CN113705870B - Prediction method for tunnel stratum settlement - Google Patents
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Abstract
The invention relates to a method for predicting the settlement of a tunnel stratum, in particular to a method for predicting the settlement of the tunnel stratum, which comprises the step of evaluating the settlement speed of the tunnel stratum according to the consolidation of the stratum and the construction parameters of an excavated tunnel. According to the method for predicting the settlement of the tunnel stratum, the settlement speed coefficient C is introduced into a three-dimensional mirror image method, a calculation formula capable of quantitatively considering construction and geological conditions and geometric parameters of a tunnel section is provided, and the influence of different soil conditions and construction conditions on the settlement speed and settlement amount of the stratum is obtained by analyzing the calculation parameters.
Description
Technical Field
The invention relates to settlement of tunnel stratum, in particular to a method for predicting the settlement of tunnel stratum.
Background
Formation deformation induced by subway tunnel construction is mainly represented by subsidence of the earth surface. Uneven formation settlement is a major cause of inclination and cracking of a surface building (structure), and thus is an important index for evaluating the influence of tunnel excavation on the surrounding environment.
The following methods are generally used for researching formation deformation caused by tunnel excavation: empirical, numerical modeling, and analytical methods, analytical methods being commonly used. The analysis method based on strict mathematical derivation can quantitatively consider the influence of geological parameters and geometric parameters, and is a practical method for predicting the deformation of the earth surface caused by tunnel construction; however, the stratum settlement obtained by the current research on stratum deformation caused by tunnel excavation is a final stratum settlement value, and the influence of stratum settlement speed and settlement amount cannot be accurately achieved.
Disclosure of Invention
In order to solve the problems, the invention provides a method for predicting the settlement of a tunnel stratum, which can accurately reflect the influence of different soil conditions and construction conditions on the settlement speed and settlement amount of the stratum, and the concrete technical scheme is as follows:
a method for predicting the settlement of a tunnel stratum comprises the step of evaluating the settlement speed of the tunnel stratum according to the consolidation of the stratum and the construction parameters of an excavated tunnel.
Preferably, the consolidation of the formation includes the permeability coefficient, compressibility, void fraction, and drainage distance of the soil body.
Preferably, the construction parameters comprise stratum settlement and stratum loss rate, tunneling speed and tunnel burial depth.
Further, the sedimentation velocity calculating method comprises the following steps:
Wherein:
h is the tunnel burial depth;
r is the tunnel excavation radius;
v is tunneling speed;
t is the time before and after the tunnel passes through the calculated section;
c y is the vertical consolidation coefficient of the soil;
alpha and beta are coefficients, and the values of the coefficients can be determined through monitoring measurement results or experience;
d is the mileage of the excavated surface, t is the time of passing through the excavated section, and d=vt;
d 0 is the monitoring section mileage, t 0 is the time to pass the monitoring section, d 0＝vt0.
Compared with the prior art, the invention has the following beneficial effects:
According to the method for predicting the settlement of the tunnel stratum, the settlement speed coefficient C is introduced into a three-dimensional mirror image method, a calculation formula capable of quantitatively considering construction and geological conditions and geometric parameters of a tunnel section is provided, and the influence of different soil conditions and construction conditions on the settlement speed and settlement amount of the stratum is obtained by analyzing the calculation parameters.
Drawings
FIG. 1 is a schematic diagram of an initial state in which a unit hole causes soil displacement;
FIG. 2 is a schematic diagram of the moment of void creation of a displacement of the soil mass per hole;
FIG. 3 is a schematic illustration of a displacement process in which a unit hole causes displacement of a soil mass;
FIG. 4 is a displacement-completed schematic of a unit hole causing displacement of the soil;
FIG. 5 is a schematic diagram of void coordinates;
FIG. 6 is a schematic illustration of tunnel excavation;
FIG. 7 is a plot of formation subsidence time course;
FIG. 8 is a plot of formation settling tanks;
FIG. 9 is a graph of formation longitudinal settlement;
FIG. 10 is a graph of downtime versus maximum slope of longitudinal settlement of the formation;
FIG. 11 is a graph of the effect of tunnel excavation speed on formation settlement speed;
FIG. 12 is a graph of tunnel excavation rate versus maximum subsidence rate for the earth's surface;
FIG. 13 is a graph of the effect of tunnel excavation speed on formation settlement;
FIG. 14 is a graph of the effect of a sedimentation velocity coefficient on the sedimentation velocity of a formation;
FIG. 15 is a graph of the sedimentation velocity coefficient versus the maximum sedimentation velocity of the earth's surface;
FIG. 16 is a graph of the effect of a sedimentation velocity system on the amount of formation sedimentation;
FIG. 17 is a graph of the effect of formation loss on formation settling velocity;
FIG. 18 is a graph of the effect of formation loss on formation settlement;
FIG. 19 is a graph of formation loss rate versus maximum surface subsidence rate and maximum formation subsidence amount.
Detailed Description
The invention will now be further described with reference to the accompanying drawings.
The stratum settlement obtained by the current research on stratum deformation caused by tunnel excavation is the final stratum settlement value, and in practice, the final settlement value is influenced by a plurality of factors, so that the accuracy of the obtained final stratum settlement value is not high.
In view of the above, the embodiment of the application introduces the sedimentation velocity coefficient C into a three-dimensional mirror image method, provides a calculation formula capable of quantitatively considering construction and geological conditions and geometric parameters of a tunnel section, and obtains the influence of different soil conditions and construction conditions on the stratum sedimentation velocity and sedimentation amount by analyzing the calculation parameters by using the method, and can reflect the change process of stratum sedimentation along with time to obtain the change rule of stratum sedimentation velocity along with time.
A method for predicting the settlement of a tunnel stratum comprises the step of evaluating the settlement speed of the tunnel stratum according to the consolidation of the stratum and the construction parameters of an excavated tunnel.
Consolidation of the formation includes the permeability coefficient, compressibility, void fraction, and drainage distance of the soil body.
The construction parameters comprise stratum settlement and stratum loss rate, tunneling speed and tunnel burial depth.
The sedimentation velocity calculation method comprises the following steps:
Wherein:
h is the tunnel burial depth;
r is the tunnel excavation radius;
v is tunneling speed;
t is the time before and after the tunnel passes through the calculated section;
c y is the vertical consolidation coefficient of the soil;
alpha and beta are coefficients, and the values of the coefficients can be determined through monitoring measurement results or experience;
d is the mileage of the excavated surface, t is the time of passing through the excavated section, and d=vt;
d 0 is the monitoring section mileage, t 0 is the time to pass the monitoring section, d 0＝vt0.
Dividing soil displacement caused by unit holes into four processes, and introducing a sedimentation velocity coefficient into a three-dimensional mirror image method to obtain a calculation formula considering stratum sedimentation time effect.
The time course of soil body displacement caused by unit holes is divided into 4 stages. It is assumed that there is a spherical void of radius a in the infinite body and the time course of this to cause displacement of the body is shown in figure 1. As shown in fig. 1, stage 1: in the initial state, the gap is not generated, the soil body is not displaced, and the soil body is in the static state. As shown in fig. 2, stage 2: the moment of the void generation moment of the spherical void with radius a is defined as 0 moment, i.e. t=0. At this time, the surrounding soil body is not displaced. As shown in fig. 3, stage 3: in the displacement development stage, the whole process has a period of 0<t < +.. At this time, the spherical void volume is gradually compressed and reduced, the displacement of the soil mass is transmitted from inside to outside, and the soil mass with a distance r from the center of the void sphere gradually moves towards the center of sphere. As shown in fig. 4, stage 4: and a displacement completion stage. At this time t= infinity. The spherical void volume is filled with soil and displacement is completed.
From the space point of view, in an infinite body, according to the assumption that a soil body is incompressible, the displacement of a certain point P caused by a spherical gap is only related to the distance from the point P to the center of the gap, when the distance r from the center of the gap is the same, namely the displacement generated by the point on any spherical surface taking the center O of the gap as the center of the sphere is the same, the spherical surface is called an equipotential spherical surface, and the final shrinkage volume of the equipotential spherical surface is equal to the volume of the spherical gap; the displacement direction of a certain point P is toward the center of the gap sphere when seen in the displacement direction.
Assuming that the volume of the unit sinking basin should be a function of time, and assuming that the volume increase rate of the unit sinking basin is proportional to the difference between the volume of the final unit sinking basin and the volume of the unit sinking basin at that time, the following assumption is made based on the principle assumption that the three-dimensional mirroring method and the two theoretical systems of the random medium theory are the same as the application method: assuming that the void of unit volume at time t causes the change rate of the volume of a certain displacement sphere in an infinite body to be in direct proportion to the difference between the final volume change amount and the volume change amount of the soil body at time t, namely:
dV(t)/dt＝C[V0-V(t)] (1)
wherein: t is time; v 0 is void volume; v (t) is the soil body change volume; c is a sedimentation velocity coefficient, which reflects the time course of the peripheral rock-soil body moving to the excavated space after the unit rock-soil body is excavated, also reflects the time course of the rock-soil movement and deformation transfer to the earth surface, and is a comprehensive time parameter reflecting the stratum deformation after the unit soil body is excavated.
From the initial conditions, a relationship between the sinking volume and time can be obtained. From the initial condition, when t=0, V (0) =0, t→infinity, V (≡) =v 0, solution:
V(t)＝V0-e-Ct (2)
Substituting V (t) =4pi [ r 3-[r-Sr(t)]3 ]/3 into the above formula yields:
3r2Sr(t)+3rSr(t)2-Sr(t)3＝3(V0-e-Ct)/4π (3)
Wherein: r is the spherical radius of the equipotential surface; s r (t) is the displacement distance of any point on the displacement sphere at the moment t.
Since the value of S r (t) is typically much smaller than the value of r, the higher order term of S r (t) is negligible. And (3) simplifying the formula to obtain S r (t) as follows:
Sr(t)＝(V0-e-Ct)/4πr2 (4)
the spatial distribution and the time-dependent change process of the soil displacement generated by the void in the infinite body can be quantitatively analyzed by the formula (4).
The three-dimensional mirror image method divides stratum settlement caused by unit holes in semi-infinite soil into three parts, namely: sedimentation caused by shear stress S z0, displacement caused by actual voids S z1, and sedimentation caused by virtual volume expansion S z2. Compared with the stratum settlement caused by the volume change of the soil body, the stratum settlement caused by the shear stress is negligible, and the total surface settlement S z caused by the unit holes can be obtained by superposition of the two parts S z1、Sz2.
For a spherical void at point Q (x 0y0,z0) in a cartesian coordinate system, as shown in fig. 5, the vertical displacement produced by any point P (x, y, z) at time t is:
In the formula:
in the coordinate system shown in fig. 5, the coordinates when P is located on the ground are assumed to be P (x, y, 0). Substituting into (5) to obtain:
Sz(t)＝Sz1(t)+Sz2(t)＝(V0-e-Ct)z0/2πr0 3 (6)
In the formula:
when the pore volume is unit volume, i.e. when V 0 = 1, formula (6) can be:
Sz(t)＝Sz1(t)+Sz2(t)＝(1-e-Ct)z0/2πr0 3 (7)
The amount of formation subsidence caused by soil loss can be obtained by integrating the formation subsidence produced by the void volume. Assuming that the cross-sectional shapes of the tunnels in the longitudinal direction are the same after the tunnel deformation, the volume lost by the stratum is the difference between two cylinder volumes of the same length. The tunnel excavation volume is omega on a certain length, the deformed volume is w, and the stratum settlement caused by stratum loss is as follows:
The specific value of C can be calculated according to the monitoring result of stratum settlement. Assuming that the tunnel excavation construction is stopped after a certain time t 0, the stratum subsidence increment measured at the moment t 1 is S t1, and the ground subsidence increment measured at the moment t 2 is S t2, the following steps are:
Dividing S t1 by S t1 yields:
and (5) solving the formula (10) to obtain the stratum sedimentation velocity coefficient C.
The stratum sedimentation velocity coefficient C obtained by the formula (10) is accurate and reasonable. However, in actual engineering, the loss caused by the shutdown of the tunnel is huge, and the forced shutdown of the tunnel may cause serious engineering problems, so that the cost and difficulty for solving the stratum settlement speed coefficient through the formula (10) are high.
In order to solve the problems, on the basis of carrying out statistical analysis on field measured data, the physical meaning of C is defined, and a general calculation method of C is determined.
The influence of the stratum on the stratum sedimentation time effect is basically the consolidation of the stratum, and the consolidation of the stratum is related to stratum parameters such as permeability coefficient, compression coefficient, void ratio, drainage distance and the like of a soil body. In the tunneling process of the tunnel, stratum settlement caused by the excavation is related to construction parameters such as stratum loss rate, tunneling speed, tunnel burial depth and the like. The sedimentation velocity coefficient C has the significance that the influence of the construction process and the stratum condition is comprehensively considered, and the sedimentation velocity coefficient C is a product integrating the soil mechanics mechanism.
The influence of stratum characteristics and a construction process on the stratum settlement time effect is comprehensively considered by introducing the vertical consolidation coefficient C y of the soil body, the tunnel burial depth h, the excavation radius r and the tunneling speed v into the calculation process of C. h and r affect the formation settling time effect by the distance that the movement and deformation of the rock and soil are transferred to the ground surface; the influence of the tunneling speed v on the stratum sedimentation time effect is mainly reflected in the quantity of stratum loss generated in unit time; the vertical consolidation coefficient C y reflects primarily the effect of formation properties on the formation settling time effect. The specific calculation method of C is as follows:
In the formula: h is the tunnel burial depth; r is the tunnel excavation radius; v is tunneling speed; t is the time before and after the tunnel passes through the calculated section; c y is the vertical consolidation coefficient of the soil; alpha and beta are coefficients, and the values of the coefficients can be determined through monitoring measurement results or experience; d is the mileage of the excavated surface, t is the time of passing through the excavated section, and d=vt; d 0 is the monitoring section mileage, t 0 is the time to pass the monitoring section, d 0＝vt0.
In order to verify the reasonability of the prediction method of the tunnel stratum settlement, field monitoring data of a tunnel project in a certain section of Shenzhen subway is selected for comparison analysis, the clear width of an excavated section is 6.3m, the clear height is 6.6m, and the construction is performed by adopting a mining method. For the convenience of calculation, the excavation section is simplified into a circle for calculation (R=3.3m), the actual measurement vault converges for 30mm (r=3.27m) in the construction process, the stratum where the tunnel is located is composed of prime filling soil, clay and full-strong weathered granite from top to bottom, wherein the tunnel is located in the strong weathered granite, the burial depth h=10.5m from the vault of the tunnel to the earth surface can be obtained through deduction calculation according to the stratum composition condition and the early actual measurement data, and the comprehensive parameters of the stratum can be obtained through deduction calculation: α= 0.1703, β= 15.3236; the compression coefficient of the soil body is 0.29/MPa, the initial pore ratio is 0.71, and the permeability coefficient is empirically obtained as 0.0578X10-4 cm/s. After the tunnel was constructed at a speed of 2.0m/d for 50d, it was stopped for 20d and then continued to be constructed at a speed of 2.0m/d, as shown in fig. 6.
And selecting the earth surface point right above the engineering shutdown working surface (after construction for 50 d) as a characteristic point, and calculating by adopting a mirror image method taking time effect into consideration, which is established by a tunnel stratum settlement prediction method, to obtain a settlement time course curve of the characteristic point, wherein the settlement time course curve is shown in figure 7. It can be seen that the formation subsidence was small (< 2 mm) 45 days before the tunnel excavation construction. When the excavation time exceeds 45 days, the tunnel excavation working face is close to the measuring point, and the stratum settlement speed begins to increase. When the tunnel excavation working face is in a shutdown state and is not excavated forwards, the stratum sedimentation value is continuously increased, but the sedimentation speed is gradually reduced, after the tunnel excavation working face is shut down for 10 days, the sedimentation speed is basically 0, and the earth surface is basically not sedimentated. After the tunnel construction is continued to be excavated, stratum settlement is further increased, and the settlement speed during construction is basically equal to the settlement speed before shutdown. The calculation result of the tunnel stratum settlement prediction method is well matched with the actual measurement result, and the accuracy of the tunnel stratum settlement prediction method is verified.
The method for predicting the settlement of the tunnel stratum is used for further analyzing the change rule of the horizontal and longitudinal settlement of the earth surface along with time when the tunnel is stopped. Fig. 8 and 9 show the transverse and longitudinal formation settlement curves during shutdown of the feature point locations, respectively. When t=0, namely, the maximum value of stratum settlement above the excavation working surface is 5mm at the beginning of shutdown, the maximum value accounts for about 1/2 of the final settlement; in the later sedimentation process, the sedimentation value gradually increases with the increase of time, the sedimentation tank gradually widens, the sedimentation rate gradually decreases, and the stratum sedimentation is basically stable by about 10 days of shutdown. From the space point of view, the surface in the range from 40m behind the shutdown working face to 20m in front of the shutdown working face has more obvious sedimentation within 10 days of shutdown, and the sedimentation value of stratum at other positions is hardly increased; the location of greatest increase in formation subsidence is at a location 4m behind the face. From time, the stratum settlement of each position is gradually stabilized along with the time; fig. 10 shows the maximum slope of the surface longitudinal settlement as a function of downtime. It can be seen that, as the downtime increases, the position of the maximum slope of the surface longitudinal settlement gradually approaches to the downtime working face, and within 0-4 days after the downtime, the maximum slope of the surface longitudinal settlement appears behind the tunnel face, and within 6-10 days, at the face; the maximum slope of the surface longitudinal settlement gradually increases with the increase of the downtime, and gradually stabilizes around 1mm/m by the 10 th day.
In order to further define the influence of all calculation parameters on the stratum settlement caused by tunnel excavation, a tunnel model with the burial depth of 20m and the excavation radius of 5.1m is established, and the influence rules of important engineering parameters such as tunnel excavation speed, stratum settlement speed coefficient, stratum loss and the like on the stratum settlement speed and settlement amount are discussed by adopting a control variable method.
Tunnel excavation speed
FIG. 11 shows the formation settling velocity as a function of time for different tunnel excavation rates. It can be seen that the greater the tunnel excavation speed, the greater the peak value of the stratum settlement speed, and the earlier the peak value occurs, the longer the distance from the monitoring point to the excavation surface when the peak value occurs, for example, when the tunnel excavation speed is 1m/d,2m/d,4m/d and 8m/d, the maximum values of the stratum settlement speed are 0.55mm/d,0.87mm/d,1.24mm/d and 1.59mm/d, respectively, the time when the maximum values occur is 6 days after passing through the measuring point, 5 days after 3 days and 2 days after the maximum values occur, the distance from the excavation surface to the measuring point is 6m,10m,12m and 16m, respectively. Fig. 12 shows the relationship between the tunnel excavation speed and the maximum subsidence speed of the earth surface. It can be seen that the maximum subsidence speed of the earth surface is in a logarithmic function with the excavation speed, namely, as the tunnel excavation speed increases, the maximum subsidence speed of the earth surface is continuously increased, but the growth speed is gradually slowed down. Therefore, in practical engineering, the tunnel excavation speed is not too high to cause sudden increase of stratum settlement, and is also not too low to cause overlarge stratum settlement acceleration, so that the ground surface is in an unstable state for a long time.
Fig. 13 shows the time dependence of the amount of stratum settlement at different excavation rates. It can be seen that the greater the tunnel excavation speed, the less the formation settlement, before and for a short period of time after passing the survey point; after the stratum passes through the measuring point for about 5 days, the stratum settlement gradually increases along with the increase of the excavation speed; over time, the curves gradually tend to a bit, which means that the tunnel excavation speed only affects the stratum settlement in a short period, and the final settlement amount of the earth surface is less affected.
Coefficient of sedimentation velocity
FIG. 14 shows the formation settling velocity versus time for different settling velocity coefficients. It can be seen that the greater the sedimentation velocity coefficient, the greater the surface maximum sedimentation velocity and the earlier the maximum occurs, such as when c=0.1, c=0.3, c=0.6 and c=0.9, the formation sedimentation velocity maximum is 1.24mm/d,2.0mm/d,2.36mm/d and 2.46mm/d, respectively, after 3 days, 2 days, 1 day and 0 day after the maximum occurs, respectively, past the survey point. The relationship between the maximum sedimentation velocity and the sedimentation velocity coefficient of the earth surface is shown in fig. 15. It can be seen that the maximum sedimentation velocity of the earth's surface is substantially a logarithmic function of the sedimentation velocity coefficient. As the formation subsidence rate coefficient increases, the maximum surface subsidence rate increases, but the growth rate slows down.
FIG. 16 shows the time dependence of the formation settlement amount when the settlement rate coefficients are different. It can be seen that in the short-term time before and after the measurement point, the larger the stratum sedimentation velocity coefficient is, the larger the stratum sedimentation amount is, and each curve gradually tends to a point along with the time, so that the stratum sedimentation velocity coefficient has no influence on the final sedimentation amount of the earth surface; as the stratum sedimentation velocity coefficient is reduced, the curve is gradually gentle, which shows that when the stratum sedimentation velocity coefficient is larger, the stratum sedimentation can be completed in a shorter time before and after passing the measuring point, and when the stratum sedimentation velocity coefficient is smaller, the time for completing the sedimentation of the earth surface can be prolonged.
Formation loss
The effect of formation loss on the rate of formation settlement is shown in figure 17. It can be seen that the greater the formation loss, the greater the final subsidence of the earth's surface, and the greater the maximum subsidence rate of the earth's surface, but the magnitude of the formation loss does not affect the time at which the maximum subsidence rate of the earth's surface occurs. FIG. 18 shows the time course of formation subsidence at various formation loss conditions. It can be seen that as the amount of formation loss increases, the formation subsidence becomes progressively greater. The relationship between the formation loss rate and the maximum amount of formation subsidence and the maximum surface subsidence velocity is shown in FIG. 19. It can be seen that both the surface maximum sedimentation velocity and the surface maximum sedimentation amount increase linearly with increasing formation loss rate. Therefore, in practical engineering, the quality of the primary support should be strictly controlled, and the stratum loss is reduced.
The method for predicting the settlement of the tunnel stratum introduces the stratum settlement speed coefficient into a mirror image method, deduces a calculation formula of the settlement of the tunnel stratum considering the time effect, and verifies the rationality of the calculation formula by combining with engineering examples.
The technical principle of the present invention is described above in connection with the specific embodiments. The description is made for the purpose of illustrating the general principles of the invention and should not be taken in any way as limiting the scope of the invention. Other embodiments of the invention will occur to those skilled in the art from consideration of the specification and practice of the invention without the need for inventive faculty, and are within the scope of the claims.
Claims (2)
1. A method for predicting the settlement of a tunnel stratum, which is characterized by comprising the steps of evaluating the settlement speed of the tunnel stratum according to the consolidation of the stratum and the construction parameters of an excavated tunnel, wherein the calculation method of the settlement speed comprises the following steps:
；
Wherein:
h is the tunnel burial depth;
r is the tunnel excavation radius;
v is tunneling speed;
t is the time of passing through the excavated section;
c y is the vertical consolidation coefficient of the soil;
alpha and beta are coefficients, and the values of the coefficients can be determined through monitoring measurement results or experience;
d is the excavation face mileage, d=vt;
d 0 is the monitoring section mileage, t 0 is the time to pass the monitoring section, d 0=vt0.
2. The method of claim 1, wherein the consolidation of the formation comprises a permeability coefficient, a compressibility coefficient, a void fraction, and a drainage distance of the soil body.
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