CN106682318A - Method for computing primary supporting opportunity on basis of longitudinal deformation curves of surrounding rock of tunnels - Google Patents

Abstract

The invention discloses a method for computing primary supporting opportunity on the basis of longitudinal deformation curves of surrounding rock of tunnels. The method includes steps of 1, building three-dimensional numerical models of the tunnels, excavating the tunnels step by step according to reasonable excavation footage and recording change conditions of displacement values of typical locations of monitoring sections of the surrounding rock of the tunnels along with advancing of excavation faces; 2, establishing function relations between surrounding rock displacement completion rates of tunnel monitoring points in three-dimensional computation models and the advancing distances of the excavation faces; 3, simulating tunnel excavation by the aid of one-step excavation schemes and recording change conditions of displacement of surrounding rock monitoring points in excavation load release procedures; 4, substituting the determined surrounding rock displacement completion rates during primary supporting into surrounding rock longitudinal section deformation curve formulas obtained at the step 2 by means of fitting and computing the distances from the excavation faces to supporting application locations which are lagged behind or pulled ahead of the excavation faces during primary supporting. The method has the advantage that computation results are the distances of the supporting application locations relative to the excavation working faces and can be directly used in engineering construction sites.

Description

A kind of initial support opportunity computational methods based on Wall Rock of Tunnel linear deformation curve

Technical field

The present invention relates to tunnel numerical simulation analysis field, specifically a kind of according to the first of country rock linear deformation curve Secondary supporting time computational methods.

Background technology

As rock is theoretical and the development of method for numerical simulation, tunnel excavation is just carried out with numerical simulation more and more Research and analyse.Under normal circumstances, rock mass is affected by factors such as various natural stress and form of construction work and technologies, and tunnel is opened Country rock is vulnerable to destruction during digging.Understand according to document, most of tunnel accident was betided after excavation in shorter a period of time, was now enclosed Rock ensures its stability mainly by self-bearing ability and initial support, therefore initial support is particularly significant.But according to theory of new Austrian tunnelling method, If too early, the self-bearing capacity of country rock fails to play completely, easily causes supporting and causes because of the extruding of surrouding rock deformation for supporting Damage, therefore an important parameter of initial support opportunity when being tunnel design.

By give full play to country rock from bearing capacity based on convergence-confinement method, highlight country rock and supporting shared Excavation loads, become tunnel stability analysis and design of its support main flow, with on-site supervision e measurement technology and numerical computations it is soft The application of part, convergence-confinement method is further improved.Country rock linear deformation curve is the important portion of convergence-confinement method Point, can intuitively reflect the steric effect of surrouding rock deformation in tunnel excavation recommendation process, surrouding rock deformation is monitored, set up country rock Relation between displacement completion rate and excavation face advance distance, can be to determine the position that initial support applies relative to excavation face Intuitively numerical basis are provided, therefore the determination of country rock linear deformation curve designs significant to tunnel support.

Country rock linear deformation curve can record monitoring point by carrying out step excavation simulation to tunnel Three-dimensional CAD Displacement is obtained with the change that excavation face is advanced, but the amount of calculation of threedimensional model is generally larger, and using in engineering will increase Plus human cost and calculating time.If the country rock linear deformation curve equation with universality, available in Practical Project Field monitoring surrounding rock displacement data carry out the fitting of linear deformation curve.

There is problems with existing initial support computational methods：(1) initial support is more according to Jing in Three-dimensional simulation Selection is tested, without clear and definite judgment principle；(2) the country rock linear deformation curve with universality that can be used in Practical Project Formula；(3) the three-dimensional simulation calculating time is long, increases workload.

The content of the invention

In view of the shortcomings of the prior art, the invention provides a kind of true based on country rock linear deformation curve matching formula Computational methods of the fixed optimal applying initial support relative to excavation face position.

The present invention is as follows to solve the technical scheme that problems of the prior art are adopted：

A kind of initial support opportunity computational methods based on Wall Rock of Tunnel linear deformation curve, comprise the steps：

Step 1, sets up the Three-dimension Numerical Model of tunnel, progressively excavates by Rational Excavation drilling depth, records as excavation face is pushed away Enter the situation of change of Wall Rock of Tunnel monitoring section exemplary position shift value；

Step 2, based on the concept of displacement completion rate, is fitted to country rock vertical section deformation curve formula, sets up three-dimensional Functional relationship in computation model between tunnel monitoring point surrounding rock displacement completion rate λ and excavation face advance distance x；

Step 3, according to the tunnel Three-dimensional CAD set up, using the once side of excavating based on broad sense Virtual-supporting-force Method Case simulates tunnel excavation, and excavation loads progressively discharge, and records the change feelings of wall rock's level point displacement during excavation loads release Condition, using at displacement increment mutation as the basis for estimation on initial support opportunity, it is determined that now corresponding to excavation loads release rate Surrounding rock displacement completion rate λ_s；

Step 4, by surrounding rock displacement completion rate λ when carrying out initial support determined by step 3_sBack substitution enters in step 2 The country rock vertical section deformation curve formula that fitting is obtained, when being calculated initial support, the applying position of supporting falls behind or advanced Excavation face apart from x.

Described step 2 specifically includes following sub-step：

Step 2.1, surrounding rock displacement completion rate λ of Three-dimension Numerical Model adopts formula (1)

λ (z, p)=u (z, p)/u (∞, p) (1)

In formula, z is the distance of excavation face and monitoring section, meets by more than 7 times holes footpath is taken before and after monitoring section and requires； U (z, p) be monitoring point p excavation face apart from monitoring section be z when shift value；(∞ is p) monitoring point p to u in excavation face distance Shift value during monitoring section infinity；

Step 2.2, sets up surrounding rock displacement completion rate λ and excavation face to the relation between the distance of monitoring section, according to public Formula (2) carries out the fitting of country rock vertical section deformation curve, determines parameter lambda₀And X；

In formula, λ is surrounding rock displacement completion rate；X is the distance of excavation face and monitoring section；λ₀It is that excavation face arrival monitoring is disconnected Surrounding rock displacement completion rate during face；X is constant,

Described step 3 is adopted based on broad sense Virtual-supporting-force Method once according to the tunnel Three-dimensional CAD set up Excavate program simulation tunnel excavation, by country rock excavation loads decile, for example, be divided into 10 parts, per part 10% is progressively applied to excavation side In boundary, the situation of change of wall rock's level point displacement during excavation loads release is recorded, calculate the displacement increment of monitoring point, country rock Displacement increment is represented using formula (3)：

Δ u (r)=u (r)-u (r-10%) (3)

In formula, u (r) is displacement of the monitoring point when excavation loads release rate is r；Δ u (r) is monitoring point displacement increment；

With the excavation loads release rate r at displacement increment mutation₀As the opportunity for applying initial support, it is determined that now excavating Load releasing rate r₀Corresponding surrounding rock displacement completion rate λ_s。

Described step 4 is specially will determine surrounding rock displacement completion rate λ when carrying out initial support in step 3_sSubstitute into step The country rock vertical section deformation curve deformation formula for obtaining, i.e. formula (3) are fitted in rapid 2：

When being calculated initial support, supporting apply position fall behind or advanced excavation face apart from x.

The invention has the advantages that：

1st, the function expression of the rock mass linear deformation based on displacement completion rate and face advance distance is established；

2nd, the design parameter of linear deformation function expression is determined by numerical result fitting；

3rd, the displacement completion rate by advising is directly substituted in the function expression of determination, can easily calculate face Advance distance (preliminary bracing distance)；

4th, the diagram method in Patents is instead of using the mathematic calculation (function expression) with universality, is carried High computational accuracy；

5th, scheme of wearing will once be dug and based on the step excavation scheme combination for restraining leash law based on Virtual-supporting-force Method Together, to provide the selection for excavating initial support opportunity, with tight logicality；

6th, country rock linear deformation curve can not only pass through the Three-dimension Numerical Model result of calculation number for intending iterative method scheme According to obtaining, and can be obtained according to formula fitting by the Monitoring Data of field monitoring point shift value, be suitable for extensive Property；

7th, the inventive method is adopted, position when result of calculation applies for supporting is relative to the distance for excavating face, letter It is clean to understand, can be directly engineering construction onsite application.

Description of the drawings

Fig. 1 is the inventive method flow chart；

Fig. 2 is computation model and monitoring section schematic diagram；

Fig. 3 is III class surrounding rock monitoring point Displacement Evolution；

Fig. 4 is that monitoring point P1 correspondings (6) fitting result is contrasted with monitoring result；

Fig. 5 is monitoring point P1 correspondings (6) fitting result and [- 20,0] place partial enlarged drawing in monitoring result；

Fig. 6 is the relation of surrounding rock displacement completion rate and excavation face propulsion；

Fig. 7 is that monitoring point P1 formulas (9) fitting result is contrasted with monitor value；

Fig. 8 is II class surrounding rock monitoring point Displacement Evolution；

Based on the contrast of formula (5), the fitting result of formula (8) and monitor value when Fig. 9 is II class surrounding rock；

Figure 10 is IV class surrounding rock monitoring point Displacement Evolution；

Figure 11 is that IV class surrounding rock is contrasted in formula (5), formula (8) fitting result and monitor value；

Figure 12 is resultant displacement increment under the conditions of II class surrounding rock with excavation loads release rate variation relation figure；

Figure 13 is II class surrounding rock condition bottom offset completion rate with excavation loads release rate variation relation figure；

Figure 14 is resultant displacement increment under the conditions of III class surrounding rock with excavation loads release rate variation relation figure；

Figure 15 is III class surrounding rock condition bottom offset completion rate with excavation loads release rate variation relation figure；

Figure 16 is resultant displacement increment under the conditions of IV class surrounding rock with excavation loads release rate variation relation figure；

Figure 17 is IV class surrounding rock condition bottom offset completion rate with excavation loads release rate variation relation figure.

Specific embodiment

Below by embodiment, and accompanying drawing is combined, technical scheme is described in further detail, such as Fig. 1 Shown, a kind of initial support opportunity computational methods based on Wall Rock of Tunnel linear deformation curve are comprised the following steps that：

Step 1, sets up the Three-dimensional CAD of tunnel, progressively excavates by a certain Rational Excavation drilling depth, records with excavation The situation of change of the shift value of face propulsion Wall Rock of Tunnel monitoring point.

Step 2, based on the concept of displacement completion rate, is fitted based on the country rock vertical section deformation curve formula for proposing, The functional relationship between tunnel monitoring point surrounding rock displacement completion rate and excavation face advance distance in Three-dimensional CAD is set up, concrete bag Include following sub-step：

Step 2.1, after tunnel excavation, early stage affects the deformation of Wall Rock of Tunnel to be mainly reflected in the space effect of excavation face Should, the effect of contraction of rock mass of the rock mass not excavated in face of tunnel excavation to having excavated is steric effect, country rock linear deformation Curve intuitively embodies the steric effect excavated in progradation.Imitate in the space that displacement completion rate λ can be defined to weigh excavation face Should, i.e., it is remote not empty by excavation face enough with excavation face distance in certain point p holes wall surrouding rock deformation value at excavation face certain distance z Between the effect of restraint same position, the ratio of deformation values in same direction that affect, the surrounding rock displacement for obtaining Three-dimension Numerical Model is complete It is as follows into rate λ formula (1)：

λ (z, p)=u (z, p)/u (∞, p) (1)

In formula, z is the distance of excavation face and monitoring section, it is considered that more than 7 times holes footpath is taken before and after monitoring section； U (z, p) be monitoring point p excavation face apart from monitoring section be z when shift value；(∞ is p) monitoring point p to u in excavation face distance Shift value during monitoring section infinity；

Step 2.2, sets up surrounding rock displacement completion rate λ and excavation face to the relation between x of monitoring section, according to public Formula (2) carries out the fitting of country rock vertical section deformation curve, determines parameter lambda 0 and X.

In formula, λ is surrounding rock displacement completion rate；X is the distance of excavation face and monitoring section；λ 0 is that excavation face arrival monitoring is disconnected Surrounding rock displacement completion rate during face；X is constant,

Step 3, according to the Three-dimensional CAD for building up, using the once digging based on broad sense Virtual-supporting-force Method scheme is worn, By country rock excavation loads decile, for example, 10 parts are divided into, per part 10% is progressively applied on excavation border, and record excavation loads are released The situation of change of wall rock's level point displacement during putting, calculates the displacement increment of monitoring point, and surrounding rock displacement increment adopts formula (3)

Δ u (r)=u (r)-u (r-10%) (3)

In formula, u (r) is displacement of the monitoring point when excavation loads release rate is r；Δ u (r) is monitoring point displacement increment；

Using the excavation loads release rate r0 at displacement increment mutation as the opportunity for applying initial support, it is determined that now excavating Surrounding rock displacement completion rate λ s corresponding to load releasing rate r0.

Step 4, surrounding rock displacement completion rate λ s back substitutions when determination is carried out into initial support enter to be fitted the country rock for obtaining vertical disconnected Facial disfigurement curve, i.e. formula (4)

When being calculated initial support, supporting apply position fall behind or advanced excavation face apart from x.

In above-mentioned computational methods, in step 2.2 with regard to surrounding rock displacement completion rate λ and excavation face to monitoring section apart from x Between relation foundation, Main Basiss are with regard to the pass of tunnel rock displacement and excavation face to monitoring section distance in prior art Be formula, i.e. formula (5)：

In formula：λ₀Surrounding rock displacement completion rate when excavation face reaches monitoring section；X is constant,The present invention is borrowed Mirror formula (5) form, i.e., describe longitudinal rule of tunnel using piecewise function form, can obtain good simulation effect.

Embodiment 1

Computation model is set up with certain water supply project water-conveyance tunnel standard paragraphs T18+800.00, wherein country rock based on III class, Tunnel buried depth 696.6m, excavates hole footpath 2R=5.49m, and model boundary is taken away from tunnel center 30m, and along hole axis direction 140m is taken, Model surrounding and bottom apply Normal Displacement constraint, and top applies vertical uniform stress to simulate top covering effect, refers to Fig. 2, Mining in Rock Mass Mohr-Coulomb yield criterions, the total nodes of model are 45443, and total unit number is 42280.In Y 4 monitoring points are set at=70m at section tunnel top, bottom and two waists and refer to monitoring point p1, p2, p3, p4 distribution position in Fig. 2 Put.It is vertical to adopt weight stress field stimulation, lateral pressure coefficient K to stress_x=K_y=0.5.

The calculating parameter of the example of table 1

By taking III class surrounding rock hole section as an example, tunnel buried depth is 696.6m, adopts driving 5m every time to push away with the excavation for simulating tunnel Enter process, record the surrounding rock displacement change of each monitoring point of monitoring section.As seen from Figure 3, in digging process, in excavation face also By monitoring section and apart from about 4 Bei Dong footpaths of monitoring section when, there is deformation, but shift value very little in monitoring point；With Excavation face is close to and passes through, and measuring point surrounding rock displacement starts rapid increase；Excavation face is gradually distance from after monitoring section, monitoring Section surrounding rock displacement continues to increase to and tend towards stability after maximum；The monitoring point P1 on hole top reaches enclosing after stablizing in monitoring section Rock shift value is maximum, about 11.4mm, and the final surrounding rock displacement of monitoring point P2, P4 of two waists is minimum, about 3.7mm.

The surrounding rock displacement data for choosing the maximum dangerous spot P1 of change in displacement are analyzed below, are calculated often step and is excavated P1 The displacement release coefficient of point, inverting is carried out using wheat quart method and general Global Optimization Method to the parameter in existing formula (5), can ：

Error analyses show, fitting variance SSE=0.0117 of formula (6), coefficient R=0.9983, whole structure compared with It is good, refer to Fig. 4 and Fig. 5.

Although the overall correlation coefficient of fitting formula (6) is higher, it has larger error of fitting in displacement initiating terminal, such as Shown in Fig. 5, i.e. formula (6) country rock when excavation face is apart from monitoring surface 5m or so starts displacement occur, and rapid after displacement increases suddenly Reach it is stable, with real process in there is deformation before excavation face not yet reaches monitoring section earlier when, and increasing suddenly Remain afterwards and be not substantially inconsistent in a rule for being stepped up section, refer to Fig. 4 and Fig. 5.Intend to the basic of formula (5) for this this patent Form is improved, and matching accuracy of the general-purpose type (5) in initiating terminal is improved, in fig. 6 it can be seen that because formula (5) is in x It is continuous at=0, thus (0, λ₀) place's structure tangential equation：

The projection that can be obtained at λ=1 and λ=0 in x-axis is respectively：X and(negative value), refers to Fig. 6.

There is opportunity to shift to an earlier date compared with theoretical derivation of displacement in country rock country rock in actual digging process, thus herein in x< 0 and x>0 part introduces respectively proportionality factors lambda₀With 1- λ₀, that is, pressRatio to X and X₁Substitute into after being amplified Can obtain in formula：

According to monitoring displacement value, data fitting and parameter determination are carried out using formula (8), can be obtained：λ₀=0.258, X= 2.845, corresponding expression formula is：

Obtained according to result of calculation：Fitting variance SSE=0.0093, coefficient R=0.9989, fitting result has been carried Height, the displacement fitting effect of simultaneous displacement initiating terminal is significantly better than formula (6), refers to Fig. 7.Meanwhile, should by the modification formula for proposing II class, IV class surrounding rock hole section are used, result of calculation is respectively as illustrated in figs. 8-11.

The displacement data that surrounding rock displacement changes maximum hazards monitoring point is fitted according to formula, there is good plan Result is closed, the universality of formula is reflected.From Figure 10 and Figure 11, the convergence observation of surrounding rock displacement is related to quality of surrounding rock, Quality of surrounding rock is poorer, and not significantly, country rock produces obvious the space constraint effect of excavation face before excavation face reaches monitoring section Displacement is more early, and surrouding rock deformation is bigger, reaches final convergence more late.

It is theoretical based on Virtual force, the analogy method for discharging by stages is worn using once digging, research Wall Rock of Tunnel is to excavate Load deformation rule by stages under release conditions, refers to shown in Figure 12-17.Can be seen that from Figure 12-17：In excavation loads release Initial stage, surrouding rock deformation increases with the increase of excavation loads, and both are approximate linear, but have arrived construction and excavation load and released Put the later stage, surrouding rock deformation is presented the trend that increase suddenly, and surrounding rock displacement increases suddenly after such as III class surrounding rock load releasing reaches 80%, explanation Tunnel periphery rock mass now will should take supporting measure into plastic yielding stage.

Formula (8) is converted to into x coordinate can obtain with regard to the formula of displacement completion rate：

Known displacement completion rate λ=λ can be corresponded to from formula (10)_sX coordinate value x_s, as supporting is relative to excavation face Distance, if x₁<0, illustrate to need advance support, if x₁>0, it is x that explanation can pass through distance in excavation face₁When apply supporting.

II class surrounding rock：

III class surrounding rock：

IV class surrounding rock：

From Figure 12-17, it is proposed that II class, III class, the displacement completion rate of IV class surrounding rock are respectively when applying supporting：λ_s= 1st, 0.689,0.129, in being substituted into corresponding expression formula (11), (12) and (13), x can be obtained_s=+∞, 3.334m ,- 1.515m, that is, represent under the conditions of II class surrounding rock, it is not necessary to supporting；Under the conditions of III class surrounding rock, lag behind at excavation face 3.334m Apply supporting；Under the conditions of IV class surrounding rock, supporting need to be ahead of the applying of excavation face 1.515m.

Protection scope of the present invention is not limited to the above embodiments, it is clear that those skilled in the art can be to this It is bright to carry out various changes and deform without deviating from scope and spirit of the present invention.If these are changed and deformation belongs to power of the present invention In the range of profit requirement and its equivalent technologies, then the intent of the present invention also comprising these changes and deforms.

Claims (4)

1. a kind of initial support opportunity computational methods based on Wall Rock of Tunnel linear deformation curve, it is characterised in that：Including as follows Step：

Step 1, sets up the Three-dimension Numerical Model of tunnel, progressively excavates by Rational Excavation drilling depth, records as excavation face advances tunnel The situation of change of hole wall rock's level section exemplary position shift value；

Step 2, based on the concept of displacement completion rate, is fitted to country rock vertical section deformation curve formula, sets up three-dimensional computations Functional relationship in model between tunnel monitoring point surrounding rock displacement completion rate λ and excavation face advance distance x；

Step 3, according to the tunnel Three-dimensional CAD set up, using based on broad sense Virtual-supporting-force Method scheme mould is once excavated Intend tunnel excavation, excavation loads progressively discharge, record the situation of change of wall rock's level point displacement during excavation loads release, with As the basis for estimation on initial support opportunity at displacement increment mutation, it is determined that the now country rock position corresponding to excavation loads release rate Move completion rate λ_s；

Step 4, by surrounding rock displacement completion rate λ when carrying out initial support determined by step 3_sBack substitution enters in step 2 to be fitted The country rock vertical section deformation curve formula for obtaining, when being calculated initial support, the applying position of supporting falls behind or is ahead of out Digging face apart from x.

2. a kind of initial support opportunity computational methods based on Wall Rock of Tunnel linear deformation curve as claimed in claim 1, its It is characterised by：Described step 2 specifically includes following sub-step：

Step 2.1, surrounding rock displacement completion rate λ of Three-dimension Numerical Model adopts formula (1)

λ (z, p)=u (z, p)/u (∞, p) (1)

In formula, z is the distance of excavation face and monitoring section, meets by more than 7 times holes footpath is taken before and after monitoring section and requires；u(z, P) be monitoring point p excavation face apart from monitoring section be z when shift value；(∞ is p) that monitoring point p is monitored in excavation face distance to u Shift value during section infinity；

Step 2.2, sets up surrounding rock displacement completion rate λ and excavation face to the relation between the distance of monitoring section, according to formula (2) fitting of country rock vertical section deformation curve is carried out, parameter lambda is determined₀And X；

$\mathrm{\&lambda;}=\left\{\begin{array}{cc}(1-{\mathrm{\&lambda;}}_0)(1-e^{-\frac{(1-{\mathrm{\&lambda;}}_0)x}{X}})+{\mathrm{\&lambda;}}_0& x\&GreaterEqual;0\\ {\mathrm{\&lambda;}}_0{e}^{\frac{{\mathrm{\&lambda;}}_{0}x}{X_1}}& x<0\end{array}\right.---\left(2\right)$

In formula, λ is surrounding rock displacement completion rate；X is the distance of excavation face and monitoring section；λ₀When being that excavation face reaches monitoring section Surrounding rock displacement completion rate；X is constant,

3. a kind of initial support opportunity computational methods based on Wall Rock of Tunnel linear deformation curve as claimed in claim 1, its It is characterised by：Described step 3 is adopted based on broad sense Virtual-supporting-force Method once according to the tunnel Three-dimensional CAD set up Excavate program simulation tunnel excavation, by country rock excavation loads decile, be such as divided into 10 parts, per part 10% is progressively applied to excavation border On, the situation of change of wall rock's level point displacement during excavation loads release is recorded, calculate the displacement increment of monitoring point, country rock position Move increment to represent using formula (3)：

Δ u (r)=u (r)-u (r-10%) (3)

In formula, u (r) is displacement of the monitoring point when excavation loads release rate is r；Δ u (r) is monitoring point displacement increment；

With the excavation loads release rate r at displacement increment mutation₀As the opportunity for applying initial support, it is determined that now excavation loads Release rate r₀Corresponding surrounding rock displacement completion rate λ_s。

4. a kind of initial support opportunity computational methods based on Wall Rock of Tunnel linear deformation curve as claimed in claim 1, its It is characterised by：Described step 4 is specially will determine surrounding rock displacement completion rate λ when carrying out initial support in step 3_sSubstitute into step The country rock vertical section deformation curve deformation formula for obtaining, i.e. formula (3) are fitted in rapid 2：

$x=\left\{\begin{array}{cc}\frac{X}{1-{\mathrm{\&lambda;}}_0}ln\left(\frac{1-{\mathrm{\&lambda;}}_0}{1-\mathrm{\&lambda;}}\right)& \mathrm{\&lambda;}\&GreaterEqual;{\mathrm{\&lambda;}}_0\\ \frac{X}{1-{\mathrm{\&lambda;}}_0}ln\frac{\mathrm{\&lambda;}}{{\mathrm{\&lambda;}}_0}& \mathrm{\&lambda;}<{\mathrm{\&lambda;}}_0\end{array}\right.---\left(3\right)$

When being calculated initial support, supporting apply position fall behind or advanced excavation face apart from x.