and flaw geometry. (a) flaws in rectangular arrangement, (b) flaws in diamond arrangement. α is the flaw angle. 2 l is the flaw length, a and b are the distance of the flaws. In rectangular flaw arrangement style, α = 30°, 45°, 60° respectively in different sub-groups of G2. In diamond flaw arrangement style, α = 45°. All of the flaws are of the same size

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In the second group (G2), different flaw angles (α = 30°, 45°, 60°) and flaw arrangement styles (“rectangular” vs “diamond”) were tested as shown in Fig. 1 a and b, respectively. All specimens had been immersed in petroleum for the same duration of 48 h before the loading test. The distribution of the flaws and the failure patterns of petroleum-immersed specimens are listed in Table 3. The other geometrical parameters are also shown below each sketch.

The third group (G3) consisted of three sub-groups of intact specimens. There were six specimens in each sub-group, which were immersed in petroleum for 1 h, 8 h and 16 h, respectively.

Loading procedure

All of the uniaxial compression tests were conducted by an INSTRON1342 servo control testing machine. Axial stress was imposed on the surface of the sandstone specimen under displacement-controlled conditions until failure. The specimens were loaded under uniaxial compression in a displacement controlled manner and the displacement rate was set to 0.1 mm/min when the loading force was less than 20 kN. It was then adjusted to 0.05 mm/min until failure of the specimen. The entire loading process was recorded continuously by a camcorder. The high speed dynamic analysis system (HG-100 K) could be triggered at any time to capture the abrupt cracking events, such as crack initiation, coalescence or the formation of a shear rupture.

Results and discussion

Influence of petroleum on the failure patterns of saturated sandstone with flaws

Figure 2 shows the failure patterns of the two sub-groups of G1, namely petroleum-immersed specimens and non-petroleum-immersed specimens under uniaxial compression. Details of the crack evolution of the two sub-groups specimens are shown in sketches of Table 2. For the non-petroleum-immersed specimen, two tensile cracks initiated from Tips A and H, which then propagated quasi-coplanar with Flaws 1 and 3 for a short distance. They then curved towards the top and bottom edges of the specimen, respectively. Meanwhile, two cracks initiated from Tips B and G extended to the center of the specimen. As the axial stress increased, a secondary crack also initiated. Note that as Cracks 1b and 3b propagated towards the edges of the specimen, coalescence between Cracks 1a and 3a occurred abruptly, which was accompanied by a loud cracking sound, and a shearing fracture resulted (see Fig. 2a).

Fig. 2
figure 2

Failure patterns of pre-cracked saturated sandstone specimens in G1, (a) petroleum-immersed specimen, (b) non-petroleum-immersed specimen

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Table 2 Crack evolution in G1specimens, (a) non-petroleum-immersed specimen and (b) petroleum-immersed specimen
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For the petroleum-immersed specimen (see Fig. 2b), the crack evolution style is remarkably different. Specifically, cracks initiated from all tips and tended to propagate towards the vertical loading direction. Secondary cracks later developed at Tips A, H, and D. Subsequently, coalescences occurred between Flaws 1 and 2, as well as between Flaws 3 and 4. Another tensile Crack c initiated when the cracks initiated earlier from Tips F and H coalesced. At the end, splitting failure occurred when Cracks 1b, 2b, 3b and c propagated towards the edges of the specimen.

The explanation for the failure patterns of the two specimens can be stated as follows. Generally speaking, the weakening mechanism of sandstone can be divided into three stages for water saturated pre-cracked sandstone specimens (Jiang et al. 2014). To begin with, the cohesion force and surface energy among the sandstone particles decreases under the influence of water. The inherent discontinuities, including pores and micro-cracks inside the sandstone material, provide the initial pathways for water invasion at the tips of the flaws under uniaxial compression (Irwin 1957). A partial volume increase then occurs due to the effect of incursive water in the inter-particle pore space. Finally, the initiation of new cracks is driven by the adverse swelling area. Imagine that the water and oil pressures among the cracks in the specimen are P w andP o . In accordance with maximum circumferential stress theory (Sih 1973) and the extension rule of mixed mode cracks in the rock mass proposed by Tang (2002), the stress intensity factors of types I and II for mixed mode cracks under external force can be expressed as Eq. 1 (Tang 2003).

$$ {K}_I \sin \theta +{K}_{I I}\left(3 \cos \theta -1\right)=0 $$
(1)

Where θ is the intersection angle between the micro-crack propagation path and the extending line of the pre-existing flaw. As shown in Fig. 3a, considering the effect of water pressureP w , the relationship among the effective normal stress σ n on the flaw face, the principal stress σ v and the flaw angle α can be expressed by Eq. 2.

$$ {\sigma}_n={\sigma}_v{ \cos}^2\alpha +{P}_w $$
(2)
Fig. 3
figure 3

Stress distribution around the flaws, where σ n and τ are the two stress components of the principal stress σ v , α is the flaw angle, “S” stands for shear failure, 휎 T is the transverse compressive stress at the tip of the flaw, and P is the seepage pressure

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The corresponding stress intensity factors of Types I and II are described by Eq. 3.

$$ \left\{\begin{array}{l}{K}_I=\left({\sigma}_v{ \cos}^2\alpha +{P}_w\right)\sqrt{\pi a}\\ {}{K}_{I I}={\sigma}_v\sqrt{\pi a} \sin \alpha \cos \alpha \end{array}\right. $$
(3)

Substituting Eq. 3 into Eq. 1, we obtain Eq. 4.

$$ \frac{3 \cos \theta -1}{ \sin \theta}=\frac{\sigma_v{ \cos}^2\alpha -{P}_w}{\sigma_v \sin \alpha \cos \alpha} $$
(4)

Eq. 4 reflects the relationships among the crack propagation angle θ, the pre-existing flaw dip angle αand the pore water pressure P w . When the specimen is immersed in petroleum, an extra pore petroleum pressure P o is attached, then Eqs.2 and 4 are transformed into Eqs. 5 and 6.

$$ {\sigma}_n={\sigma}_v{ \cos}^2\alpha +{P}_w+{P}_o $$
(5)
$$ \frac{3 \cos \theta -1}{ \sin \theta}=\frac{\sigma_v{ \cos}^2\alpha -{P}_w-{P}_o}{\sigma_v \sin \alpha \cos \alpha} $$
(6)

On the basis of this theory, the variation trend of the crack dip angle with the increase of the pore pressure is presented as Fig. 3b. It can be seen that the crack dip angle increases rapidly at first, then slowly, and finally stabilizes around 77°, suggesting that the propagation path tends to shift towards the direction of the maximum stress.

For the petroleum-saturated specimen, the pore pressure is further improved. Moreover, it is well known that the density of petroleum is much lower than that of water, hence a lubrication effect will be produced by the petroleum particles at the outermost layer, which impairs the frictional force gathered at the tips of the flaws, intensifying the slippage of the trajectories. As a result, splitting ruptures play a major role at the macro level. As is well known, the energy dissipation when forming a tensile crack is considerably less than that of a shear crack (Chen and Zhang 2010), so we can conclude that when pre-cracked sandstone is immersed in petroleum, failures tend to be easier to generate than in the non-petroleumcase.

Influence of petroleum on the failure pattern of sandstone with different flaw angles and arrangements

This section presents the results of tests on the G2 specimens. The final failure patterns under uniaxial compression condition are showed in Fig. 4.

Fig. 4
figure 4

Failure patterns of petroleum-immersed specimens with different flaw angles in G2, (a) α = 30°, (b) α = 45° and (c) α = 60°

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As shown in Table 3a for α = 30°, the first cracks initiated from tips of Flaw 1 and Flaw 3 and propagated along the right diagonal. The bearing capacity of the specimen decreased dramatically and then an abrupt shear failure was generated because of the coalescence of the two cracks initiated from Tips B and G.

Table 3 Coalescence patterns of pre-cracked specimens with flaws in different inclinations in G2
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The failure pattern differs markedly for α = 45°. Crack coalescences formed between the vertical pairwise tips of FH, EG, BD and AC. Meanwhile, a spalling zone developed near Tip H. Note that the final failure in this flaw configuration is mainly attributed to splitting when tensile cracks from Tips A, C and H propagated vertically to the top and bottom edges of the specimen.

As shown in Table 3c, when the flaw inclination α is 60°, a long narrow macroscopic localization band forms among the flaws in the right diagonal direction. The cracks from Tips C and F show obvious shearing properties and their trajectories are consistent with the inclination of the flaws. However, unlike the specimen in Table 3a, abrupt shear failures were not observed around the crack coalescence zone.

It should be noted that the failure patterns of petroleum-immersed specimens with different flaw angles differ from each other distinctly. From the depiction above we can conclude that the failure of specimens with flaw angle α = 60° shows shear mode, while α = 45° shows splitting mode. For α = 30°, a splitting-shearing mixed failure mode happens, suggesting that the damage of petroleum-immersed specimens with flaws in 45° are more likely to happen than the ones with flaws in 30° and 60° under uniaxial compression.

As for specimens with the same inclination (α =45°) but in a different style—rectangular (Fig.5a) and diamond (Fig.5b), respectively, the crack patterns are different. The crack pattern for the rectangular flaw arrangement has been described earlier (see Table 3b). For the flaws in the diamond arrangement (see Fig.5b), the first cracks initiated from Tips C and E of Flaws 2 and 4, respectively, and propagated towards to the vertical loading direction. Furthermore, tensile cracks initiated from Tips E and D and then coalesced by a shear crack. As a result, the nature of the coalescence changed from splitting mode to splitting-shearing mixed mode when the flaw arrangement was rectangular rather than diamond.

Fig. 5
figure 5

Failure patterns of specimens in different flaw arrangements in G2 (a) Flaws in rectangular arrangement (b) Flaws in diamond arrangement

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Correlation between duration in petroleum and the strength of intact saturated sandstone

Typical uniaxial compression stress-strain curves of the specimens in G3 are shown in Fig. 6. In accordance with Fig. 6, we can find that at the beginning of the test, there is a small period of consolidation. As time progresses, the curves show linear increases with the force to the peak point, which stands for the maximum uniaxial bearing capacity. After that, the samples begin to crack progressively, leading to the sudden loss of bearing capacity. Since the rock mass around a water-sealed petroleum storage depot is always in a water saturated condition, we hereafter mainly discuss the influence of different petroleum immersion times on saturated sandstone specimens. For each sub-group that had been immersed in petroleum for 1 h, 8 h and 16 h, the average peak stress was 76.84 MPa, 77.19 MPa and 80.48 MPa, respectively. The data indicate that when specimens have been immersed in petroleum for 8 h and 16 h, the corresponding strength increased by 0.4% and 4.4% as compared with those immersed in petroleum for 1 h.

Fig. 6
figure 6

Stress-strain curves of specimens under uniaxial compression, where the square, circle and triangle symbols stand for immersion times of 1 h, 8 h and 16 h in petroleum, respectively

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The main attribute of this phenomenon is the principle of effective stress as shown in Eq. 7, where σ is the uniaxial stress, σ ′ and μ w are stresses shared by sandstone and water particles. When the void among the sandstone particles is filled with petroleum, Eq. 7 can be transformed into Eq. 8, where μ g is the stress shared by petroleum particles. Since the adhesiveness of petroleum is much higher than that of water, petroleum molecules dispersing in the sandstone particles will share a certain amount of axial stress. Meanwhile, petroleum particles will also exert an extra counterforce to the sandstone particles, hence an extra liquid stress form under uniaxial compression (see Fig. 7).

$$ \sigma ={\sigma}^{\prime }+{\mu}_w $$
(7)
$$ \sigma ={\sigma}^{\prime }+{\mu}_w+{\mu}_g $$
(8)
Fig. 7
figure 7

Schematic diagram of the microstructure inside the petroleum-immersed sandstone specimen, where the huge irregular particles stand for sandstone, the yellow and blue particles stand for petroleum and water particles, respectively, and σ1 stands for the principle stress

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To sum up, the extent of the influence of petroleum on the strength and cracking behavior is different on intact versus pre-cracked sandstone specimens. For the intact specimens, uniaxial compressive strength increases with immersion time in petroleum. For the pre-cracked sandstone specimens, the influence of flaws appear to be dominant, and the fracturing degree of the specimens is higher due to the influence of petroleum.

An underground water-sealed petroleum storage depot is usually rimmed by an excavation damage zone. Due to the coupled cyclic loading effect of petroleum, the integrity of the rock mass around such a storage depot is impaired over time. The present preliminary experimental study provides insights on this issue.

Conclusions

With the aid of a high speed camera and a camcorder, a systematic experimental investigation was conducted to study the influence of petroleum on the cracking process and failure patterns of intact and pre-cracked saturated sandstone under uniaxial compression. On the basis of the experimental results, the following conclusions can be drawn:

The result of G1 shows that when pre-cracked saturated sandstone was immersed in petroleum, the failure pattern under uniaxial compression test changed from splitting-shearing mode to splitting mode. The result indicates that immersion in petroleum makes the failure easier to generate for pre-cracked saturated sandstone specimens. In G2, the failure mode progressed from splitting to mixed splitting-shearing when the flaw inclinations, α, were 60°, 45° and 30°, respectively, suggesting that the damage of petroleum-immersed specimens with flaws at 45° are more likely to happen than the ones with flaws at 30° and 60° under uniaxial compression. The nature of the coalescence changed from splitting mode to splitting-shearing mixed mode when the flaw arrangement changed from rectangular to diamond. In addition, comparing the uniaxial strength of specimens in G3, the immersion in petroleum appears to contribute to increase of the uniaxial strength of intact sandstone.

Although some preliminary conclusions were obtained, there are still several limitations and insufficiencies in this experimental investigation. For instance, the sizes and forms of the pre-existing flaws in the sandstone specimens were confined to certain kinds, whereas in natural circumstance, the conditions may be more complex. In addition, the scale situation is an important factor that affects the experimental results, and current research conditions were limited to small dimension problems. Furthermore, the depth or pressure of the immersion in petroleum for sandstone specimens were not taken into account, which are also important factors that affect the properties of the studied material. All these issues will be studied specifically in further investigations.