杭州新奥土木工程技术有限公司 | 岩土及隧道设计工具箱

Tunnel Blasting Design

Tunnel Blasting Design

Delay-Charge Distribution

Maximum Charge Vibration Analysis

Rock Mass Strength based on Generalized Hoek-Brown Criterion

Select Evaluation Position:

Prj

Tnl

CLn

Chn

Input Parameters: (Stress unit: MPa)

Modulus Estimation Method:

Method

Hoek-Brown Criterion:

m_b
s
a

Rock Mass Parameters:

σ_t			σ_c
σ_cm			E_rm

Input Parameters
intact uni. comp. strength (σ_ci)=MPa
GSI= m_i= Disturbance factor (D)=
intact modulus (E_i)=MPa
Hoek-Brown Criterion
m_b= s= a=

Rock Mass Parameters
tensile strength (σ_t)=MPa
uni. comp. strength (σ_c)=MPa
global strength (σ_cm)=MPa
modulus of deformation (E_rm)=MPa
Mohr-Coulomb Fit
cohesion(c)=MPa friction angle(φ)=°

References:

Uniaxial Compressive Strength of Intact Rock σ_ci Dialog

Field estimate of strength

Examples

Uniaxial Compressive Strength (MPa)

Specimen can only be chipped with a geological hammer

Fresh basalt, chert, diabase, gneiss, granite, quartzite

Specimen requires many blows of a geological hammer to fracture it

Amphibolite, sandstone, basalt, gabbro, gneiss, granodiorite, limestone, marble, rhyolite, tuff

Specimen requires more than one blow of a geological hammer to fracture it

Limestone, marble, phyllite, sandstone, schist, shale

Cannot be scraped or peeled with a pocket knife, specimen can be fractured with a single blow from a geological hammer

Claystone, coal, concrete, schist, shale, siltstone

Can be peeled with a pocket knife with difficulty, shallow indentation made by firm blow with point of a geological hammer

Chalk, rocksalt, potash

Crumbles under firm blows with point of a geological hammer, can be peeled by a pocket knife

Highly weathered or altered rock

Indented by thumbnail

Stiff fault gouge

uniaxial compressive strength (σ_ci)

MPa

GSI Calculation Dialog

S_i (Spacing between each set of discontinuity)
J_a (Joint Alteration Number)
J_r (Joint Roughness Number)
J_cond89
J_v(Volumetric Joint Count)
RQD

Rock Type

GSI Value

Mi Dialog

Select mi value from the list and click x to close the dialog.
	mi

Disturbance Factor (D) Dialog

Tunnel Slope

Appearance of rock mass	Description of rock mass	Suggested value of D
	Excellent quality controlled blasting or excavation by Tunnel Boring Machine results in minimal disturbance to the confined rock mass surrounding a tunnel.
	Mechanical or hand excavation in poor quality rock masses (no blasting) results in minimal disturbance to the surrounding rock mass.
	Where squeezing problems result in significant floor heave, disturbance can be severe unless a temporary invert, as shown in the photograph, is placed.	No invert
	Very poor quality blasting in a hard rock tunnel results in severe local damage, extending 2 or 3 m, in the surrounding rock mass.

Appearance of rock mass	Description of rock mass	Suggested value of D
	Small scale blasting in civil engineering slopes results in modest rock mass damage, particularly if controlled blasting is used as shown on the left hand side of the photograph. However, stress relief results in some disturbance.	Good blasting
		Poor blasting
	Very large open pit mine slopes suffer significant disturbance due to heavy production blasting and also due to stress relief from overburden removal. In some softer rocks excavation can be carried out by ripping and dozing and the degree of damage to the slopes is less.	Production blasting
		Mechanical excavation

Disturbance factor D

Intact Rock Elastic Modulus (Ei) Dialog

Select the modulus ratio (MR). Intact modulus (Ei) will be automatically calculated by multiplication of the modulus ratio (MR) by the uniaxial compressive strength of the intact rock (σ_ci):
Ei = MR x σ_ci

MR
σ_ci
Ei

关于...

Hoek-Brown强度准则在国际上已广泛应用于矿业工程、隧道工程、高边坡工程等行业，该方法的理论系统性和基于工程实践的合理性也逐渐被国内岩石力学学术界所认识与接受，但在设计、施工等工程界却尚未得到广泛应用。本网页旨在生产部门应用该准则提供便利的工具。

发展历程：

Hoek-Brown强度准则是用于预测岩石破裂的经验公式。1980年，Evert Hoek（津巴布韦裔加拿大人）和E. T. Brown（澳大利亚布里斯班人）两人在研究地下开挖工程时，推导出该经验公式；1988年，两人又合作发表文章，把该理论推广至露天开采和边坡稳定性的研究；2002年，Hoek等人引入地质强度指标（GSI）参数，给岩土工程师提供了定量分析岩体应力状态和Bieniawski的岩体质量指标（RMR）及地质强度指标理论（GSI）理论之间的关系，尽可能的反映原岩的各项物理参数以及岩体的结构面状态。2018年进一步更新了相关参数。

人物简介：

Evert Hoek （1933-2024），岩石力学专家，他于1958年开始研究南非深部金矿中的脆性岩石力学问题，并于1965年在开普敦大学攻读博士学位。同年他在英国帝国理工学院皇家矿业学院建立了岩石力学中心。1968年，他在那里开发了岩石力学三轴试验。1975年，他成为多伦多大学的教授，同时在温哥华的Golder Associates担任高级咨询工程师长达12年。退休后一直以独立咨询师的身份参与岩石力学研究与工程。

局限与改进：

二维Hoek-Brown（H-B）强度准则未考虑中间主应力影响，亚利桑那州立大学章连洋教授、同济大学朱合华教授等提出了Generalized Zhang-Zhu（GZZ）强度准则，以反映中间主应力对岩体强度的影响规律，揭示岩体强度和破坏模式在π平面和子午面上的双重非线性拉压（脆-延）转化规律，且与二维H-B准则共享参数体系，是真正意义上的三维H-B强度准则。该准则已被国际岩石力学界高度认可，本网页后续将增加该准则。

备注：

The front-end HTML code of this webpage is partly based on the work of Dr. Mikola.

Support Pressure Curve (Based on Longitudinal Displacement Profiles for Convergence Confinement Analysis)

Select Evaluation Position:

Prj

Tnl

CLn

Chn

Input Parameters:

Section ID
Area		m²
Bolt longitudinal spacing		m
Advance length		m
Poisson's Ratio
Plastic zone radius		m (optional)
Elastic Plastic(R<=2) Plastic(R>2)

Output Parameters:

Dist. btw face and bolts, X		m
Equivalent radius, R_t		m
Normalised dist. to face		m
Radial convergence
Support pressure		%

Staging:

0. Excavation		%
1. Install bolts, pre-tension & grout		%
2. Bolts fully bonded		%
3. Additional stage		%
4. Fully exvacated		%
5. Bench excavation		%
6. Tunnel fully excavated		%

Empirical Longitudinal Displacement Profiles

Panet's (1995) Empirical Correlation for Elastic Solution (X/Rt >= 0)
Unlu & Gercek's (2003) Empirical Correlation for Elastic Solution (X/Rt < 0)
Chern's (1998) Empirical Correlation for Plastic Solution

Modified Longitudinal Displacement Profiles Considering Plastic Zone

Studies by the Vlachopoulos & Diederichs (2009) have shown that the longitudinal displacement profile function proposed by Panet (1995) and by Unlu and Gercek (2003) is reasonable for plastic analysis provided that the radius of the plastic zone does not exceed 2 tunnel radii and provided that the yielding zone in the tunnel face does not interact with the developing yield zone around the tunnel walls.
In order to account for the influence of increased overall yielding on the shape of the normalized longitudinal displacement profile, the most logical index to relate to the longitudinal displacement profile function is the normalized plastic zone radius, R* = R_P / R_T, where R_P stands for plastic zone radius.

References:

Improved Longitudinal Displacement Profiles for Convergence Confinement Analysis of Deep Tunnels

关于...

1. 在二维有限元分析中模拟隧道开挖和支护时，需要通过施加支护力（support pressure）的方式来模拟掌子面附近发生的约束和松弛，这通常可以采用收敛-约束分析法和隧道纵向位移曲线。

2. 对于埋深较浅或者岩质较硬的隧道，预期隧道周边的收敛变形仍处于弹性阶段，此时，可以使用Panet（1995）提出、并被国际著名岩石力学专家Hoek等人（2008）肯定的经验公式进行评估，对于掌子面前方尚未开挖段，即围岩体内的变形量，则可以采用Unlu & Gercek（2003）提出的经验公式进行评估。

3. 在埋深、或者高地应力、或者软岩情况下，隧道开挖可能会出现大量岩体屈服，在这些情况下，可以采用Chern（1998）提出的经验公式进行评估。

4. Vlachopoulos和Diederichs（2009）的进一步研究表明，Panet， Unlu & Gercek提出的纵向位移曲线合理性的前提是塑性区的半径不超过2倍隧道半径，并且隧道掌子面前方的屈服区未与隧道四周的屈服区贯通。否则，他们建议对Chern提出的曲线进行修正，具体地说就是引入了归一化塑性区半径，R*=R_p/R_t，其中R_p代表塑性区的半径。

5. 本网页同时对隧道开挖模拟过程中各施工步（staging）的设定、以及对应的支护压力比例提出了建议。

6. 更详细的背景知识可参阅参考文献。

Support Stiffness vs Time Curve

Select support type

Project

Tunnel

SC parameters(unit: MPa)

fc_1d	3d	28d
strength gain	Include the fibre capacity?	Model
Residual tensile strength f_r1	f_r4	f_r1.5
Concrete Density(kg/m³)	Poisson ratio	alpha_E
Ultimate tensile strain	Compressive stress-strain mode	alpha_cc

Steel parameters(unit: MPa)

fy(MPa)

E(MPa)

Use lattice gird

No	Diameter(mm)	Depth(mm)	Spacing(mm)	Install state
1
2
3
4

Use steelset

Type	Depth(mm)	Spacing(mm)	Install stage

Construction parameters

cut arear(m²)		step length(m)		shift time(h)
Thickness(mm)				Initial Age(h)

Tools:

EA, EI results

Distance from face	Age of oldest shotcrete		SC thickness	Axial stiffness	Bending stiffness	Equivalent layer properties			RS2 STAGING FACTORS		PROPORTION OF ORIGINAL INDUCED STRESS
				Axial stiffness	Bending stiffness	Poisson's ratio	Thickness	Modulus	RS2 STAGING FACTORS		PROPORTION OF ORIGINAL INDUCED STRESS
				EA	EI	ν	t_equiv	E_equiv	Thickness	Young's Modulus	Panet	Chern
(m)	(h)	(d)	(mm)	(MN/m)	(MN.m²/m)		(m)	(MPa)	Thickness	Young's Modulus	Panet	Chern

The values of "distance from excavation face" corresponding to construction step 8 in the table and curve graph are for illustration only, and should actually be the distance corresponding to the 28 day age;
Click on the construction step number to view the corresponding support bearing capacity M-N envelope diagram and export it;
When using steel arches, the bearing capacity M-N is an approximate value.

Axial and Bending Stiffness Curve

Support Presure Curve

SC Stress vs Age Curve

About...

1. As the strength and elastic modulus of sprayed concrete are related to its age, the development of the stiffness of the sprayed concrete lining over time (or distance from the face of the tunnel) should also be considered when using finite element analysis for calculation.

2. Knowing the development process of stiffness EA and EI over time, the stiffness reduction factors for each construction step can be set in finite element software, such as in Rocscience RS2.

3. f_ci=f_c28*e^{(s*(1-sqrt(24 * 28 / t)))}, s refers to strength gain factor, 0.33 as default.

4. E_ci=0.043*ρ^1.5*sqrt(0.9*f_ci*(1.2875-0.001875*f_ci)), ρ refers to density, 2400kg/m³ as default.

5. This tool can consider spraying the sprayed concrete lining in up to 5 times, with the option to set the "thickness of each layer t (mm)" separately. The time interval between the two sprays is the "duration of each shift (h)". During this time interval, the tunnel advances forward by one "construction step distance (m)".

6. This tool also provides calculation of support force, including Panet's (1995) empirical formula and Chern's (1998) empirical formula. For more detailed background knowledge, please refer to the "Support Pressure Time Curve" tool.

StageCapacity(M-N Diagram)

隧道洞门土压力荷载
HB Eq

边坡参数

仰坡坡度:
仰坡坡角ε(°):
计算内摩擦角φ(°):
边坡土重度γ(kN/m³):
基底摩擦系数f:
基地控制压应力(kPa):
坡角与墙顶距离a(m):
土压计算模式不确定系数ξ:

挡墙参数

宽度B(m):
高度H(m):
计算条带宽度T(m):
容重γ(kN/m³):
墙面倾角α(°):

计算结果

土压力E(kN):
作用点高度h'(m):
抗倾覆安全系数K_o
抗倾覆安全系数K_e
基底压应力σ(kPa):

明洞设计荷载计算
HB Eq

隧道参数

围岩级别s:
隧道宽度B(m):
隧道高度H_t(m):
埋深H(m):
设计填土面坡度角α(°):
回填土石面坡率m:
开挖边坡坡率n:

拱背回填土

重度γ₁(kN/m³):
计算内摩擦角φ₁:
回填土石与开挖边坡面间的摩擦系数μ:
侧压力作用方向与水平线夹角ρ(°):

墙背回填土

重度γ₂(kN/m³):
计算内摩擦角φ₂(°):

拱圈计算结果

计算点深度h_i(m):
垂直压力q_i(kPa):
拱圈侧压力e_i(按无限土体计算)(kPa):
拱圈侧压力e_i(按有限土体计算)(kPa):

边墙计算结果

计算点深度h_i(m):
边墙内侧侧压力e_i(kPa):
边墙外侧侧压力e_i(kPa):
侧压力e_i(坡面水平)(kPa):

偏压隧道衬砌荷载
HB Eq

基本参数

围岩级别s:
隧道宽度B(m):
隧道高度H_t(m):
埋深H(m):
重度γ(kN/m³):
地面坡角α(°):
计算内摩擦角φ(°):
顶板土柱两侧摩擦角θ(°):

计算结果

垂直压力Q(kN):
内侧压力q₁(kPa):
外侧压力q₂(kPa):
内侧水平侧压力e_i(kPa):
内侧水平侧压力e₂(kPa):
外侧水平侧压力e₁(kPa):
外侧水平侧压力e₂(kPa):

深埋/浅埋隧道荷载
HB Eq

隧道参数

围岩级别s:
隧道宽度B(m):
隧道高度H_t(m):
埋深H(m):
重度γ(kN/m³):
水平侧压力系数e:
计算内摩擦角φ(°):
滑面摩擦角θ(°):

计算结果

荷载等效高度h_q(m):
浅埋隧道分界深度H_p(m):
深埋(H>Hp,适用于VI级)
深埋(H>Hp,适用于I-V级围岩)
浅埋1(埋深H＜hq)
浅埋2(hq＜H＜Hp)
垂直均布压力q(kPa):
平均水平侧压力e(kPa):
侧压力e₁(kPa):
侧压力e₂(kPa):

Rockburst Proneness Index (RPI) Calculator

Parameteres

Depth of Cover(H, meters):
UCS of Intact Rock (σ_ci, MPa)::
m_bof HB model:
s of HB model:
a of HB model:

Rockburst Proneness Index (RPI)

σ_max=(0.0273*H)+16.807:
σ₃=(0.0341*H)+4.423:
σ_rm:
RPI:

reference Novel rockburst criterion based on the TBM tunnel construction of the Neelum–Jhelum (NJ) hydroelectric project in Pakistan

Canopy designer

Geotech

Variable	Unit	Description
γ	kN/m³	Specific weight of ground
c	kN/m²	Cohesion
φ	°	Friction angle
λ	-	Horiz. earth pressure coef.
w	m	Width of the tunnel
H	m	Overburden
p	kN/m²	Load on ground surface

Canopy Tubes

L_f	m	Length of canopy tubes
d_o	mm	Outer diameter of canopy tube
t	mm	Tube wall thickness
fy	MPa	Yield stress of canopy tube
E_S	MPa	Modulus of canopy tube steel
E_G	MPa	Modulus of cement grout
b_i	m	Spacing of canopy tube
β	°	Vertical inclination of canopy tube
R	m	Radius of tunnel crown
M_{el, th}	kNm	E-moment for threaded connection

Steel set or lattice girder

d	m	Spacing of lattice girders
L₁	m	Advance length
h	m	Excavation height
δ	°	Angle of the excavated tunnel face

Factors

η	-	Factor to determine location of full fixity
l_f	-	Load factor
γ_s	-	Partial material factor for steel

Equivalent load

L_c=R/sinβ=	m	Length to notional centre point for installtion of canopy tubes
α=b_i/b_f=	rad
b=(L_c+L_f)*α=	m	Influence width @ canopy tubes end
R_m=	m	Mean radius of the silo
p₁ =	kN/m/tube	Total load on canopy tube area
p₀ =	kN/m/tube	Load on single canopy tube

1. Bending moment check

Variable	Unit	Boundary condition

M_A=M_B=-p₁*l²/12=	kN.m	Fixed on both ends
M_A=0...M_B=-p₁*l²/8=	kN.m	Pinned - fixed support

Section modulus
Z_tube=		mm³	Z_grout,tube=		mm³

Moment capacity		Fixed+Fiexed	Pinned+Fixed
M_allow=	kN.m
M_allow,grout=	kN.m
M_allow,thread=	kN.m

2. Back-analysis (unit: m)

Variable	Value	Result
b_req=
b_req,thread=
b_req,A=
b_req,B=

3. Maximum load (unit: kN/m)

Variable	Value
p₀=
p_0,thread=
p_0,A=
p_0,B=
p_max=
p_max,thread=

Tools

Rock-support Interaction

Rock mass

Variable	Unit	Description
d	m	Depth of cover to tunnel crown
γ_g	MN/m³	Unit weight of ground
σ_c	MPa	Intact rock UCS
m_i	-	Hoek Brown contants for original rockmass
s_i		Hoek Brown contants for original rockmass
E	MPa	Young's modulus for original rockmass
ν	-	Poisson's ratio for original rockmass
m_r	-	Hoek Brown contants for broken rock mass
s_r	-	Hoek Brown contants for broken rock mass
γ_r	MN/m³	Unit weight of broken rock mass
r_i	m	Radius of tunnel
p_o	MPa	Initial vertical stress
p_icr	MPa	Critical support pressure
p_icr/p_o	MPa

Concrete or shotcrete lining

E_c	MPa	Modulus of elasticity of concrete or shotcrete
ν_c	-	Poisson's ratio of concrete or shotcrete
t_c	m	Thickness of lining
σ_c	MPa	Uniaxial compressive strength of concrete or shotcrete
γ_c	kN/m³	Unit weight of concrete or shotcrete
u_i	m	Deformation before support installation
k_c	MPa	Support stiffness
p_scmax	m	Maximum support pressure

Ungrouted mechanically or chemically anchored bolts

L	m	Free bolt or cable length
d_b	m	Bolt diameter
E_b	MPa	Modulus of elasticity of bolt
Q	m/MN	Load-deformation constant for anchor and head (anchor stiffness)
T_bf	MN	Ultimate failure load from pull-out test
s_c	m	Circumferential bolt spacing
s_l	m	Longitudinal bolt spacing
u_i	m	Deformation before support installation
k_c	MPa	Support stiffness
p_scmax	m	Maximum support pressure

Blocked steel sets

Section
S	m	Steel set spacing along tunnel axis
θ	°	Angle between blocking points
t_B	m	Thickness of blocking
E_B	MPa	Elastic modulus of block material
W	m	Flange width of steel set
X	m	Depth of section of steel set
A_s	m²	Cross-sectional area of steel set
I_s	m⁴	Moment of inertia of steel section
E_s	MPa	Modulus of elasticity of steel section
σ_ys	MPa	Yield strength of steel
u_i	m	Deformation before support installation
k_c	MPa	Support stiffness
p_scmax	m	Maximum support pressure

Tools

Rock-support Interaction Curve

Curve type:	Tunnel deformation vs Support Pressure Relative tunnel deformation vs Support Pressure
X/Y axial range:	X:	Y:

Ground stiffenining by pre-stressed anchors

Rock mass & bolts

Variable	Unit	Description
σ_o	MPa	Insitu hydrostatic stress
r_o	m	Tunnel radius
c	MPa	Rock mass cohesion
φ	°	Rock mass friction angle
n	-	No. of anchors around circumference / metre length
l	m	Length of bolts
A	kN	Pre-stress force in each anchor

Calculation of support pressure

Variable	Unit	Description
p	MPa	Support pressure for general ground
	%	As a percentage of insitu stress
p	MPa	Support pressure for cohesion-less ground
	%	As a percentage of insitu stress

Reference: Kolymbas, Tunnelling and tunnel mechanics - a rational approach to tunnelling, 2005

Intermediate Calculations	Formula	Value
		m (equivalent depth, γ=25kN/m³)
		m (circumference)
		radians
		m (average bolt spacing)
		MN
Kp	(1+SIN(φ))/(1-SIN(φ))
ro÷(ro+l)	ro/(ro+len)
1st term	sig(1-SIN(φ))ratio^(Kp-1)
2nd term	nA/(2PI()ro)(1-ratio^Kp)
3rd term	c/TAN(φ)*(1-ratio^(Kp-1))
4th term	cCOS(φ)ratio^(Kp-1)

Shotcrete - Equivalent Support Pressure

Shotcrete lining parameters

	1d	3d	7d	28d
Characteristic compressive strength, f_c (MPa)
Partial strength factor, γ:
Concrete Density (kg/m³):
Design compressive strength, σ_c (MPa)
Young's modulus, E_c (MPa):
Poisson's ratio, ν_c:
Equivalent tunnel radius, r_i (m):
Factor of Safety, FoS:

Shotcrete lining equivalent support pressure

Shotcrete thickness, t_c (mm)
Maximum support pressure (kPa)	1d
	3d
	7d
	28d
Design support pressure (kPa)	1d
	3d
	7d
	28d

Support stiffness

Shotcrete thickness, t_c (m)
Support Stiffness (MPa)	1d
	3d
	7d
	28d

Maximum support pressure curve Curve type: Maximum support pressure Design support pressure Support Stiffness

Tunnel Rock Mass Properties

Poisson Ratio		Elastic Modulus (GPa)
Rock Density (kg/m³)		UCS (MPa)
Tensile Strength (MPa)		Cohesion (MPa)
Internal Friction Angle (°)		Rock Quality Designation (%)
hard average soft K		β

Crosssection (example) m x x: y: Add a borehole

Blastholes (example)

No	X	Y	Group	Type	Diameter (mm)	Depth (m)	Linear charge load (g/m)	Length (m)	Coupling Ratio	Weight	Actions
template for new blasthole

Delay-Charge Distribution

Max. Charge Vibration Analysis Any distance: m -> PPV: mm/s Go to Ventilation Design

Set up parameters for automatic blastholes layout

Distance between cut-holes (mm)
Distance between cut-hole rows (mm)
Distance between aux-holes (mm)
Layer thickness W (mm)
Distance between perimeter holes (mm)
Distance between bottom holes (mm)
Coupling ratio
Turning point index between crown and invert

Application

Unit Weight

Tunnel Depth