This paper studies the anisotropic characteristics of shale and the difference in mechanical performance between deep shale and outcrop shale. The outcrop shale was collected from the Shuanghe section in Changning County, southern Sichuan, and the deep shale was collected from the Wells Yi201 and Lu202. Study their basic mechanical parameters, failure modes, and wave velocity responses through laboratory tests. Research shows that with the increase of bedding angle, the deformation mode has the trend from elastic deformation to plastic deformation in high-stress state. When the bedding angles are 0°, 30°, and 45°, the weak bedding surface plays a leading role in the formation of the failure surface trend. As the bedding angle increases to 60° and 90°, its influence is weakened. The tensile strength, elastic modulus, and wave velocity decrease with the increase of bedding angle. The compressive strength and Poisson’s ratio have the law of U-type change, there are higher values at 0° and 90°, and the lowest values are at 30°. The brittleness index first increases and then decreases with the increase of the bedding angle. The tensile strength and Poisson’s ratio of outcrop shale and deep shale are close, but the compressive strength of deep shale is only 1/3 of outcrop shale, the elastic modulus is only 3/4 of outcrop shale, and the failure of deep shale is accompanied by instability failure.

Shale gas will play an important role in the global energy structure in the future [

At present, many scholars have made great progress in the study of shale anisotropy. Jaeger et al. [

The shale has obvious bedding characteristics under the influence of deposition mode. The existing studies show that the shale mechanical parameters of different blocks are diversified, coupled with the heterogeneity of shale and the difficulty of sample preparation far, and there is no conclusion on the complete system of shale anisotropy. Based on the previous research experience, this paper makes an in-depth study of outcrop shale of Longmaxi Formation in Sichuan Basin on the difference of multidirectional mechanical properties of shale. The stress-strain curve, compressive strength, tensile strength, elastic modulus, Poisson’s ratio, brittleness index, and failure mode of shale during shale failure are analyzed. The anisotropy of mechanical parameters is compared, and the elastic constants of Longmaxi shale based on transverse isotropic model are obtained.

In addition, the basic research of shale mechanical parameters is used for underground shale gas exploration. Most of the existing research data are the results of outcrop shale measurements. The mechanical properties of outcrop/deep shale are not completely the same due to the influence of stratum structure, light, and temperature and cannot be applied arbitrarily. Therefore, this paper selects the deep shale of Longmaxi Formation in Sichuan Basin, China, to carry out general mechanical experiments, and makes a comparative analysis and summary of the similarities and differences between outcrop and deep shale mechanical parameters, in order to better match and apply the existing research results of outcrop shale anisotropy to deep shale gas reservoir exploitation in the future and provide basic data support for shale gas exploration and development.

The southern Sichuan Basin is the largest shale gas production base in China. In recent years, PetroChina has vigorously promoted the exploration and development of shale gas resources in southern Sichuan, in which the Longmaxi Formation shale is the main exploration block [_{1}^{1} strata of Longmaxi Formation (see document [

Sampling site and stratigraphic histogram.

Large shale samples without weathering and with obvious bedding characteristics were selected from the surface. Establish a Cartesian coordinate system based on bedding plane, as shown in Figure

Schematic diagram of multidirectional sample preparation. (a) Azimuth angle and bedding angle in the coordinate system. (b) Sample drilling direction. (c) Direction of bedding angle in uniaxial compression experiment. (d) Direction of bedding angle in Brazilian splitting experiment.

Shale sample. (a) Multidirectional outcrop shale sample. (b) Deep shale sample.

Shale uniaxial compression test and Brazilian splitting test instruments use SANS CMT-5504 electronic universal testing machine with maximum axial load up to 1000 kN and strain data recorded by the DH5923N dynamic signal test and analysis system with accuracy less than 0.5%. Displacement loading control is used in loading mode, and the rate is set 0.02 mm/s. The instrument for measuring wave velocity is based on DS5-8B series full information acoustic emission signal analyzer, whose probe frequency is 50∼400 KHz and the center frequency is 150 KHz. The specific research programme is shown in Table

Research categories and objectives.

Experimental category | Shale type | Bedding angle/azimuth | Objective |
---|---|---|---|

Uniaxial compression | Outcrop shale | 0°, 30°, 45° | Anisotropy |

Deep shale | 90° | Deep/outcrop shale comparison of mechanical performance |

The stress-strain curves of outcrop shale with square angle

Stress-strain curves of shale at different bedding angles with azimuth angle

The stress-strain curves of 5 different bedding angles coincide at the initial compaction stage, and the strain increases gradually with the increase of axial stress. The turning point of 5 curve strike occurs near the axial strain ^{−3}. The five curves show different trends, from top to bottom, which are 0°, 30°, 45°, 60°, and 90° bedding angle. The larger bedding angle, the lower slope, indicating that the elastic modulus decreases gradually with the increase of bedding angle.

The change of bedding angle will affect the deformation mode before the sample is destroyed. The elastic stage of the stress-strain curve is longer, especially the curve of 0°, 30°, and 45° approaches a straight line, indicating that most of the deformation is elastic after compaction and before the failure of the specimens. When the bedding angle increases to 60° and 90°, the slope of the curve decreases in the high-stress section before the sample is destroyed, which indicates that the curve has plastic deformation after reaching the elastic limit. With the increase of bedding angle, the loading deformation of shale under high stress tends to change from elastic deformation to plastic deformation. The larger the bedding angle, the longer the plastic deformation stage.

Because of the tight nature of shale, bedding as a weak surface is the main factor affecting the type of shale failure. The experimental results show that there are two main failure modes of shale under uniaxial load: tensile splitting failure and shear failure. The failure modes with different bedding angles are shown in Figure

When

When

When

When

When

Failure modes of shale specimens at different bedding angles with azimuth angle

The experimental results show that with the increase of bedding angle, the failure mode of shale firstly changes from vertical splitting tensile failure to shear slip failure along the weak bedding plane and finally evolves into splitting tension failure of the cross-cut bedding plane. When the bedding angles are 0°, 30°, and 45°, the weak bedding surface plays a leading role in the formation of the failure surface trend. As the bedding angle increases to 60° and 90°, its influence is weakened.

Figure

Compressive strength of shale in different directions.

Figure

Compressive strength variation with bedding angle.

Figure

Elastic modulus and Poisson’s ratio variation with bedding angle.

Table

Summary of tensile strength of outcrop shale.

Bedding angle | Tensile strength (MPa) | Average value (MPa) | ||
---|---|---|---|---|

1^{#} | 2^{#} | 3^{#} | ||

0 | 3.44 | 4.22 | 3.80 | 3.82 |

15 | 3.33 | 4.35 | 3.98 | 3.88 |

30 | 4.31 | 5.20 | 4.18 | 4.56 |

45 | 5.68 | 5.81 | 5.88 | 5.79 |

60 | 6.90 | 6.35 | 6.49 | 6.58 |

75 | 7.62 | 6.98 | 7.26 | 7.28 |

90 | 7.68 | 7.90 | 7.16 | 7.58 |

Tensile strength of outcrop shale variation with bedding angle.

Due to the energy attenuation of ultrasonic wave propagating through the weak bedding plane in shale, the velocity of ultrasonic wave propagating in shale shows anisotropic characteristics. The wave velocity of ultrasonic wave passing through bedding in different directions is measured as shown in Figure

Schematic diagram of ultrasonic wave velocity measurement.

Shale ultrasonic wave velocity.

Transverse wave velocity | Average value | Vertical wave velocity | Average value | |||||
---|---|---|---|---|---|---|---|---|

0 | 2520 | 2752 | 2586 | 2619 | 4732 | 4812 | 4917 | 4820 |

15 | 2405 | 2552 | 2654 | 2537 | 4761 | 4703 | 4899 | 4787 |

30 | 2305 | 2479 | 2420 | 2401 | 4627 | 4714 | 4638 | 4659 |

45 | 2289 | 2458 | 2358 | 2368 | 4589 | 4500 | 4674 | 4587 |

60 | 2113 | 2454 | 2389 | 2318 | 4397 | 4561 | 4433 | 4463 |

75 | 2199 | 2342 | 2307 | 2282 | 4097 | 4161 | 4196 | 4151 |

90 | 2076 | 2090 | 2280 | 2148 | 4060 | 4196 | 3939 | 4065 |

Variation of wave velocity with bedding angle. (a) Transverse wave velocity. (b) Vertical wave velocity.

Figure

In order to directly compare the differences between deep shale and outcrop shale, this paper measures the mineral composition and microstructure of deep shale and outcrop shale.

Figure

Shale mineral content analysis results. (a) Mineral composition of deep shale in Well Yi 201. (b) Mineral composition of outcrop shale.

Figure

Microstructure analysis images of shale. (a) Deep shale in Well Yi 201 SEM photos. (b) Outcrop shale SEM photos.

In this paper, the basic mechanical parameters of deep shale are measured. Since the preparation of deep samples is difficult, only samples with bedding angle 90° are obtained in this experiment, and six samples as shown in Figure

Value of compressive and tensile strength of deep shale.

Location | Compressive strength (MPa) | Average value (MPa) | Elastic modulus (MPa) | Poisson’s ratio | ||

1^{#} | 2^{#} | 3^{#} | ||||

Well Yi201 | 57 | — | — | 57 | 3560 | 0.28 |

Well Lu202 | 57 | — | — | 57 | 4800 | 0.36 |

Tensile strength/MPa | ||||||

1^{#} | 2^{#} | 3^{#} | ||||

Well Yi201 | 5.33 | 4.24 | — | 4.78 | — | — |

Well Lu202 | 7.16 | 7.88 | — | 7.52 | — | — |

The data in Table

Figure ^{−2}, the curvature of the curve increases gradually, which indicates that there is an obvious compaction stage in the process. When the strain is greater than 1.64 × 10^{−2}, the curve enters the plastic failure zone, and the curve fluctuates violently and forms two stress drops. The second drop value is relatively large, and it decreases from the peak value of 56.6 MPa to 53 MPa. At this time, the specimen does not lose the supporting force. With the increase of vertical load, when the stress gradually increases to 56 MPa, the specimen loses its supporting force instantly after failure. The whole process is characterized by plastic failure.

Stress-strain curve and failure characteristics of deep shale in Well Lu 202. (a) Stress-strain curve. (b) Postdestruction form.

Figure

In conclusion, there are similarities and differences in mechanical performance between deep shale and outcrop shale. The compression stage of deep shale is obvious while that of outcrop shale is not obvious. However, both of them have a long elastic stage and tend to change from elastic deformation to plastic deformation in high-stress state. Compared with outcrop shale, deep shale is accompanied by instability failure when the stress reaches the maximum bearing capacity. However, the angle between loading direction and bedding is the main factor affecting deep/outcrop shale failure mode. In terms of mechanical parameters, the compressive strength and elastic modulus of deep shale are smaller than that of outcrop shale. However, the tensile strength and Poisson’s ratio in deep/outcrop shale are close to each other.

Because they have similar mineral composition, it is thought that the difference in microstructure may lead to the different mechanical performance of deep/outcrop shale. The experimental results indicate that it is feasible to study deep shale with outcrop shale as reference, but the differences of mechanical performance between outcrop shale and deep shale should be considered when applying outcrop shale research results to deep shale.

The property that the mechanical parameters of shale change in one direction with the change in this direction is called anisotropy. The third section shows that the mechanical parameters of shale change with the bedding angle. The following is an analysis of the anisotropy of the mechanical parameters including compressive strength, tensile strength, elastic modulus, Poisson’s ratio, brittleness, and velocity of ultrasonic wave propagation with the change of bedding angle.

Referring to the degree of strength anisotropy defined by the Saroglou and Tsiambaos [_{c} is the degree of anisotropy of compressive strength; _{cmax} is the maximum value of compressive strength; and _{cmin} is the minimum value of compressive strength.

According to formula (_{C} = 1.5. Through analysis, it is considered that the angle between the bedding plane and the principal stress leads to the anisotropic characteristics of compressive strength. When the bedding angle is 30°, the shear slip failure occurs along the direction of the weak bedding plane. The compressive strength largely depends on the shear capacity of the weak bedding plane. The low shear strength of the bedding plane directly leads to the reduction of the compressive strength. When the bedding angle is 0° and 90°, the compressive strength mainly depends on the shale matrix itself, so the compressive strength is higher than that at the bedding angle of 30°.

Define the degree of anisotropy of tensile strength as_{T} is the degree of anisotropy of tensile strength; _{max} is the maximum value of tensile strength; and _{min} is the minimum value of tensile strength.

According to formula (_{T} = 2.0. It is considered that the difference of failure modes under different bedding angles leads to the anisotropy of tensile strength. When the bedding angle is small, the failure mode is splitting failure along the direction of bedding plane. In this case, the tensile strength is mainly dependent on the tensile strength of weak bedding plane, so the tensile strength is lower. When the bedding angle is 90°, the failure mode of shale is splitting failure through the bedding plane. Its tensile strength is affected by the shale matrix; thus, the tensile strength increases by two times than 0°.

Similarly, the anisotropy of elastic modulus and Poisson’s ratio are defined as_{E} is the degree of anisotropy of elastic modulus; _{max} and _{min} are the maximum and minimum values of elastic modulus; A_{υ} is the degree of anisotropy of Poisson’s ratio; and _{max} and _{min} are the maximum and minimum values of Poisson’s ratio.

According to formula (_{E} = 1.4 and Poisson’s ratio _{υ} = 2.1. The elastic modulus and Poisson’s ratio reflect the brittleness of the specimen. Using the normalized average method of elastic modulus and Poisson’s ratio proposed by Rickman and Mullen [_{st} is the static elastic modulus in 10 GPa units; _{st} is the static Poisson’s ratio; _{no} is the normalized elastic modulus; and _{no} is the normalized Poisson’s ratio.

Figure

Variation of brittleness index with bedding angle.

Define the degree of anisotropy of brittleness index as_{BI} is the degree of anisotropy of brittleness index and BI_{max} and BI_{min} are the maximum and minimum values of brittleness index.

According to formula (_{BI} = 11, which indicates that bedding angle has great influence on shale brittleness index.

Define the degree of anisotropy of wave velocity as_{0°} is the velocity of ultrasonic wave in the direction of 0°; _{90°} is the velocity of ultrasonic wave in the direction of 90°.

According to formula (_{Vb} = 1.13, and the anisotropy of vertical wave velocity _{Vp} = 1.19. After analysis, it is considered that the anisotropy of wave velocity is caused by the blocking effect of weak bedding plane. When the bedding angle is 0°, the direction of ultrasonic propagation is consistent with the direction of bedding and does not need to cross the bedding plane. When the bedding angle is 90°, the ultrasonic propagation direction is vertical to the bedding plane. In this case, the mineral components, clay, and complex spatial morphology of the bedding plane impede the propagation of waves, so the wave velocity is slower.

When the bedding angle increases from 0° to 90° the propagation direction of ultrasonic wave gradually changes from parallel bedding direction to vertical bedding direction. The number of layers of bedding plane needed to be penetrated increases, and the energy attenuation in the propagation process increases. So, the propagation velocity of wave tends to slow down gradually.

In summary, due to the differences in composition and spatial structure between the bedding plane and shale matrix, shale has different mechanical characterization along different bedding directions. In this paper, the degree of anisotropy of mechanical parameters (compressive strength, elastic modulus, Poisson’s ratio, and tensile strength), ultrasonic wave velocity, and brittleness parameters of shale are calculated. These parameters are affected by bedding plane, from high to low, which are brittleness index _{BI} = 11, Poisson’s ratio _{υ} = 2.1, tensile strength _{T} = 2.0, compressive strength _{c} = 1.5, Elastic modulus _{E} = 1.4, vertical wave velocity _{Vp} = 1.19, and transverse wave velocity _{Vb} = 1.13.

Taking the bedding plane as the basic plane, the spatial coordinate system is established, as shown in Figure

Figure

Variation of compressive strength with azimuth angle.

Figure

Variation of compressive strength with bedding in two vertical planes.

Like shale, this material has the same elastic parameters in all directions (called transverse) of the parallel bedding plane, unlike the elastic parameters in the vertical direction (called longitudinal), which is called transverse isotropic in engineering. The number of independent elastic constants for transverse isotropies decreases from 21 to 5 compared to extreme anisotropic elastomers [

As shown in Figure _{1} is the elastic modulus in the bedding plane; _{2} is the elastic modulus perpendicular to bedding direction; _{1} is Poisson’s ratio in the bedding plane; _{2} is Poisson’s ratio perpendicular to bedding direction; _{1} is the shear modulus in the bedding plane; and _{2} is the shear modulus perpendicular to bedding direction.

Transversely isotropic material coordinate system.

Because _{1} = _{1}/2(1+_{1}), _{1} is not an independent elastic constant. To describe the transversely isotropic elastic body of shale, there are only 5 independent elastic constants _{1}, _{2}, _{1}, _{2}, and _{2}. The first four parameters can be directly measured by the bedding angle _{2} can be obtained by fitting the elastic modulus in the direction of multiple bedding angles.

By means of coordinate system transformation, Niandou et al. [_{β} of transversely isotropic body under any bedding angle:

The following formula can be obtained from formula (

Formula (

As shown in Figure _{β} is the elastic modulus in the direction of

Reciprocal fitting curve of elastic modulus.

By comparing the fitting curve formula (_{2} can be retrieved. 5 independent elastic constants of outcrop shale of Longmaxi Formation can be obtained as shown in Table

Five elastic constants of outcrop shale of Longmaxi Formation.

_{1} (GPa) | E_{2} (GPa) | _{2} | _{2} | G_{2} (GPa) |
---|---|---|---|---|

7.51 | 5.22 | 0.36 | 0.40 | 1.93 |

The stress-strain curve of outcrop shale has no obvious compaction stage. The elastic stage is longer, and the distinction between elastic stage and plastic stage is not obvious. With the increase of bedding angle, the deformation mode trends to from elastic deformation to plastic deformation in high-stress state. The larger the bedding angle, the longer the plastic deformation stage.

When the bedding angle is 0°, 30°, and 45°, the direction of failure plane is basically the same as that of bedding plane. Tensile failure and shear failure occur along the bedding direction, and the bedding plane plays a leading role in the formation of failure surface. When the bedding angle is 60° and 90°, the influence of the bedding plane on the trend of failure surface is weakened. Under the action of the maximum principal stress, the inclined shear failure surface along the bedding plane and the vertical tensile splitting failure surface along the direction of maximum principal stress are produced.

The anisotropy of mechanical parameters of shale along different directions of bedding angle is obvious. Tensile strength, elastic modulus, and ultrasonic wave velocity decrease with the increase of bedding angle. Compressive strength and Poisson’s ratio show a U-type change pattern, which are higher at 0°/90° and lower at 30°. The angle of anisotropy of mechanical parameters affected by bedding from high to low is brittleness index, Poisson’s ratio, tensile strength, compressive strength, elastic modulus, vertical wave velocity, and transverse wave velocity.

The similarities between the deep shale and the outcrops are that the tensile strength and Poisson’s ratio. Their stress-strain curves have a long elastic stage and change from elastic deformation to plastic deformation under high-stress state. The difference between deep shale and outcrop shale shows that the stress-strain curve of deep shale has obvious compaction stage. The compressive strength and elastic modulus of deep shale are only 1/3 and 3/4 of outcrop shale. In failure mode, the deep shale is accompanied by destabilization failure when the stress reaches the maximum bearing capacity. The reason for this phenomenon may be the difference in microstructure between deep shale and outcrop shale.

Shale belongs to the transverse isotropy in engineering material. The change of azimuth angle will not affect the mechanical parameters of shale in this direction. Outcrop shale of Longmaxi Formation has five elastic constants based on transverse isotropic model: _{1} = 7.51 GPa, _{2} = 5.22 GPa, _{1} = 0.36, _{2} = 0.40, and _{2} = 1.93 GPa.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

The authors gratefully acknowledge the financial support given by the China National Science and Technology Major Project (grant no. 2017ZX05037001) and the Project of Discipline Innovation Team of Liaoning Technical University (grant no. LNTU20TD-11).