CN110306548B - Method for calculating anchoring force of long anchor cable penetrating through full-filling karst cave - Google Patents
Method for calculating anchoring force of long anchor cable penetrating through full-filling karst cave Download PDFInfo
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- E—FIXED CONSTRUCTIONS
- E02—HYDRAULIC ENGINEERING; FOUNDATIONS; SOIL SHIFTING
- E02D—FOUNDATIONS; EXCAVATIONS; EMBANKMENTS; UNDERGROUND OR UNDERWATER STRUCTURES
- E02D33/00—Testing foundations or foundation structures
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- E—FIXED CONSTRUCTIONS
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- E02D—FOUNDATIONS; EXCAVATIONS; EMBANKMENTS; UNDERGROUND OR UNDERWATER STRUCTURES
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Abstract
The invention discloses a method for calculating the anchoring force of a long anchor cable penetrating through a full-filling karst cave, which comprises the steps of establishing a corresponding coordinate system according to the relative position relationship between a karst cave section and an anchoring shear stress section, through which a long anchor cable penetrates; then considering the weakening influence of the existence of the karst cave on the length of the anchor cable penetrating through the non-karst cave section, and determining the weakened effective length from the anchoring initial end to the karst cave; further regarding the long anchor cable passing through the karst cave section as an ideal elastic axial tensile rod piece, calculating the relative displacement of two ends of the long anchor cable when the long anchor cable passes through the unfilled karst cave, and obtaining the calculation method of the anchoring force of the long anchor cable passing through the unfilled karst cave; and finally, equating the uniformly distributed shear stress borne by the anchor cable passing through the full-filling karst cave part to one end close to the anchoring initial end of the anchor cable, and determining the equivalent length of the karst cave of the filling part to the equivalent rock mass length of the non-karst cave rock mass, so that the full-filling karst cave is converted into the non-filling karst cave, and the method for calculating the anchoring force of the long anchor cable passing through the full-filling karst cave is obtained.
Description
Technical Field
The invention relates to the technical field of underground engineering, in particular to a method for calculating the anchoring force of a long anchor cable penetrating through a full-filling karst cave.
Background
With the continuous promotion of urban three-dimensional traffic construction and deep foundation pit engineering in China, anchor cable anchoring construction operation becomes one of key factors influencing the safety of a supporting structure. The anchor cable support can give full play to the energy of the rock-soil mass, improve the unfavorable stress state of the rock-soil mass, mobilize and improve the self-strength and self-stability of the rock-soil, thereby greatly lightening the dead weight of the support structure, saving engineering materials and shortening the construction period, and therefore, the anchor cable support is widely applied. The wide application of the anchor cable promotes the research of anchor design and calculation. Because the stratum penetrated by the anchor cable is generally complex, the regularity of the change of the anchor cable is difficult to reflect by the calculation of the anchoring force of the anchor cable by using a numerical simulation method, and the anchoring mechanism of the anchor cable is difficult to study. Therefore, many scholars have attempted to reflect changes in the anchorage force of the anchor line in the form of analytical solutions.
In order to ensure the safety of a supporting structure in construction, the conventional anchor cable anchoring force calculation formula generally regards an anchor cable as an ideal elastic body, and establishes the calculation formula of the anchor cable anchoring force under the ideal condition based on the assumed condition that the anchoring body is in a limit state and the shearing stress is uniformly distributed along an anchoring section. The formulas can guide anchor construction operation of the anchor cable to a certain degree and reflect the variation trend of the anchoring force, but the standard value given by the formulas is still conservative due to the fact that actual engineering conditions are not considered, and the tensile capacity of the anchor cable is limited to a certain degree. In the related theoretical analysis of similar problems, most of the actual stratum conditions are not comprehensively considered, the elastoplasticity ideal condition and the ideal stratum condition are usually only considered independently, and in fact, once the stratum is discontinuous, the full-filling karst stratum is usually generated, and the part of the anchor cable anchoring body penetrating through the karst cave is reduced to a certain extent due to the fact that the shearing rigidity of the filling material is reduced to a certain extent compared with the shearing rigidity of the stratum of the non-karst cave section, so that the corresponding anchor cable anchoring force is reduced to a certain extent.
Therefore, how to establish a method for calculating the anchoring force of the long anchor cable in the fully-filled karst stratum to guide the construction of the anchor cable and ensure the safety of the deep foundation pit is a problem to be solved urgently in the field of construction safety of the current supporting structure.
Disclosure of Invention
The invention aims to solve the technical problem of providing an anchor cable anchoring force calculation method considering the influence of penetration of a full-filling type karst stratum aiming at the defects of the existing long anchor cable anchoring force calculation method.
In order to achieve the technical purpose, the technical scheme of the invention is that,
a method for calculating the anchoring force of a long anchor cable penetrating through a full-filling karst cave comprises the following steps: establishing a corresponding coordinate system according to the relative position relation between the karst cave section through which the long anchor cable passes and the anchoring shear stress section; then considering the weakening influence of the existence of the karst cave on the length of the anchor cable penetrating through the non-karst cave section, and determining the weakened effective length from the anchoring initial end to the karst cave; further regarding the long anchor cable passing through the karst cave section as an ideal elastic axial tensile rod piece, calculating the relative displacement of two ends of the long anchor cable when the long anchor cable passes through the unfilled karst cave, and obtaining the calculation method of the anchoring force of the long anchor cable passing through the unfilled karst cave; and finally, equating the uniformly distributed shear stress borne by the anchor cable passing through the full-filling karst cave part to one end close to the anchoring initial end of the anchor cable, and determining the equivalent length of the karst cave of the filling part to the equivalent rock mass length of the non-karst cave rock mass, so that the full-filling karst cave is converted into the non-filling karst cave, and the method for calculating the anchoring force of the long anchor cable passing through the full-filling karst cave is obtained.
The method for calculating the anchoring force of the long anchor cable penetrating through the full-filling karst cave comprises the following steps of: and establishing a z-axis coordinate system by taking the anchoring initial end of the anchor cable as an original point and the length direction of the anchor cable as a z-axis. The coordinate system established comprises only the z-axis
The method for calculating the anchoring force of the long anchor cable penetrating through the full-filling karst cave takes the weakened effective length from an anchoring initial end to the karst cave as xi x; wherein x is the distance between the karst cave section and the anchoring initial end; xi is a reduction coefficient of the length of the anchor cable passing through the non-karst cave considering the existence of the karst cave, and the value range is more than or equal to 0 and less than or equal to 1. The reduction coefficient is related to the mechanical strength of the rock mass in the non-karst cave section, and the higher the strength of the rock mass is, the larger the value is. For example, common limestone, which has a value of 0.5.
The method for calculating the anchoring force of the long anchor cable penetrating through the full-filling karst cave is characterized in that the relative displacement delta l of the two ends of the long anchor cable penetrating through the non-filling type karst cave is calculated according to the following formula:
Δl＝C1cosh(βξx)+C2sinh(βξx)-C3cosh[β(ξx+s)]-C4sinh[β(ξx+s)]；
wherein:
wherein C is1、C2Respectively is a constant coefficient of a shear stress function of an anchoring initial section of the non-solution cavity section of the anchoring body; c3、C4The constant coefficient is the shear stress function of the anchoring tail section of the non-solution cavity section of the anchoring body; d is the diameter of the anchor hole; d is the diameter of the anchor cable; tau is1maxThe elastic limit bonding strength of the grouting body;
beta is a contact parameter of the non-karst cave section anchoring body and the rock mass; k1For anchoring body formation shear stiffness, EaIs the composite modulus of elasticity; s is the diameter of the karst cave; l ismIs the anchoring length; sinh is a hyperbolic sine function; cosh is a hyperbolic cosine function; and tanh is a hyperbolic tangent function, P is the anchoring force of the long anchor cable penetrating through the unfilled karst cave, and pi is the circumferential rate.
The method for calculating the anchoring force of the long anchor cable penetrating through the full-filling karst cave, EaCalculated using the formula:
wherein ErAnd EsRespectively is the elastic modulus of the grouting body and the elastic modulus of the anchor cable, and n is the number of the anchor cables.
The method for calculating the anchoring force of the long anchor cable penetrating through the full-filling type karst cave comprises the following steps:
the method for calculating the anchoring force of the long anchor cable penetrating through the full-filling karst cave is characterized in that the uniformly distributed shear stress borne by the anchor cable penetrating through the full-filling type karst cave part is equivalent to one end which is closer to the anchoring initial end of the anchor cable, and the equivalent rock mass length l from the filling part karst cave to the non-karst cave rock mass is as follows:
wherein M, f and a are constants related to the length l of the equivalent rock mass respectively.
According to the method for calculating the anchoring force of the long anchor cable penetrating through the full-filling karst cave, M is calculated by adopting the following formula:
wherein, K2Shear stiffness for a full-filling type karst cave filling;
lambda is a contact parameter of the anchor body of the full-filling karst cave section and the filler; b. c are constants related to the equivalent anchoring length, respectively; f and a are calculated by the following formula: f ═ C1sinh(βx)-C2cosh(βx)；a＝C1cosh(βx)-C2sinh(βx)。
In the method for calculating the anchoring force of the long anchor cable penetrating through the full-filling karst cave, b and c are respectively calculated by adopting the following formulas:
b＝C3{cosh[β(x+s)]-tanh(βLm)sinh[β(x+s)]}；
c＝cosh(λx)sinh[λ(x+s)]-sinh(λx)cosh[λ(x+s)]；
the method for calculating the anchoring force of the long anchor cable penetrating through the full-filling type karst cave comprises the following steps:
wherein, PmaxThe ultimate anchoring force of the long anchor cable penetrating through the full-filling karst cave.
Compared with the prior art, the invention has the beneficial effects that: the invention belongs to an analytic calculation method, which has the characteristics of quickness, simplicity, convenience, reliability and low calculation cost; firstly, the anchoring force of the anchor rope without the filled karst cave part is not considered in calculation, the section without the filled karst cave is regarded as a section without shear stress, the influence of the karst cave without the filled cave on the stress of the anchor rope anchoring body can be considered, and the influence of the strain at two ends of the karst cave can be considered, so that the actual stress state of the anchor rope passing through the karst stratum without the filled cave can be simulated more reasonably, and the calculation of the anchoring force of the anchor rope passing through the karst stratum without the filled cave is more accurate and reliable; and the full-filling karst cave section is equivalent, the equivalent length is calculated, the calculation can be carried out according to the non-filling type karst cave, the calculation formula of the anchorage force of the anchor cable of the karst stratum is enriched, and the calculation formula is more fit with the actual engineering conditions.
Drawings
FIG. 1 is a diagram of the calculation steps;
FIG. 2 is a model diagram of the distribution of shear stress of the anchor cable anchoring body of the fully-filled karst cave stratum in the invention;
FIG. 3 is a model diagram of the distribution of the equivalent shear stress of the anchor cable of the full-filling karst cave portion of the present invention.
In the figure: 1, anchor cable; 2-anchoring body at the side close to the anchoring initial end, the length of the anchoring body is x, and the shear stiffness of the anchoring body is K1(ii) a 3-passing through the part of the karst cave anchoring body, with the length of s and the shear rigidity of K2(ii) a 4-the anchoring body is closer to the anchoring tail end, the length is Lm-s-x, and the shear stiffness is K1(ii) a 5-the anchor rope passes through the equivalent anchoring length of the full-filling karst cave section, the length is l, and the shearing rigidity is K1. FIG. 2 is a schematic diagram showing the distribution of shear stress when an anchor cable penetrates through a full-filling type karst cave, wherein the shear stiffness of the anchor body penetrating through the karst cave is different from the anchor body on the side closer to the anchor starting end and the anchor body on the side closer to the anchor tail end, so that the shear stress distributed on the anchor bodies of the 3 parts is equivalent to the 1 part, the shear stiffness of the equivalent part of the 3 parts is identical to the shear stiffness of the 2 parts and the shear stiffness of the equivalent part of the 3 parts, but the equivalent part of the 3 parts is identical to the shear stiffness of theThe length is shortened to l.
Detailed Description
The invention discloses a method for calculating the anchoring force of a long anchor cable penetrating through a full-filling karst cave, which comprises the steps of establishing a corresponding coordinate system according to the relative position relationship between a karst cave section and an anchoring shear stress section, through which a long anchor cable penetrates; then considering the weakening influence of the existence of the karst cave on the length of the anchor cable penetrating through the non-karst cave section, and determining the weakened effective length from the anchoring initial end to the karst cave; further regarding the long anchor cable passing through the karst cave section as an ideal elastic axial tensile rod piece, calculating the relative displacement of two ends of the long anchor cable when the long anchor cable passes through the unfilled karst cave, and obtaining the calculation method of the anchoring force of the long anchor cable passing through the unfilled karst cave; and finally, equating the uniformly distributed shear stress borne by the anchor cable passing through the full-filling karst cave part to one end close to the anchoring initial end of the anchor cable, and determining the equivalent length of the karst cave of the filling part to the equivalent rock mass length of the non-karst cave rock mass, so that the full-filling karst cave is converted into the non-filling karst cave, and the method for calculating the anchoring force of the long anchor cable passing through the full-filling karst cave is obtained.
The method specifically comprises the following calculation steps:
(1) and (4) determining relevant parameters according to the relative position relation between the karst cave section through which the long anchor cable passes and the anchoring shear stress section. The anchoring initial end of the anchor cable is used as an original point, and the length direction of the anchor cable is used as a z-axis. I.e. a coordinate system comprising only the z-axis is established.
(2) The weakened effective length from the anchoring initial end to the karst cave is xi x; x is the distance between the karst cave section and the anchoring initial end; xi is a reduction coefficient of the length of the anchor cable passing through the non-karst cave considering the existence of the karst cave, and the value range is more than or equal to 0 and less than or equal to 1. The reduction coefficient is related to the mechanical strength of the rock mass in the non-karst cave section, and the higher the strength of the rock mass is, the larger the value is. For example, the value of common limestone is 0.5.
(3) When the long anchor cable penetrates through the non-filled karst cave, the relative displacement delta l of the two ends is as follows:
Δl＝C1ch(βξx)+C2sh(βξx)-C3ch[β(ξx+s)]-C4sh[β(ξx+s)]；
wherein:
C1、C2respectively is a constant coefficient of a shear stress function of an anchoring initial section of the non-solution cavity section of the anchoring body; c3、C4The constant coefficient is the shear stress function of the anchoring tail section of the non-solution cavity section of the anchoring body; d is the diameter of the anchor hole; d is the diameter of the anchor cable; tau is1maxThe elastic limit bonding strength of the grouting body;
beta is a contact parameter of the non-karst cave section anchoring body and the rock mass; k1For anchoring body formation shear stiffness, EaIs the composite modulus of elasticity; s is the diameter of the karst cave; l ismIs the anchoring length; sinh is a hyperbolic sine function; cosh is a hyperbolic cosine function; and tanh is a hyperbolic tangent function, P is the anchoring force of the long anchor cable penetrating through the unfilled karst cave, and pi is the circumferential rate.
(4)EaCalculated using the following formula:
Erand EsRespectively representing the elastic modulus of the grouting body and the elastic modulus of the anchor cable, wherein n is the number of the anchor cables; and pi is the circumferential ratio.
(5) After the relative displacement delta l of the two ends of the long anchor cable penetrating through the non-filled karst cave is obtained through calculation, the anchoring force of the long anchor cable penetrating through the non-filled karst cave is further calculated, and the corresponding calculation formula is as follows:
wherein, the delta l is specifically expressed as a corresponding partial value on the right side of the formula according to the calculation formula.
(6) The equivalent length l of the filling part karst cave to the equivalent rock mass of the non-karst cave rock mass is as follows:
wherein M, f and a are constants related to the length l of the equivalent rock mass respectively.
(7) The full-filling karst cave calculation parameter M is calculated by adopting the following formula:
wherein, K2Shear stiffness for a full-filling type karst cave filling;
lambda is a contact parameter of the anchor body of the full-filling karst cave section and the filler; b. c are constants related to the equivalent anchor lengths, respectively.
(8) The full-filling karst cave calculation parameters f, a, b and c are calculated by adopting the following formula:
f＝C1sinh(βx)-C2cosh(βx)；
a＝C1cosh(βx)-C2sinh(βx)；
b＝C3{cosh[β(x+s)]-tanh(βLm)sinh[β(x+s)]}；
c＝cosh(λx)sinh[λ(x+s)]-sinh(λx)cosh[λ(x+s)]；
(9) the calculation formula of the anchoring force of the long anchor cable penetrating through the full-filling karst cave is as follows:
wherein, PmaxThe ultimate anchoring force of the long anchor cable penetrating through the full-filling karst cave.
Claims (10)
1. A method for calculating the anchoring force of a long anchor cable penetrating through a full-filling karst cave is characterized by comprising the following steps: establishing a corresponding coordinate system according to the relative position relation between the karst cave section through which the long anchor cable passes and the anchoring shear stress section; then considering the weakening influence of the existence of the karst cave on the length of the anchor cable penetrating through the non-karst cave section, and determining the weakened effective length from the anchoring initial end to the karst cave; further regarding the long anchor cable passing through the karst cave section as an ideal elastic axial tensile rod piece, calculating the relative displacement of two ends of the long anchor cable when the long anchor cable passes through the unfilled karst cave, and obtaining the calculation method of the anchoring force of the long anchor cable passing through the unfilled karst cave; and finally, equating the uniformly distributed shear stress borne by the anchor cable passing through the full-filling karst cave part to one end close to the anchoring initial end of the anchor cable, and determining the equivalent length of the karst cave of the filling part to the equivalent rock mass length of the non-karst cave rock mass, so that the full-filling karst cave is converted into the non-filling karst cave, and the method for calculating the anchoring force of the long anchor cable passing through the full-filling karst cave is obtained.
2. The method for calculating the anchorage force of the long anchor cable penetrating through the full-filling karst cave according to claim 1, wherein the establishing of the corresponding coordinate system is as follows: and establishing a z-axis coordinate system by taking the anchoring initial end of the anchor cable as an original point and the length direction of the anchor cable as a z-axis.
3. The method for calculating the anchoring force of the penetrating full-filling karst cave long anchor rope according to claim 1, wherein the weakened effective length from an anchoring initial end to the karst cave is ξ x; wherein x is the distance between the karst cave section and the anchoring initial end; xi is a reduction coefficient of the length of the anchor cable passing through the non-karst cave considering the existence of the karst cave, and the value range is more than or equal to 0 and less than or equal to 1.
4. The method for calculating the anchoring force of the long anchor cable penetrating through the full-filling type karst cave according to claim 3, wherein the relative displacement delta l of the two ends of the long anchor cable penetrating through the unfilled type karst cave is calculated by the following formula:
Δl＝C1cosh(βξx)+C2sinh(βξx)-C3cosh[β(ξx+s)]-C4sinh[β(ξx+s)]；
wherein:
wherein C is1、C2Respectively is a constant coefficient of a shear stress function of an anchoring initial section of the non-solution cavity section of the anchoring body; c3、C4The constant coefficient is the shear stress function of the anchoring tail section of the non-solution cavity section of the anchoring body; d is the diameter of the anchor hole; d is the diameter of the anchor cable; tau is1maxThe elastic limit bonding strength of the grouting body;
beta is a contact parameter of the non-karst cave section anchoring body and the rock mass; k1For anchoring body formation shear stiffness, EaIs the composite modulus of elasticity; s is the diameter of the karst cave; l ismIs the anchoring length; sinh is a hyperbolic sine function; cosh is a hyperbolic cosine function; and tanh is a hyperbolic tangent function, P is the anchoring force of the long anchor cable penetrating through the unfilled karst cave, and pi is the circumferential rate.
5. The method for calculating the anchorage force of the long anchor cable penetrating through full-filling karst cave according to claim 4, wherein E isaCalculated using the formula:
wherein ErAnd EsRespectively is the elastic modulus of the grouting body and the elastic modulus of the anchor cable, and n is the number of the anchor cables.
6. The method for calculating the anchorage force of the traversing full-filling type karst cave long anchor cable according to claim 4, wherein the calculation formula of the anchorage force of the traversing non-filling type karst cave long anchor cable is as follows:
Δl＝C1cosh(βξx)+C2sinh(βξx)-C3cosh[β(ξx+s)]-C4sinh[β(ξx+s)]
7. the method for calculating the anchoring force of the anchor cable penetrating through the full-filling type karst cave according to claim 4, wherein the uniformly distributed shear stress borne by the anchor cable penetrating through the full-filling type karst cave part is equivalent to one end which is closer to the anchoring initial end of the anchor cable, and the length of the filling part of the karst cave equivalent to the equivalent rock mass length l of the un-karst cave rock mass is as follows:
wherein M, f and a are constants related to the length l of the equivalent rock mass respectively.
8. The method for calculating the anchorage force of the long anchor cable penetrating through the full-filling karst cave according to claim 7,
m is calculated by the following formula:
wherein, K2Shear stiffness for a full-filling type karst cave filling;
lambda is a contact parameter of the anchor body of the full-filling karst cave section and the filler; b. c are constants related to the equivalent anchoring length, respectively; f and a are calculated by the following formula:
f＝C1sinh(βx)-C2cosh(βx)；a＝C1cosh(βx)-C2sinh(βx)。
9. the method for calculating the anchorage force of the long anchor cable penetrating through the full-filling karst cave according to claim 8, wherein b and c are respectively calculated by adopting the following formulas:
b＝C3{cosh[β(x+s)]-tanh(βLm)sinh[β(x+s)]}；
c＝cosh(λx)sinh[λ(x+s)]-sinh(λx)cosh[λ(x+s)]。
10. the method for calculating the anchorage force of the traversing full-filling type karst cave long anchor cable according to claim 4, wherein the calculation formula of the anchorage force of the traversing full-filling type karst cave long anchor cable is as follows:
wherein, PmaxThe ultimate anchoring force of the long anchor cable penetrating through the full-filling karst cave.
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