Study on the Mechanical Properties of Anisotropic Red Sandstone under Point Load Strength Test and Uniaxial Compression Strength

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Study on the Mechanical Properties of Anisotropic Red Sandstone under Point Load Strength Test and Uniaxial Compression Strength

https://doi.org/10.21203/rs.3.rs-2220458/v1

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The red sandstone of Xiaopu 3# branch Cave in Yuxi section of the Central Yunnan Water Diversion Project was taken as the research object. The uniaxial compression strength and point load strength test are conducted from the perspectives of vertical and parallel stratifications, respectively, and then the anisotropy of red sandstone was analyzed in detail. The data obtained from field and laborator test was analyzed, and the conversion relationship between point load strength index and uniaxial compression strength is power function under both parallel stratification and vertical stratification. The study results showed that: The mechanical properties of red sandstone has obvious anisotropy. The difference in its mechanical properties is particularly evident in UCS and point load tests, and I_s(50) and UCS under vertical stratification is significantly greater than I_s(50) under parallel stratification. The point load strength correction index m of red sandstone is m = 0.4096 under parallel stratification, and m = 0.4408 under vertical stratification.

Physical sciences/Engineering

Physical sciences/Materials science

UCS is one of the most important strength parameters of rocks in geotechnical engineering design ^1–3, and UCS is also widely used in the basic classification of rock mass, the determination of the engineering rock mass level, the assessment of engineering geologicaland so on, which has an important reference value for the safety and stability of mine engineering, underground engineering, slope and ground foundation engineering. The UCS test requires the preparation of the standard rock samples, and the samples are only can be tested in the laboratory according to the standards such as ISRM ⁴ and ASTM ⁵. There are some limitation on ⁶ in the number, type and preparation of samples, so the UCS test became more difficult ⁷ especially for the preparation of the samples for soft rocks and highly weathered rocks. Consequently, construction of a practical field test method to replace the UCS test has been an important target for researchers. PLT is one of the indirect methods to estimate the UCS of rock, which is widely applied in rock engineering and geotechnical engineering ⁸ owing to the point load tester is portable, the test is easy and low cost. The sample of PLT can be easily prepared in the field or laboratory, and the and the rock samples can be cylindrical, massive, or irregular ⁹. PLT is usually utilized to test irregular samples and also solve other thorny problems in routine test due to its convenience and efficiency, so PLT has been widely used in the engineering site.

Protodyakonov ¹⁰ first put forward the idea of PLT with irregular blocks, then D'Andrea ¹¹ and Franklin ¹² studied the transformation between rock's I_s(50) and UCS. At present, there are three main conversion relational function between sandstone I_s(50) and UCS: the zero intercept linear function, the non-zero intercept linear function and the power function, as shown in Table 1.

Table 1

Conversion relationship between Is(50) and UCS of sandstone
Researcher	Year	Conversion relationship	Main rock type	Ref.	Note
Broch and Franklin	1972	UCS = 24∙I_s(50)	Sandstone	¹³
Bieniawski	1975	UCS = 23∙I_s(50)	Sandstone	¹⁴
Guifu Xiang	1981	UCS=(18–19)∙I_s(50)(R² = 0.88)	Granite porphyry, calcareous siliceous siltstone	¹⁵	Axial
Vallejo et al༎	1989	UCS = 17.4∙I_s(50)	Sandstone	¹⁶
Tsiambaos et al༎	2004	UCS = 13∙I_s(50), (I_s(50)༜2MPa), (R² = 0.67)	Hard mudstone, sandstone, limestone	¹⁷
		UCS = 24∙I_s(50), (2MPa༜I_s(50)༜5MPa), (R² = 0.63)
		UCS = 28∙I_s(50), (I_s(50)༞5MPa), (R² = 0.74)
State Standard of PRC	2013	UCS = 22.82∙(I_s(50))^0.75(R² = 0.90)		¹⁸
Mishra and Basu	2013	UCS = 12.95∙I_s(50)-5.19	Sandstone	¹⁹
Zhiliang Fu et al༎	2013	UCS = 14.074∙I_s(50) + 7.201(R² = 0.985)	Siltstone, fine sandstone, medium sandstone, coarse sandstone, sandy mudstone, mudstone	²⁰	Axial
Zhiliang Fu et al༎	2013	UCS = 17.529∙I_s(50) + 13.938(R² = 0.971)		²⁰	Diametral
Lubin He et al༎	2014	UCS = 16.081∙I_s(50) (R² = 0.748)	Sandstone, siltstone, mudstone	²¹	Irregular
Elhakim	2015	UCS = 2.59∙I_s(50) + 0.21 (R² = 0.65)	Calcareous sandstone	²²
Quan Jiang et al.	2017	UCS=(17.65 ~ 25.2)∙I_s(50)	Sandstone, dolomite, basalt	²³
Jiaqi Chen et al.	2018	UCS = 22.72∙(I_s(50))^0.82 (R² = 0.860)	Sandstone, mudstone, limestone	²⁴	Irregular
Jiaqi Chen et al.		UCS = 26.24∙(I_s(50))^0.72 (R² = 0.860)	Sandstone, mudstone, limestone		Regular
Yanhui Guo et al.	2019	UCS = 20.61∙I_s(50)	Sandstone	²⁵	Dry
Yanhui Guo et al.	2019	UCS = 22.11∙I_s(50)	Sandstone	²⁵	Saturated
	2019	UCS = 21.65∙I_s(50)	Red sandstone	²⁶
Ling Dai et al.	2021	UCS = 17.01∙I_s(50)	Red sandstone	²⁷	Formula correction method
		UCS = 17.40∙I_s(50)			Graphing method
		UCS = 17.30∙I_s(50)			Radial
This study	UCS = 11.687∙(I_s(50))^0.8687 (R² = 0.9538)	Red sandstone		Vertical stratification
This study	UCS = 13.641∙(I_s(50))^0.9231 (R² = 0.9031)	Red sandstone		Parallel stratification

Many researchers have been studied on the correction index m. Wong et al. ²⁸ studied the granite samples with different weathering degrees, finding that the actual correction index m obtained by the regression of strength data of samples with different sizes was quite different from its recommended value in the specification. Yin et al. ²⁹ also found that in the size correction function, the correction index value m of slightly-weathered granite was around 0.443-0.600, and that of moderately-weathered granite was between 0.545–5.562. Li et al. ³⁰ used different loading methods (axial test and diametral test) to carry out the PLT, and obtained a correction index of 0.5. Yao et al. ³¹ conducted both the PLS test and UCS test on rock samples with vertical and parallel stratifications respectively, revealing that the correction index of gneiss was m = 0.44 under vertical stratification and m = 0.42 under parallel stratification. Dai et al. ²⁷ carried out the axial tests on three disc-shaped samples with different coring diameters, and obtained the results that the correction indexes m of marbles and red sandstones were 0.44 and 0.53 respectively.

At present, different researchers keep different conclusions about the empirical relationship and the correction index m between I_s(50) and UCS. Particularly, the relationship between I_s(50) and UCS of anisotropic rock need to be further investigated.

In this study, the red sandstone of Sinian Chengjiang Group retrieved from the downstream of Xiaopu 3# branch Cave in Yuxi section of the CYWD Project was taken as the research object. From the perspectives of parallel and vertical stratification, the UCS and the multiple sizes PLT of are conducted respectively, and the mechanical properties are analyzed in detail. The empirical relationship between I_s(50) and UCS, and the reference value of correction index m were obtained of red sandstone in Yuxi section of the CYWD Project.

2.1 Study Area

In this study, the red sandstone of Sinian Chengjiang Group retrieved from the downstream of Xiaopu 3# branch Cave in Yuxi section of the CYWD Project was taken as the research object. The samples’ location is E 102 42'24.92 ", N 24 35" 4.43 ", and the rock sample is purple red. According to the rock ore identification, fine-extremely fine-grained feldspar-quartz sandstone contains a small amount of very fine sand, silt composition contains quartz, feldspar, eruptive rock, aphanite, quartzite, chert, dolomite and other components. The composition of sandstone is complex, including quartz 81%, feldspar 10.5%, eruptive rock 1.0%, aphanite 1.5%, quartzite 2.0%, chert 2.5%, dolomite 14.0%, and the orthogonal polarimetric photograph of the sandstone microscope is shown in Fig. 1.


(a) Fine-extremely fine-grained sandy structure	(b) Containing fine-extremely fine-grained feldspar-quartz sandstone
Figure 1. Microscopic analysis for sample under microscope

2.2. Uniaxial Compressive Strength Test

Prepared by the automatic double-blade rock-core cutting machine (SCQ-4A), the diameter of the cylindrical core sample is set to 43.493–109.42 mm, the length of the core is 58.25-103.62 mm, and the aspect ratio is defaulted as 0.877 ~ 2.084. Following the ISRM ⁴ standard, red sandstone are tested, and their average value is taken as UCS of the sample (Table 2). According to ISRM ³², the aspect ratio of UCS is 2.0 (50mm×100mm). However, if the length diameter ratio is not 2.0, the USC is corrected on the basis of Eq. 1 ³³. During the test, both ends of the sample must be smooth and flat. The sample is loaded by the electro-hydraulic pressure tester (HYE-2000), the loading rate is controlled within the range of 1,000–2,000 N/s, and the maximum loading capacity is set to 2,000 kN. The processing and testing of red sandstone core is shown in Fig. 2.

Where L is length, D is diameter, and UCS^* is the UCS of the specimen at a ratio of L/D.




Figure 2. Test process of rock samples. (a) The rock core samples taken from the field, (b) Processed rock core sample, (c) Test process of UCS, (d) The rock core samples after test.

2.3. Point Load Test Index

PLTs of irregular blocks were carried out on red sandstone samples, as shown in Fig. 3.


Figure 3. PLTs of irregular blocks
The irregular specimen can be calculated by the method of equivalent core diameter, and the I_s(50) is determined by ASTM ³⁴ and standards ¹⁸ as Eq. 2–5:

$${D}_{e}^{2}=\frac{4\bullet W\bullet D}{\pi }$$

$${I}_{s}=\frac{P}{{D}_{e}^{2}}$$

$${I}_{s\left(50\right)}={I}_{s}\bullet F$$

$$F={\left(\frac{{D}_{e}}{50}\right)}^{m}$$

where P is the failure load and De is the equivalent diameter of irregular blocks, D and W are of the maximum length and average width of the failure surface in millimetres, m is the correction index.

Table 2

The test results of the PLT and UCS
Entry	D (mm)	W (mm)	De² (mm)	P (KN)	I_s(50) (MPa)	UCS (MPa)	Type
H-12	30.00	37.00	1414.01	8.89	5.55	69.52	∥
H-13	25.30	33.00	1063.57	7.02	5.47	58.00	∥
H-14	36.00	50.00	2292.99	14.96	6.40	85.31	∥
H-15	29.00	36.00	1329.94	7.55	4.94	59.36	∥
H-16	33.00	50.00	2101.91	11.94	5.47	64.39	∥
H-17	30.00	40.00	1528.66	8.25	4.84	58.09	∥
H-18	22.00	34.90	978.09	7.34	6.11	73.65	∥
H-19	25.00	30.00	955.41	6.78	5.75	68.93	∥
H-20	26.00	30.00	993.63	10.23	8.41	92.98	∥
H-21	26.00	29.00	960.51	4.55	3.84	47.60	∥
H-1	33.50	37.00	1578.98	27.87	16.08	129.6	⊥
H-2	28.60	35.00	1275.16	15.66	10.71	91.2	⊥
H-3	32.70	46.00	1916.18	24.08	11.91	101.2	⊥
H-4	38.00	45.00	2178.34	28.63	12.78	103.35	⊥
H-5	30.60	43.50	1695.67	26.47	14.43	123.35	⊥
H-6	23.00	30.00	878.98	13.83	12.73	109.69	⊥
H-7	29.00	39.00	1440.76	19.90	12.35	102.39	⊥
H-8	26.00	38.00	1258.60	18.85	13.03	106.9	⊥
H-9	34.00	40.20	1741.15	25.83	13.79	114.04	⊥
H-10	43.50	55.00	3047.77	35.31	12.06	103.78	⊥
H-11	30.60	35.00	1364.33	22.60	14.65	118.49	⊥

Various sizes of rock samples were selected for the PLT, and the results were corrected by Eq. 2–5. The results showed that I_s(50) under vertical stratification is significantly greater than I_s(50) under parallel stratification, and the point load strength of red sandstone has obvious anisotropy. This obvious difference of strength can be expressed by the point load strength anisotropy index β, and β = I'_s(50) / I"_s(50) = 2.31 (I'_s(50) is the point load strength index of vertical stratification, and I"_s(50) is the point load strength index of parallel stratification).

3.1. The Calculation of the Correction Index

According to the Standard for test methods of engineering rock mass ^[18], the correction index m = 2(1-n), where n is the slope of the logP-logD²e curve. The logP-logD²e curves of parallel stratification was showed in Fig. 4, and the logP-logD²e curves of vertical stratification was showed in Fig. 5.


Figure 4. The logP-logD²e curves of parallel stratification.	Figure 5. The logP-logD²e curves of vertical stratification.

The parallel stratification, n = 0.7952, m = 0.4096. The vertical stratification, n = 0.7796, m = 0.4408. The R² was 0.6223 and 0.8346, respectively, indicating that correlation for logP and logD²e was pretty. Meanwhile, the correction index was 0.4096 and 0.4408, both between 0.40 and 0.45^[18], indicating the feasibility of the PLT.

3.2. The Conversion Relationship between the I_s(50) and the UCS

SPSS 26.0 was adopted to analyze the data of I_s(50) and UCS, and the least square regression method was employed for I_s(50) - UCS fitting. Firstly, assume thatis a weight function, as a fitting function, determine, so that (Eq. 6–7):

The fitting function can be obtained.

R² is used to evaluate both the advantages and disadvantages of the model, i.e. the percentage of the regression squares' sum in the total squares' sum, as shown in Eq. 8.

The value range of R² is 0 ≤ R² ≤ 1. The closer R² is to 1, that is, the better the sample data fit the selected model, the higher the goodness of fit of the model. The statistical quantity can reflect the extent to which the model explains the variability of the dependent variable, and can also be interpreted as the percentage of the total variation of the dependent variable reduced by the regression Equation. The hypothesis test on the goodness of fit of the regression Equation based on the determination coefficient R² is completely equivalent to the analysis of variance of the entire regression Equation. See Eq. 9 for the calculation.

Where p is the number of independent variables in the model and n is the sample size.

3.2.1. The Conversion Relationship between the I_s(50) and the UCS for Parallel Stratification

The conversion relationship of I_s(50) and UCS for parallel stratification is shown in Fig. 6.


(a) Exponential function.	(b) Linear function.	(c) Logarithmic function.

(d) Quadratic function.	(e) Power function.
Figure 6. The functional relationship of I_s(50) and UCS for parallel stratification.

The R² of exponential, linear, logarithmic, quadratic and power functions is between 0.869–0.9031, indicating that the correlation for I_s(50) and UCS was pretty. The closer R² is near to 1, the higher the fitness is. Combining the inherent properties of the rock itself, the power function between I_s(50) and UCS was selected as the conversion relationship for the parallel stratification (Fig. 6).

3.2.2. The Conversion Relationship between the I_s(50) and the UCS for Vertical stratification

The conversion relationship of I_s(50) and UCS for vertical stratification is shown in Fig. 7.


(a) Exponential function.	(b) Linear function.	(c) Logarithmic function.

(d) Quadratic function.	(e) Power function.
Figure 7. The functional relationship of I_s(50) and UCS for vertical stratification

The R² of exponential, linear, logarithmic, quadratic and power functions is between 0.9478–0.9538, indicating that the correlation for I_s(50) and UCS was pretty. The closer R² is near to 1, the higher the fitness is. Combining the inherent properties of the rock itself, the power function between I_s(50) and UCS was selected as the conversion relationship for the vertical stratification (Fig. 7).

3.3. Compasion analysis with the other researchers’ study

Combined with the previous research results about the fitting function between I_s(50) and UCS of the red sandstone, the UCS calculated by using I_s(50) from different researchers are compared, and the results of the comparison was shown in Fig. 8.


Figure 8. The comparison of the conversion relationship between I_s(50) and UCS from different researchers

Parallel stratification’s I_s(50) is between 3.84–8.41 MPa, and vertical stratification’s I_s(50) is between 10.71–16.08 MPa. According to the I_s(50) and UCS conversion obtained in Fig. 8, both parallel stratification and vertical stratification are basically consistent with Jiaqi Chen’s results ^[24] (a) rule shape and standard ^[18], indicating that the power function relationship between I_s(50) and UCS of red sandstone is of great guiding significance.

In summary, the red sandstone of Xiaopu 3# branch Cave in Yuxi section of the CYWD Project was taken as the research object. The UCS and PLT of are conducted from the perspectives of vertical and parallel stratifications, respectively. The effection of correction index m on calculating red sandstone strength parameters was anylized and discussed, and the main conclusion are as follows:

1. The mechanical properties of red sandstone had obvious anisotropy. The difference in its mechanical properties is particularly evident in UCS and PLT, and I_s(50) and UCS under vertical stratification is significantly greater than I_s(50) under parallel stratification.

2. PLT is utilized to determine the degree of anisotropy of the rock. The anisotropy index of the red sandstone is β = 2.31.

3. The point load strength correction index m of red sandstone is m = 0.4096 under parallel stratification and m = 0.4408 under vertical stratification, which can be used as a reference for similar rocks.

4. The data obtained from field and laborator test was analyzed, and the conversion relationship between I_s(50) and UCS is power function under both parallel stratification and vertical stratification. The power function can provide a reference for engineering applications in Yuxi section of the CYWD Project.

Declarations

Competing interests

The authors declare no competing interests.

Acknowledgments

The Major Science and Technology Special Plan of Yunnan Province Science and Technology Department (202002AF080003), Gratitude to the sponsorship from National Natural Science Foundation of China (51669009), and the fund of Yunnan Institute of Water and Hydropower Engineering Investigation, Design and Research (KKKF0202006249).

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Abbreviations

Additional information

Correspondence and requests for materials should be addressed to M. W.

PRC		The People's Republic of China
CYWD Project		Central Yunnan Water Diversion Project
ASTM		American society for testing and materials
ISRM		International society for rock mechanics
UCS	Uniaxial compressive strength	PLT	Point load test
I_s(50)	Point load strength index	R²	Correlation coefficient

No competing interests reported.

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Study on the Mechanical Properties of Anisotropic Red Sandstone under Point Load Strength Test and Uniaxial Compression Strength

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Version 1

Abstract

1. Introduction

2. Study Area and Material

2.1 Study Area

2.2. Uniaxial Compressive Strength Test

2.3. Point Load Test Index

3. Result and Discussion

3.1. The Calculation of the Correction Index

3.2. The Conversion Relationship between the I_s(50) and the UCS

3.2.1. The Conversion Relationship between the I_s(50) and the UCS for Parallel Stratification

3.2.2. The Conversion Relationship between the I_s(50) and the UCS for Vertical stratification

3.3. Compasion analysis with the other researchers’ study

4. Conclusion

Declarations

Declarations

Acknowledgments

References

Unsectioned Paragraphs

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Additional Declarations

Status:

Version 1

Study on the Mechanical Properties of Anisotropic Red Sandstone under Point Load Strength Test and Uniaxial Compression Strength

Status:

Version 1

Abstract

1. Introduction

2. Study Area and Material

2.1 Study Area

2.2. Uniaxial Compressive Strength Test

2.3. Point Load Test Index

3. Result and Discussion

3.1. The Calculation of the Correction Index

3.2. The Conversion Relationship between the Is(50) and the UCS

3.2.1. The Conversion Relationship between the Is(50) and the UCS for Parallel Stratification

3.2.2. The Conversion Relationship between the Is(50) and the UCS for Vertical stratification

3.3. Compasion analysis with the other researchers’ study

4. Conclusion

Declarations

Declarations

Acknowledgments

References

Unsectioned Paragraphs

Unsectioned Tables

Additional Declarations

Status:

Version 1

3.2. The Conversion Relationship between the I_s(50) and the UCS

3.2.1. The Conversion Relationship between the I_s(50) and the UCS for Parallel Stratification

3.2.2. The Conversion Relationship between the I_s(50) and the UCS for Vertical stratification