Effect of Compaction Banding on the Hydraulic Properties of Porous Rock: Part I—Experimental Investigation

First results from compression tests under dry conditions are presented. Figure 5 shows four specimens that were tested under triaxial conditions at different confining pressures. The failure mode of the specimens indicates a transition from shear to compaction failure with increasing confining stress. The specimen in Fig. 5a was tested in uniaxial compression and failed forming a steep angle shear band. The second specimen (Fig. 5b) was tested at a confining stress of 1 MPa and failed as well by forming a steep angle shear band, even though the inclination of the shear band to the vertical axes in this case seems to be somewhat smaller than for the specimen in Fig. 5a. The third specimen in Fig. 5c was tested at 1.5 MPa and presents the formation of low-angle diffuse shear bands in the upper part of the specimen. The specimen shown in Fig. 5d was tested at a confining stress of 2.5 MPa and shows several horizontal compaction bands in the upper part. The lower part looks intact.

The compaction bands in the specimen were discrete and the cementation locally dissolved as a result of the compaction process. This led to the formation of discontinuities in the specimen that opened when the specimen was unloaded. The failure pattern indicates that the compaction process started at the upper part of the specimen and propagated downwards with increasing axial strain. In Fig. 6, the response curves of the different uniaxial tests are presented. In Fig. 6a, the deviatoric stress is plotted against the external axial strain. One test was performed controlling the axial strain rate and the other test controlling the circumferential strain rate. The advantage of the circumferential strain control is the fact that the post-failure response can be followed more closely. Instead of the abrupt stress reduction usually observed, in this case, the decrease of the axial strain during inelastic deformation can be clearly seen. Figure 6b shows the circumferential strain plotted against axial strain for both test methods. The values for the circumferential strain are similar for both tests, but the different control variables are visible in the curve progression. Figure 7 shows the specimens after both uniaxial compression tests. In Fig. 7a, the specimen that was tested under circumferential strain control and, in Fig. 7b, the specimen after the axial strain controlled test are shown. The pictures demonstrate that both specimens failed by the formation of a steep angle shear band. On a more detailed visual examination of the specimen in Fig. 7a, it was found that the fracture had a discontinuous inclination and propagated from imperfection to imperfection on the surface of the specimen. In the other specimen, no correlation could be established between the imperfections of the rock and the geometry of the shear band.

In Fig. 8a, the differential stress is plotted against the axial strain for low confining pressures up to 1.5 MPa. The failure is brittle for the test performed at a confining pressure of 1 MPa. For the triaxial test at a confining pressure of 1.5 MPa, the behavior observed is between brittle and ductile, as the initial reduction in axial stress is only slight and subsequently followed by a plateau. The results of triaxial tests at high confining pressures are given in Fig. 8b. The overall response is ductile and plateaus of different lengths were observed in all tests. It is assumed that the spontaneous stress drops observed in the curve progression are a result of the formation of compaction bands in the specimens, which further indicates the formation of discrete rather than diffuse zones of localized deformation. The hardening phase starts at the end of the plateau, which becomes shorter for higher confining pressures. This means that there is less axial deformation in the compaction process under increasing confining pressure. Figure 9 shows pictures of the specimens after the triaxial tests with different confining pressures. Several discrete compaction bands are visible in all specimens. Figure 10 shows the results of the isotropic compression tests. In Fig. 10a, the confining pressure is plotted against external axial strain. The stress response is typical for an isotropic test and differs from the one of the triaxial tests, because the stress increases further after the yield point, meaning that the hardening starts with the onset of plastic deformation. In Fig. 10, volumetric strain is plotted against mean stress. The volumetric strain is calculated under the assumption of a homogeneous deformation behavior in the inelastic deformation regime. This means that the volumetric strain is calculated with the results of the local strain measurements in radial and in axial direction: \(\epsilon _{\text {v}} = \epsilon _{\text {r}}+\epsilon _{\text {a}}\), with \(\epsilon _{\text {r}}\) for radial strain and \(\epsilon _{\text {a}}\) for local axial strain. The experimental results of the present study are plotted together with those from Papazoglou (2018) who used the same material. The comparison of the results shows that the behavior from the stress-controlled tests and the one from Papazoglou (2018) are similar to each other. After the test, no discrete compaction band was visually observed in the specimen and no destructuration was visible at the initial inspection. However, after being placed in water, the specimen fell apart, indicating that debonding had taken place.

In Fig. 11, the local strain measurements during different compression tests are plotted against the external axial strain. The circumferential strain is plotted against the external axial strain in Fig. 11a. Since the specimens are cored perpendicular to the bedding plane and the material is homogeneous on the macro scale, it can be assumed that the circumferential strain is equal to the radial strain. In triaxial compression tests with low confining pressures, such as 1 MPa, the circumferential strain increases during the inelastic deformation, as a result of the formation of shear fractures. In the tests under higher confining pressures, the circumferential strain stays constant at the onset of plastic deformation. As shown by the failure pattern of the specimen tested at 2.5 MPa confining pressure in Fig. 5d, the compaction process begins at the upper end of the specimen, and with increasing axial deformation, the compaction zone propagates to the middle. The circumferential strain is measured in the middle of the sample. Therefore, the circumferential strain begins to change as soon as the compaction front has reached the middle of the specimen. In the test at a confining pressure of 3.25 MPa, the circumferential strain shows extensions when the compaction process in axial direction reaches the middle of the specimen, then remains constant as the rest of the specimen compacts, and increases again when the whole specimen is fully compacted and the hardening starts. In the visual inspection of the specimen, a discrete compaction band under the chain was observed, and additionally, the sleeve showed a fold at the band. This could have influenced the measurement. For higher confining stresses, 5 MPa and 6 MPa, the circumferential stress decreases when the compaction front reaches the middle of the specimen and increases when the hardening of the specimen begins. When comparing the results of the different tests, during the plateau phase, radial extension at ‘low’ confining pressures and radial compaction at ‘high’ confining pressures is documented. The onset of the deformation takes place earlier with increasing confining stress, as one would expect from the fact that the stress plateaus become shorter with increasing confining stress.

For some triaxial tests, the local axial strain was measured with two extensometers on the surface of the specimen. These measurements are used to investigate the influence of the boundary conditions at the end plates on the measurement. In Fig. 11b, the axial strain measured with extensometers for different confining pressures is plotted against the axial strain measured by the displacement of the axial piston. In the test with a confining pressure of 1 MPa, the local axial strain increases monotonically from the beginning of the test. However, the inclination of the curve is smaller than 1.0, meaning that the axial strain measured with the displacement of the piston is larger than the axial strain measured with the extensometers. This could be due to the friction between the end plates and the specimen, but is most likely a result of the smaller stiffness of the interface between end plates and specimen. In the tests with high confining pressure, the axial strain of the extensometers stays constant from the onset of plastic deformation. This is also a result of the localized deformation, because the compaction process starts at the upper part of the specimen. When the compaction front reaches the measurement range of the local axial strain, the axial strain increases again. For the measurement of the elastic modulus and the Poisson’s ratio, unloading and reloading cycles have been conducted in the elastic part of the compression tests. In Table 1, the elastic parameters are presented for different confining pressures. The elastic modulus, the Poisson ratio, the secant modulus, and the bulk modulus were measured externally and locally. The fraction of the global modulus to the local modulus ranges from 0.37 to 0.75. This means that the local stiffness is in all cases significantly higher than the global one. It can also be stated that the global secant moduli do not exhibit a marked dependence on the confining pressure.

In the following, the results of drained triaxial tests with different confining pressures and with saturated specimens are presented. The results demonstrate that the failure mode is the same under water saturated as under dry conditions. In Fig. 12, the mean stress is plotted against the axial strain for four different confining pressures. Under the confining pressure of 2.5 MPa, the material response was ductile. In every specimen, compaction bands were observed, with small ruptures that are a result of the destruction of the cementation between the grains. In Fig. 13, three specimens after the triaxial tests at different confining pressures are shown. The entrapment of air voids, which can be observed in the specimen in Fig. 13c, is a result of the unloading after the test, when the pore pressure was set to zero. The specimen in Fig. 13c, close to the plastic onset of the wet rock, exhibits a strong deformation in the radial direction.

To determine the tensile strength of the rock, indirect tensile strength test was conducted under dry conditions. For these tests, a uniaxial testing machine was used that has a maximum testing force in the axial direction of 550 kN and a regulation range for the displacement rate from 0.001 to 500 mm/min. The tests were performed according to the recommendation of the DGGT Lepique (2008) and the tensile strength is calculated with the following equation:with F as the maximum force, D as the diameter, and as l the length of the specimen. The results of the tensile strength test are given in Table 2. It was not possible to conduct indirect tensile strength tests under drained conditions. With the results of the compression tests and the tensile strength test, it is possible to plot the peak stresses of the water saturated and the dry rock. In Fig. 14, the differential stress is plotted against the mean effective stress and the two yield loci are illustrated. Comparison of the strength of the wet and the dry material indicates that the wet material is failing at lower stresses than the dry specimens. According to different studies (Castellanza and Nova 2004; Cai et al. 2019), this is to be expected, especially in a calcitic material, as in this case. The shape of the yield surfaces shows a cap in both cases. The yield locus of the dry rock appears non-convex in the cap part. Therefore, the triaxial compression test at a confining pressure of 4 MPa, marked in the figure, was performed a second time and the same value for the peak stress at the onset of plastic deformation was measured in this test.

The permeability during the drained triaxial compression tests with different confining stresses was measured. In Fig. 15, the permeability in the axial direction is plotted in logarithmic scale against the axial strain for four different confining pressures.

As expected, the permeability decreases with increasing axial strain. The permeability of the specimens that have been tested at 2.5 MPa and 3.25 MPa confining stress shows the same response. The other two curves exhibit a different inclination. The permeability of the specimens tested at a confining stress of 4 MPa and 5 MPa show a sharp decrease with the onset of plastic deformation. One reason for this behavior could be the strong deformation of the specimen shown in Fig. 13. The permeability decrease in total is around one order of magnitude. However, as the permeability is still decreasing at an axial strain of 10%, the limit of the test device, it is possible that the permeability could decrease further with further deformation.

The results of the oedometric test under dry conditions are qualitatively similar to the ones of the isotropic compression tests, in the sense that no clear plateau and no spontaneous unloadings were observed. The axial stress is plotted against the axial strain in Fig. 16b. After reaching the yield point, the axial stress continues to increase with further deformation. This is to be expected, as the prevention of the lateral displacement leads to an increase of the lateral stress with growing axial strain.

In Fig. 16a, the results of the two oedometer tests under drained conditions in two different test setups are presented. The axial stress is plotted against the axial strain. The unloadings in the stress–strain curve are a result of the strong creep and relaxation of the wet rock between the measuring points. The two curves are very similar. They both form a plateau after reaching the yield point and start showing hardening at an axial strain of 16%. In comparison to the results of the oedometer tests under dry conditions, it can be observed that the rock exhibits a pronounced plateau in the presence of water, which was absent in the dry specimens. At the same time, the stress in the saturated specimens is only slightly lower and the exponential hardening starts at only slightly larger deformations.

Figure 17 shows the results of the permeability measurements of the drained oedometer test in test setup 01, the results of the precompacted specimen (test 01), and the results of the oedoemeter test in test setup 02 (test 02). The permeability decrease begins in both curves with the onset of plastic deformation. The curves are close to linear in semi-logarithmic scale, at least until a strain of about 25%, which means that the permeability decreases in the form of a power function. This is different to the results of the drained triaxial tests and can be a result of the increasing lateral stress. As the curve labeled with test 01 and test 03 is forming a plateau at an axial strain of 37%, it could be deduced that the permeability is not decreasing as rapidly with further deformation, though additional points would be necessary to assess this conclusion with certainty. That would mean that the compaction process is completed. The complete permeability reduction is nearly three orders of magnitude. In the curve labeled as test 02, a plateau is not observed. That means that the permeability is decreasing with further deformation. The total permeability decrease is also of about three orders of magnitude. The difference between the two results is small and can be a result of scatter in the mechanical properties of the rock. Especially, the results of the normal compacted and precompacted specimen are in good accordance, even though the test setup and test methods are different.

Thin sections of the specimens were produced pre- and post-mortem using blue epoxy. The main objective of this analysis was to clarify whether and to what extent grain crushing occurs during compaction The thin sections were investigated under a polarized microscope and images were taken for comparison.

Thin sections of the intact rock are compared with thin sections of a specimen compacted in an oedometer test under dry conditions. The blue space is the void space. The intact rock has a initial porosity of 52% and the compacted rock has a porosity of 36%. Figure 18a shows an image of a thin section of the intact rock at \(\times\)100 magnification and Fig. 18b shows an image of a thin section of the compacted rock with the same magnification. The images of the thin sections show that the grains of the rock have a size of 50–150 \(\upmu {\text {m}}\) and that they are mostly composed of different fragments of shells and corals. Furthermore, the rock has a high intra-particle porosity within the shell fragments. These structures are from a static point of view more unstable and collapse with compaction of the rock. In the comparison of the two figures in Fig. 18, the decrease of the porosity and also grain breakage are visible.

In Fig. 19, the thin section of the compacted rock with a magnification of \(\times\)200 is shown. In the middle of the image, a circular shell fragment that has been fragmented during the test is visible. Other fragmented grains are also visible in the figure, with examples marked in red ellipses. The thin sections demonstrate that pronounced grain crushing is present in the rock during the compaction process in the oedometer test under dry conditions. No thin sections were prepared from the specimens tested under triaxial conditions. In the literature Baxevanis et al. (2006) suggests that some grain crushing takes place, but it would be reasonable to expect a lesser extent of the phenomenon, given the lower mean pressures.