Study of Mechanical Behavior and Deformation Field Characteristics of Sandstone under Cyclic Loading

. The sandstone yield strength and tensile strength were increased under cyclic loading paths by using the Brazilian splitting method. The experiment shows that (1) the sandstone specimens exhibit multiple penetrating crack damage by cyclic loading, while the tensile strength slightly increases; (2) the sandstone horizontal strain (E xx ) concentration area decreases, and the shear strain (E xy ) concentration area increases under cyclic loading, and the damage form changes from completely brittle tensile damage to ductile mixed tensile-shear damage; (3) the mechanism of the increase in tensile strength of the specimen under cyclic loading was explained by digital image correlation (DIC) technique. The results indicate that a time lag occurs in the horizontal strain concentration zone, and the area of the penetration zone decreases from the cyclic loading e ﬀ ect, while the reduced stress concentration leads to increased tensile strength of the specimens.


Introduction
The tight sandstone reservoirs in Shengli Oilfield have the characteristics of poor permeability and complex physical properties, which causes certain difficulties for the sustainable production of oil and gas resources.With the increasing extraction time, the production of oil and gas resources is decreasing.Methods are needed to artificially fracture the sandstone reservoirs, to create advantageous channels, and to achieve the purpose of increasing production and seepage.
Measures to increase production and seepage in sandstone reservoirs often use the injection of high-displacement slick water to hydraulically fracture the rock [1][2][3], thus artificially creating a complex fracture network, which can significantly increase the reservoir permeability and inflow capacity to increase the recovery of oil and gas resources.
The conventional hydraulic fracturing process often performs volume fracturing by repeatedly injecting a massive volume of fracturing fluid to maximize reservoir permeability and inflow capacity.According to the basic principle of hydraulic fracturing, the common damage to rocks during hydraulic fracturing [4] is tensile, and the fracture pattern formed is closely related to the tensile strength of rocks; meanwhile, the water injection process has a great influence on the fracture pattern produced by sandstone fracture.The fracture pattern produced under different loading methods is highly variable, while the mechanism of rock fracture pattern formation is still unclear.
In the process of reservoir modification through hydraulic fracturing, repeated water injection is often used to improve the efficiency of reservoir modification to achieve efficient utilization of oil and gas resources.The mechanical properties of rocks under cyclic loads are significantly different from those under uniaxial loads.Studying the evolution of rock mechanical properties and crack propagation under cyclic loads plays an important role in improving the efficiency of reservoir transformation.
Yuanlong et al. [5] studied the deformation and fracture characteristics of shale containing natural fissures under cyclic loads and found that shale under cyclic loads partially deteriorated, the peak strength was slightly reduced, and the fracture morphology showed a pull-shear mixed form.Yonghong et al. [6] proposed to use of digital image correlation technology to study the deformation of rocks containing microcracks.The study showed that the displacement field information under different load levels can be used to reflect rock damage, and digital image correlation technology can be used to obtain the evolution characteristics of microcracks inside rocks under different load levels.
Jiawen et al. [7] studied the reasons for the significant decrease in the peak strength of rocks under cyclic loads; that is, the increase and accumulation of rock damage under cyclic loading and unloading led to a decrease in rock strength.Through the synchronous observation test of the strain response and surface crack image of the red sandstone sample, Zhende et al. [8] introduced physical quantities such as crack damage degree and damage tensor, quantitatively evaluated the dynamic progressive propagation damage characteristics of the red sandstone prefabricated mesoscopic crack under the water-bearing state, and further understood the evolution law of mesoscopic crack propagation under uniaxial compression.
Xiaobin et al. [9,10] have carried out relevant research on the evolution characteristics of nonuniform deformation of granite under the cyclic process, and the results show that with the increase in the number of cycles, the degree of nonuniform deformation of rocks increases significantly, and the width of deformation localization belt increases.It is found that the localization band displacement of the cyclic loading and unloading process fluctuates with the loading and unloading stress, the displacement evolution has a lag in time, and there is a significant cumulative effect of the displacement with the increase of the number of cycles.
Gao and Zhou [11] give a theoretical description of the digital speckle correlation method, derive a general procedure for measuring the deformation field on the surface of an object, and transform the deformation measurement problem in mechanics into a purely numerical calculation problem.Zhao et al. [12] propose the use of digital image correlation techniques to analyze the deformation in the process of rock damage.
By conducting the type I fracturing test under uniaxial load and cyclic load on the sandstone specimen, the loaddisplacement curve during the loading of the specimen was obtained, and the whole process from loading to damage of the rock was captured by a high-speed camera, and the information of the deformation field during the loading of the specimen was analyzed by using DIC technology.
DIC technology can obtain the information characteristics of rock surface deformation field, which is a nondestructive testing method that can observe the full field strain of rock.
Huaiwen et al. [13] introduced the basic principles and mathematical models of digital image correlation technology and predicted the possible development trend of this technology.Yimin et al. [14,15] studied the deformation field characteristics of the uniaxial failure process of red sandstone, studied the information on the displacement localization zone of the rock deformation failure process, and pointed out that the energy release and energy accumulation law of the rock sample during the loading process were related to the evolution of the localization zone.
Based on DIC technology [16], the deformation characteristics of marble under cyclic loading are obtained.A statistic that describes the localized characteristics of the deformation field is defined to represent the evolution of the strain field.Based on the MTS815 rock mechanics test system [17], the constant lower limit cyclic loading and unloading test was carried out on red sandstone.The results show that the average compressive strength of the rock under constant lower limit cyclic loading and unloading is slightly improved compared with the uniaxial compression test.
There are relatively few studies on the evolution characteristics of rock tensile strength under cyclic loads.The phenomenon of increased tensile strength of sandstone under cyclic loads is analyzed by digital image correlation technology.In this paper, the evolution characteristics of sandstone full-field deformation field under different cyclic loading and unloading paths are obtained by digital image correlation technology.

Experimental Method
2.1.Materials 2.1.1.Rock Parameters.Cylindrical cores in the test were drilled on-site and cut into standard Brazilian disc specimens with a diameter of 50 mm and a length of 25 mm in the laboratory [18], and the ends of the specimens were polished to ensure the flatness of the ends of the specimens.The specimens were divided into two groups for Brazilian splitting tests, in which group A was fractured by uniaxial loading and group B was fractured by cyclic loading.The basic parameters of the samples are shown in Table 1.

Speckle Spraying.
The surface of the sandstone specimen needs to be sprayed with speckle spots before the test so that the information on the deformation field during crack evolution can be analyzed using DIC.The specimens were sprayed by adjusting the angle of the spray paint, and the size of the speckle spots was about 3~5 pixel points.The Brazilian disc specimens before spraying and after spraying the spots are shown in Figure 1.

Experimental Principal.
The Brazilian splitting method, as an indirect method to measure the tensile strength of rocks, has a series of advantages such as easy operation and accurate results.The Brazilian test [19,20] was officially proposed by the International Society for Rock Mechanics 2 Geofluids (ISRM) as a suggested method for determining the tensile strength of rock materials.Mingqing and Chengdong [21] effectively improved the stress state at the loading point by introducing a platform as the loading surface in the Brazilian disk specimen.The rock tensile strength was calculated by the following equation: where σ t is the tensile strength of the rock in MPa, P is the specimen breaking load in N, D is the diameter of the specimen in mm, and L is the thickness of the specimen in mm.The load and displacement data of the sandstone specimen in the loading process were recorded by the MTS rock mechanics test system; meanwhile, the specimen loading process was captured by a high-speed camera system with a shooting frame rate of 100 fps, which means 100 images per second.
The Brazilian splitting test under uniaxial load was carried out on the sandstone specimens to determine the peak strength of the batch, and then, the test of the cyclic loading at all levels would be determined.The specimens were loaded by stress-controlled loading with a loading rate of 5 kN/min and an unloading rate of 5 kN/min.To ensure the existence of prestress, the unloading values of the cyclic process at all levels were set to 400 N by repeated cyclic loading [22,23] until the sandstone specimen is damaged.The loading path schematic diagram is shown in Figure 2.  3 Geofluids finally, the crack extension stage, in which the specimen undergoes penetration-type damage after the load level reaches its peak strength.6-8.Compared with the single penetration-type crack damage pattern under uniaxial loading, the rock damage under cyclic loading showed multiple penetration-type cracks with a large number of secondary microcracks, and the specimens were broken to a higher degree and more significantly damaged.

Tensile Strength Calculation.
The peak strength of the specimens and the corresponding peak displacement were obtained from the load-displacement curve, and the tensile strength of the specimen under different loading methods was calculated, as shown in Table 2.
The average tensile strength of group A specimens under uniaxial loading is 4.671 MPa, and the average tensile strength of group B specimens under cyclic loading is 5.318 MPa, which increased the average tensile strength by 13.8%.As result, the tensile strength of sandstone slightly increased under cyclic loading, and this phenomenon was explained by digital image correlation techniques in this paper.4 Geofluids surface by correlating some subset of pixels in the reference image with the corresponding subset of pixels in the deformed image:

Discussion
where ∂x i is the postdeformation position, ∂X j is the predeformation position, and F ij is the deformation gradient from which the Lagrangian strain can be calculated [25].
where E is the Lagrangian strain and F is the deformation gradient.
Wang et al. [26] conducted a related study on the deformation field characteristics of mudstone with different humidity carried out at the microscopic scale by DIC technique; the deformation field characteristics of the Brazilian splitting process of sandstone specimens under different loading methods were analyzed, and the local strain tensor (horizontal strain E xx and shear strain field E xy ) variation process was obtained by DIC technique.5 Geofluids sandstone sample failure process under uniaxial load are shown in Figure 9.The specimen upper and lower end displacement value is the largest.With the increase of load level, when T = 117:9 s, a relatively obvious transition zone appeared in the center of the sample, and when the sample was damaged at T = 118:2 s, the center appeared discontinuous displacement in the horizontal direction.

Vertical Displacement Field V.
The values of vertical direction displacement field of sandstone specimens under uniaxial load were all negative in Figure 10 with the increase of load level.A vertical displacement zone with up and down staggering along the central region of the specimen was formed at T = 117:9 s, and a discontinuity of vertical direction displacement appeared in the specimen at T = 118:2 s.

Deformation Field in Horizontal Direction E xx .
According to the evolution characteristics of the deformation field E xx in the horizontal direction in Figure 11, the     6 Geofluids rock damage process under uniaxial loading can be divided into four stages.
(1) The overall deformation during the elastic deformation period (before 50% of the peak strength) is small, and only small strain concentrations of more than 0.4% locally exist (2) Plastic deformation period (between 60% and 90% of the peak strength) of the specimen as a whole appears to have local stress concentrations, which can be seen in the central region where the value exceeds 0.7% of the stress concentration zone (3) A more obvious local stressing zone exists during the crack emergence period (after 90% of the peak strength), with a gradual increase in local deformation and a concentration zone of more than 1% (4) In fracture propagation period (after reaching the peak strength), there is a larger area of deformation 7 Geofluids localized stressing zone, and through-type cracks appear 4.2.4.Shear Deformation Field E xy .In Figure 12, the specimens under uniaxial loading did not show shear deformation before the damage, and the damage occurred at T = 117:9 s when a discontinuous shear deformation concentration zone appeared near the crack, and a local discontinuous deformation concentration zone (secondary crack) appeared near the main crack at T = 118:2 s. 9 Geofluids uniaxial loading, the large deformation area over 0.8% appeared with a time lag, and through the area was reduced, the deformation concentration.The area of large deformation concentration is more dispersed, thus explaining the slight decrease of tensile strength under cyclic loading.

Deformation Field in
Shear Direction E xy .The deformation field in the shear direction of the specimen under cyclic loading is the same as that of uniaxial loading in Figure 16, and the shear deformation concentration zone is less during the cyclic loading and unloading the specimen.

Conclusion
By analyzing the sandstone Brazilian splitting experiments under different cyclic loading and unloading paths, it was found that the tensile strength of sandstone under cyclic loading increased slightly compared with that under uniaxial loading, and the displacement field and deformation field information under different loading methods were evaluated by DIC techniques, and the results show the following: (1) Uniaxial loading showed single main crack damage, while cyclic loading showed multiple penetrating 10 Geofluids main crack damage, and the number of main cracks showed a positive correlation with the number of cycles (2) Compared uniaxial loading, the tensile strength of sandstone increases cyclic loading.By analyzing the information of the deformation field in the horizontal direction, it is found that cyclic loading leads to the reduction of area and continuity of large deformation area and the reduction of stress concentration, which leads to the increase of tensile strength (3) According to the deformation field evolution characteristics the horizontal direction, it is found that the specimens exhibit fully brittle tensile damage form under uniaxial loading and ductile mixed tensile-shear damage form under cyclic loading

3. 1 . 2 .
Cyclic Load Load-Displacement Curve.The cyclic loading load-displacement curve and specimen failure diagram are shown in Figures

4. 1 .
Introduction to Digital Image Correlation Principles.DIC is a technique where the deformation gradient[24] can be approximated by averaging an infinitesimal gradient over a
Load-displacement curve (b) Crack pattern

4. 2 . 1 .
Horizontal Displacement Field U. The evolution characteristics of the horizontal displacement field of the
Load-displacement curve (b) Crack pattern
Load-displacement curve (b) Crack pattern

Table 1 :
Table of basic parameters of rock samples.

Table 2 :
Tensile strength parameters of sandstone.