09-202412-G23-0869一文审稿意见与作者答复

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03-202411-G23-0753⼀⽂审稿意⻅与作者答复 Download(2260KB)

03-202411-G23-0753⼀⽂审稿意⻅与作者答复

2024, 46(11): 2265-2274.

Three-dimensional limit equilibrium method for rock slopes by constructing normal stress distribution over sliding surface and its application .

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简写符号	表达式	简写符号	表达式	简写符号	表达式
$ {D_1} $	$ \iint { - {S_y}{\sigma _0}{\text{d}}x{\text{d}}y} $	$ {A_{14}} $	$ \iint {{S_x}}{\sigma _0}{\text{d}}x{\text{d}}y $	$ {A_{31}} $	$ \iint {{\sigma _0}(x + }S \cdot {S_x}){\text{d}}x{\text{d}}y $
$ {D_2} $	$ \iint { - {S_y}{\sigma _0}x{\text{d}}x{\text{d}}y} $	$ {A'_{14}} $	$ \iint { - (c + {\sigma _0}\tan \varphi )\frac{\mathit{\Delta }}{{{\mathit{\Delta } '}}}}{\text{d}}x{\text{d}}y $	$ {A'_{31}} $	$ \iint {(x{S_x} - S)\frac{\mathit{\Delta }}{{{\mathit{\Delta } '}}}\tan \varphi {\sigma _0}}{\text{d}}x{\text{d}}y $
$ {D_3} $	$ \iint { - {S_y}{\sigma _0}y{\text{d}}x{\text{d}}y} $	$ {A_{21}} $	$ \iint {{\sigma _0}{\text{d}}x{\text{d}}y} $	$ {A_{32}} $	$ \iint {{\sigma _0}(x + }S \cdot {S_x})x{\text{d}}x{\text{d}}y $
$ {D_4} $	$ \iint {{S_y}{\sigma _0}{\text{d}}x{\text{d}}y} $	$ {A'_{21}} $	$ \iint {{S_x}\frac{\mathit{\Delta }}{{{\mathit{\Delta } '}}}\tan \varphi }{\sigma _0}{\text{d}}x{\text{d}}y $	$ {A'_{32}} $	$ \iint {(x{S_x} - S)\frac{\mathit{\Delta }}{{{\mathit{\Delta } '}}}\tan \varphi {\sigma _0}}x{\text{d}}x{\text{d}}y $
$ {A_{11}} $	$ \iint { - {S_x}}{\sigma _0}{\text{d}}x{\text{d}}y $	$ {A_{22}} $	$ \iint {{\sigma _0}x{\text{d}}x{\text{d}}y} $	$ {A_{33}} $	$ \iint {{\sigma _0}(x + }S \cdot {S_x})y{\text{d}}x{\text{d}}y $
$ {A'_{11}} $	$ \iint {\frac{\mathit{\Delta }}{{{\mathit{\Delta } '}}}\tan \varphi }{\sigma _0}{\text{d}}x{\text{d}}y $	$ {A'_{22}} $	$ \iint {{S_x}\frac{\mathit{\Delta }}{{{\mathit{\Delta } '}}}\tan \varphi }{\sigma _0}x{\text{d}}x{\text{d}}y $	$ {A'_{33}} $	$ \iint {(x{S_x} - S)\frac{\mathit{\Delta }}{{{\mathit{\Delta } '}}}\tan \varphi {\sigma _0}}y{\text{d}}x{\text{d}}y $
$ {A_{12}} $	$ \iint { - {S_x}}{\sigma _0}x{\text{d}}x{\text{d}}y $	$ {A_{23}} $	$ \iint {{\sigma _0}y{\text{d}}x{\text{d}}y} $	$ {A_{34}} $	$ M - \iint {{\sigma _0}(x + }S \cdot {S_x}){\text{d}}x{\text{d}}y $
$ {A'_{12}} $	$ \iint {\frac{\mathit{\Delta }}{{{\mathit{\Delta } '}}}\tan \varphi }{\sigma _0}x{\text{d}}x{\text{d}}y $	$ {A'_{23}} $	$ \iint {{S_x}\frac{\mathit{\Delta }}{{{\mathit{\Delta } '}}}\tan \varphi }{\sigma _0}y{\text{d}}x{\text{d}}y $	$ {A'_{34}} $	$ \iint { - (c + {\sigma _0}\tan \varphi )(x{S_x} - S)\frac{\mathit{\Delta }}{{{\mathit{\Delta } '}}}}{\text{d}}x{\text{d}}y $
$ {A_{13}} $	$ \iint { - {S_x}}{\sigma _0}y{\text{d}}x{\text{d}}y $	$ {A_{24}} $	$ W - \iint {{\sigma _0}{\text{d}}x{\text{d}}y} $
$ {A'_{13}} $	$ \iint {\frac{\mathit{\Delta }}{{{\mathit{\Delta } '}}}\tan \varphi }{\sigma _0}y{\text{d}}x{\text{d}}y $	$ {A'_{24}} $	$ \iint { - (c + {\sigma _0}\tan \varphi ){S_x}\frac{\mathit{\Delta }}{{{\mathit{\Delta } '}}}}{\text{d}}x{\text{d}}y $

Symbols corresponding to specific expressions

参数	滑面ABC	滑面ABD
重度γ/(kN·m^-3)	25.0	25.0
单轴抗压强度σ_ci/MPa	0.818	0.682
完整岩石材料参数m_i	20	15
地质强度指标GSI	100	75
扰动因子D	0	0
m_b	20	6.142
s	1	6.22×10^-2
a	0.5	0.501

Material parameters of rock mass

计算方法计算结果误差/%

逐点等效M-C(本文方法) 3.562

广义H-B（Deng^[20]） 3.593 0.86

等效M-C（Deng^[20]） 4.657 23.51

Calculated results of stability coefficient of example 1

计算方法	计算结果	误差/%
逐点等效M-C(本文方法)	3.562
广义H-B（Deng^[20]）	3.593	0.86
等效M-C（Deng^[20]）	4.657	23.51

参数	取值
重度γ/(kN·m^-3)	25.0
单轴抗压强度σ_ci/MPa	0.4
完整岩石材料参数m_i	8
地质强度指标GSI	60
扰动因子D	0
m_b	1.917
s	1.17×10^-2
a	0.503
σ_tm/kPa	2.44
A	0.5630
B	0.6933

Parameters of rock mass and Hoek-Brown criterion

计算方法	计算结果	误差/%
逐点等效M-C(本文方法)	1.614
常规等效M-C(卢坤林等^[8])	1.913	15.63
常规等效M-C（三维楔形体法）	1.921	15.98

计算方法	计算结果	误差/%
逐点等效M-C(本文方法)	2.547
常规等效M-C（朱大勇等^[3]）	2.922	12.83

参数	取值
重度γ/(kN·m^-3)	23.0
单轴抗压强度σ_ci/MPa	0.081
完整岩石材料参数m_i	15
地质强度指标GSI	70
扰动因子D	0
m_b	5.138
s	3.57×10^-2
a	0.501
σ_tm/kPa	0.842
A	0.7771
B	0.7101

Material parameters of rock mass

n	逐点等效M-C（本文）	常规等效M-C（朱大勇等^[3]）	二维（Li等^[21]）	误差/%
1	1.100	1.210		9.15
2	1.079	1.179		8.46
5	1.073	1.170		8.27
10	1.072	1.168		8.23
20	1.072	1.168		8.22
∞			1.002

Calculated results of stability coefficient of example 4

参数	取值
重度γ/(kN·m^-3)	28.0
单轴抗压强度σ_ci /MPa	10
完整岩石材料参数m_i	6
地质强度指标GSI	26
扰动因子D	0.8
m_b	0.0733
s	1.4×10^-5
a	0.529

计算方法	计算结果	误差/%
逐点等效M-C(本文方法)	0.942
常规等效M-C（朱大勇等^[3]）	1.154	18.37

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