CN111680383B - Method for predicting additional confining pressure change of lower shield tunnel caused by foundation pit excavation - Google Patents
Method for predicting additional confining pressure change of lower shield tunnel caused by foundation pit excavation Download PDFInfo
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Abstract
The invention discloses a prediction method of additional confining pressure change of a lower shield tunnel caused by foundation pit excavation, which comprises the steps of calculating additional load distribution on a tunnel cross section according to an unloading model of the foundation pit excavation; the method for calculating the transverse additional confining pressure of the shield tunnel by considering the acting force between the longitudinal deformation rings is provided. The method can predict the change of the lining confining pressure of the lower shield tunnel caused by excavation of the foundation pit, and is suitable for the working conditions of crossing shield operation tunnels on foundation pits with different excavation sizes; theoretical support is provided for the stress of the tunnel structure under the corresponding working condition, the full-size shield segment loading test and the subway tunnel operation safety; the potential of overlarge surrounding pressure and stress changes can be pre-warned, safety accidents are prevented from being caused, the engineering is prevented and guided, and the construction cost can be saved.
Description
Technical Field
The invention belongs to the technical field of underground engineering, and particularly relates to a method for predicting the additional confining pressure change of a lower shield tunnel caused by foundation pit excavation.
Background
With urban rail transit development and underground space development and utilization, the situation of crossing operation shield tunnels on foundation pit engineering is more and more increased. When a foundation pit is excavated, the excavation unloading effect is directly transmitted to the shield tunnel below through soil bodies by the excavated surface. The tunnel bulges with the soil layer and simultaneously generates a large additional load on the tunnel structure. Because the excavation unloading amount of the foundation pit is large, the unloading effect generated by the structure can damage the stress balance of the segment structure, so that deformation and even damage are generated, and the safety of the shield tunnel in operation is greatly influenced. In order to ensure the safe operation of the rail transit line, the subway tunnel has stricter deformation control requirements, so that the research of the influence of foundation pit excavation on the stress deformation of the shield tunnel below has important application value. Therefore, the theoretical calculation method for the change of the confining pressure of the shield tunnel under the foundation pit excavation needs to be further studied, and theoretical support is provided for subway tunnel operation safety and related full-size structure loading tests.
The engineering problems have been paid attention to at home and abroad, and the main research methods at present mainly comprise the following steps: statistical analysis of measured data, numerical simulation, theoretical calculation and centrifugal model test. At present, a research result of shield tunnel confining pressure change caused by foundation pit excavation is mainly obtained by finite element simulation and a centrifugal model, and a result obtained by a conventional finite element simulation method at present can only be used as a basis for qualitative judgment, so that a quantitative accurate result is difficult to obtain. The refined numerical simulation has higher requirements on a calculation model and operation equipment, and higher operation cost is needed. The centrifugal model test requires large-scale supergravity centrifuges, high-precision sensors, model experiment boxes and other experimental equipment, and has high test research cost. The theoretical calculation method for the shield tunnel confining pressure change caused by the foundation pit is less in research, and particularly the result of the theoretical calculation method for the additional confining pressure of the shield tunnel below caused by the foundation pit excavation is not reported yet.
Disclosure of Invention
The invention aims to provide a method for predicting the additional confining pressure change of a lower shield tunnel caused by excavation of a foundation pit aiming at the defects of the prior art. The tunnel confining pressure obtained by the method is overlapped with normal working condition load combination, so that the influence of foundation pit excavation on the shield tunnel below can be effectively evaluated.
The aim of the invention is realized by the following technical scheme: a method for predicting the additional confining pressure change of a lower shield tunnel caused by foundation pit excavation comprises the following steps:
(1) And establishing a coordinate system at the center o of the foundation pit, wherein the x-axis is perpendicular to the axis of the tunnel, the y-axis is parallel to the axis of the tunnel, and the z-axis is in a positive direction vertically downwards.
(2) According to the coordinate system established in the step 1, calculating the unloading of the bottom excavation surface of the foundation pit caused by the excavation of the foundation pit above, and obtaining the vertical additional stress and the horizontal additional stress distribution on the cross section of the shield tunnel below caused by the unloading of the bottom excavation surface of the foundation pit, wherein the method specifically comprises the following sub-steps:
(2.1) unloading of the excavation surface at the bottom of the foundation pit is uniformly distributed load vertically upwards at the bottom of the foundation pit, and calculating unloading p at the bottom of the foundation pit:
p＝(1-α 0 )γd (1)
wherein: gamma is the soil weight, and a weighted average value of soil layers excavated above the foundation pit bottom is taken; d is the excavation depth of the foundation pit; alpha 0 Is the residual stress coefficient.
(2.2) calculating to obtain vertical additional stress sigma on the cross section of the lower shield tunnel under excavation unloading of the foundation pit by taking the excavation surface of the foundation pit bottom as an integral area according to Mindlin stress solution az (θ, l) and horizontal additional stress σ ax (θ, l) are respectively:
wherein: θ is the position angle of the calculation point on the cross section of the shield tunnel below, the vertex above is 0 DEG, and the angle in the clockwise direction is increased; b is the excavation size of the foundation pit along the x-axis direction; l is the excavation size of the foundation pit along the y-axis direction; d is the excavation depth of the foundation pit; h is the tunnel burial depth; d is the outer diameter of the shield tunnel below; a is the horizontal distance between the center of the foundation pit and the tunnel axis, and l is the y coordinate value corresponding to any point on the tunnel axis in the coordinate system; x is x 1 As a first integral variable, y 1 Sigma, the second integral variable zz For Mindlin vertical stress solution, sigma xz Is Mindlin horizontal stress solution.
(3) According to the on-site monitoring data of the longitudinal deformation of the tunnel, the vertical displacement of the tunnel is combined to obtain the distribution of the resultant force of the action between the vertical rings of the segment, and the method specifically comprises the following sub-steps:
(3.1) measuring the total vertical displacement w (l) of the tunnel along the longitudinal direction, measuring the displacement caused by the corner between segment rings, and calculating the vertical inter-ring shearing force Q between the segment ring at the l position and the segment ring at the previous segment L (l) Vertical inter-ring shearing force Q between the segment ring and the following segment ring R (l)：
Q L (l)＝(1-j)[w(l-D t )-w(l)]×k d (4)
Q R (l)＝(1-j)[w(l)-w(l-D t )]×k sl (5)
Wherein j is the ratio of the displacement amount caused by the rotation angle between adjacent segment rings to the total vertical displacement, D t Is the width of the segment ring, k sl For the inter-ring shear stiffness of the tunnel, Q L (l) Upward acting in the direction of action, Q R (l) The action direction is downward positive.
(3.2) according to Q L (l) And Q R (l) Obtaining the acting force F between the vertical rings of the segment on the segment ring at the position l Sz (l)：
F sz (l)＝Q R (l)-Q L (l) (6)
(4) The vertical additional stress sigma on the cross section of the lower shield tunnel obtained according to the step (2.2) az (θ, l) and horizontal additional stress σ ax (theta, l) calculating additional load distribution in all directions of different parts on the lining of the lower shield tunnel:
wherein p is az (theta, l) is vertical additional load of the upper half lining of the lower shield tunnel, p' ax (theta, l) is the level of the left side lining of the lower shield tunnelTo additional load, P ax And (theta, l) is the horizontal additional load of the right lining of the lower shield tunnel.
And then, according to additional load distribution in each direction of different parts on the lower shield tunnel lining, an additional confining pressure change model of the lower shield tunnel lining is established:
wherein F is sx To apply a force between the rings in the horizontal direction, F sz Acting as a resultant force between the rings in the vertical direction, delta qR Is the unloading amount of the arch bottom vertical counterforce.
(5) Selecting a calculated section to be analyzed of the lower shield tunnel according to the evaluation requirement, and introducing additional load on the tunnel lining at the position of the calculated section obtained in the step (4) and the combined force of the actions between the vertical rings of the pipe piece at the position of the calculated section obtained in the step (3) into the additional confining pressure change model of the tunnel lining of the lower shield tunnel established in the step (4) to obtain combined force F of the actions between the horizontal rings at the position of the calculated section sx Unloading delta of arch bottom vertical counter force qR 。
(6) According to the distribution of additional loads in different directions of different parts on the lining of the lower shield tunnel and the unloading delta of the vertical counter force of the arch bottom qR Obtaining the additional confining pressure p of the lining of the lower shield tunnel after deformation stabilization ar (θ，l)：
Compared with the prior art, the invention has the beneficial effects that:
(1) The method is applicable to working conditions of crossing operation shield tunnels of foundation pits with different excavation sizes and different position relations of the foundation pits;
(2) According to the method, engineering geological hydrologic information and design parameters which are necessary for corresponding engineering are adopted in the process of predicting the confining pressure change condition of the shield tunnel below before the foundation pit is constructed and excavated, and additional investigation and design cost investment is not required to be increased.
(3) The method can predict the confining pressure change of the lower shield tunnel caused by foundation pit excavation, and provides theoretical support for stress of a tunnel structure, full-size shield segment loading test and subway tunnel operation safety under corresponding working conditions; the potential of overlarge surrounding pressure and stress changes can be pre-warned, safety accidents are prevented from being caused, the engineering is prevented and guided, and the construction cost can be saved.
Drawings
FIG. 1 is a schematic illustration of the effect of foundation pit excavation on an underlying shield tunnel;
FIG. 2 is a diagram of the positional relationship between a foundation pit and a shield tunnel;
FIG. 3 is a schematic view of the redistribution of the confining pressure of the tunnel under the additional load of the excavation of the foundation pit, wherein (a) is a schematic view of the first stage, (b) is a schematic view of the second stage, and (c) is a schematic view of the third stage;
FIG. 4 is a schematic diagram of initial load combination and additional load combination, wherein (a) is a schematic diagram of load combination under an initial working condition of a tunnel, and (b) is a schematic diagram of additional confining pressure of a tunnel lining after tunnel deformation is stabilized;
FIG. 5 is a graph comparing confining pressure before and after excavation of a foundation pit;
FIG. 6 is a graph showing the comparison of additional confining pressure of a shield tunnel caused by excavation of an upper foundation pit;
fig. 7 is a graph comparing measured values and calculated values of deformation of a lower tunnel caused by excavation of a foundation pit in a horizontal direction with additional convergence.
Detailed Description
The invention is further illustrated by the following examples and figures.
Fig. 1 is a schematic diagram of the influence of foundation pit excavation on a lower shield tunnel, and as shown in fig. 1, the upper span of the lower shield tunnel in foundation pit engineering can not only enable the axis of the lower shield tunnel to generate longitudinal bulge deformation, but also enable the section of a tunnel lining in the influence range to generate integral displacement and ovalization deformation. Fig. 2 is a diagram of the position relationship between a foundation pit and a shield tunnel under the working condition, wherein the upper foundation pit spans the lower shield tunnel, D is the excavation depth of the foundation pit, h is the burial depth of the tunnel, D is the outer diameter of the lower shield tunnel, and a is the horizontal distance between the center of the foundation pit and the axis of the tunnel, as shown in fig. 2.
The invention discloses a method for predicting the additional confining pressure change of a lower shield tunnel caused by foundation pit excavation, which comprises the following steps:
(1) According to design data, as shown in fig. 1-2, a coordinate system is established at the center o of the foundation pit, the x-axis is perpendicular to the axis of the tunnel, the y-axis is parallel to the axis of the tunnel, and the z-axis is in a positive direction from vertical downward.
(2) According to the coordinate system established in the step 1, calculating the unloading of the bottom excavation surface of the foundation pit caused by the excavation of the foundation pit above, and obtaining the vertical additional stress and the horizontal additional stress distribution on the cross section of the shield tunnel below caused by the unloading of the bottom excavation surface of the foundation pit, wherein the method specifically comprises the following sub-steps:
(2.1) unloading of the excavation surface at the bottom of the foundation pit is uniformly distributed load vertically upwards at the bottom of the foundation pit, and calculating unloading p at the bottom of the foundation pit:
p＝(1- 0 )γd (1)
wherein: gamma is the soil weight, and a weighted average value of soil layers excavated above the foundation pit bottom is taken; d is the excavation depth of the foundation pit; α0 is a residual stress coefficient that can be used to account for incomplete release of foundation pit bottom stress.
(2.2) calculating to obtain vertical additional stress sigma on the cross section of the lower shield tunnel under excavation unloading of the foundation pit by taking the excavation surface of the foundation pit bottom as an integral area according to Mindlin stress solution az (θ, l) and horizontal additional stress σ ax (θ, l) are respectively:
wherein: θ is the position angle of the calculation point on the cross section of the shield tunnel below, the vertex above is 0 DEG, and the angle in the clockwise direction is increased; b is the excavation size of the foundation pit along the x-axis direction; l is the excavation size of the foundation pit along the y-axis direction; as shown in fig. 2, D is the excavation depth of the foundation pit, h is the burial depth of the tunnel, D is the outer diameter of the shield tunnel below, and a is the horizontal distance between the center of the foundation pit and the axis of the tunnel; l is a y coordinate value corresponding to any point on the tunnel axis in the coordinate system; x is x 1 As a first integral variable, y 1 Sigma, the second integral variable zz For Mindlin vertical stress solution, sigma xz Is Mindlin horizontal stress solution.
(3) According to the on-site monitoring data of the longitudinal deformation of the tunnel, the vertical displacement of the tunnel is combined to obtain the distribution of the resultant force of the action between the vertical rings of the segment, and the method specifically comprises the following sub-steps:
(3.1) measuring the total vertical displacement w (l) of the tunnel along the longitudinal direction, measuring the displacement caused by the corner between segment rings, and calculating the vertical inter-ring shearing force Q between the segment ring at the l position and the segment ring at the previous segment L (l) Vertical inter-ring shearing force Q between the segment ring and the following segment ring R (l)：
Q L (l)＝(1-j)[w(l-D t )-w(l)]×k sl (4)
Q R (l)＝(1-j)[w(l)-w(l-D t )]×k sl (5)
Wherein j is the ratio of the displacement amount caused by the rotation angle between adjacent segment rings to the total vertical displacement, D t Is the width of the segment ring, k sl For the inter-ring shear stiffness of the tunnel, Q L (l) Upward acting in the direction of action, Q R (l) The action direction is downward positive.
(3.2) according to Q L (l) And Q R (l) Obtaining the segment at the position lForce F acting between vertical rings of segments to which the rings are subjected sz (l)：
F sz (l)＝Q R (l)-Q L (l) (6)
(4) FIG. 3 is a schematic view showing the redistribution of the tunnel confining pressure under the additional load of the excavation of the foundation pit, wherein the tunnel confining pressure is divided into 3 stages, and the first stage is as shown in FIG. 3 (a), and the excavation of the foundation pit causes the vertical additional load p of the lining of the upper half part of the tunnel below az And horizontal additional load p 'of lining on the left side and the right side' ax And P' ax According to the vertical additional stress sigma on the cross section of the lower shield tunnel obtained in the step (2.2) az (θ, l) and horizontal additional stress σ ax (theta, l) calculating additional load distribution in all directions of different parts on the lining of the lower shield tunnel:
wherein p is az (theta, l) is vertical additional load of the upper half lining of the lower shield tunnel, p' ax (theta, l) is the horizontal additional load of the left lining of the lower shield tunnel, P ax And (theta, l) is the horizontal additional load of the right lining of the lower shield tunnel.
In the second stage, as shown in fig. 3 (b), the balance of the confining pressure of the tunnel is broken by the additional load, the whole cross section of the tunnel is displaced, and the longitudinal axis is deformed. Due to the non-uniform deformation of the tunnel in the longitudinal direction, relative displacement occurs between adjacent segment rings. Adjacent segment rings connected by longitudinal bolts are constrained to each other and exert an inter-ring force.
In the third stage, as shown in fig. 3 (c), the unloading of the upper part of the tunnel is finally transferred to the bottom through the structure, the arch bottom vertical counterforce of the bottom of the tunnel is partially unloaded, the arch bottom counterforce is usually regarded as a rectangular load in the practical structural design, the arch bottom counterforce acts on the lining vertically upwards, and the additional confining pressure change model of the lining of the lower shield tunnel is built according to the additional load distribution of different parts on the lining of the lower shield tunnel in all directions:
wherein F is sx To apply a force between the rings in the horizontal direction, F sz Acting as a resultant force between the rings in the vertical direction, delta qR Is the unloading amount of the arch bottom vertical counterforce.
(5) The horizontal displacement of the tunnel below the foundation pit and the inter-ring horizontal acting force caused by the horizontal displacement are mainly caused by asymmetrical unloading in the horizontal direction of the confining pressure of the whole ring lining of the tunnel, and under the condition of considering the mutual influence of longitudinal and transverse stress, the key of researching the variation of the confining pressure of the tunnel below is to combine the longitudinal inter-ring acting force on the basis of the transverse stress of the tunnel, so that the calculated section to be analyzed of the shield tunnel below is selected according to the evaluation requirement, the additional load on the tunnel lining at the calculated section position obtained in the step (4) and the combined force of the vertical inter-ring acting force of the segment at the calculated section position obtained in the step (3) are led into the additional confining pressure variation model of the shield tunnel lining below established in the step (4), and the combined force F of the horizontal inter-ring acting force at the calculated section is obtained sx Unloading delta of arch bottom vertical counter force qR 。
(6) According to the distribution of additional loads in different directions of different parts on the lining of the lower shield tunnel and the unloading delta of the vertical counter force of the arch bottom qR Obtaining the lining additional enclosure of the lower shield tunnel after deformation stabilizationPressure p ar (θ，l)：
The invention obtains the additional confining pressure of the tunnel lining, and the initial confining pressure can be obtained by combining loads under the initial working condition of the tunnel. The load combination under the initial working condition of the tunnel considered by the invention is shown in fig. 4 (a). The initial working condition load combination in the figure comprises: (1) lining dead weight g; (2) upper earthing vertical soil pressure q; (3) Lateral active soil pressure p e The method comprises the steps of carrying out a first treatment on the surface of the (4) Hydrostatic pressure p w The method comprises the steps of carrying out a first treatment on the surface of the (5) Arch bottom counterforce q R The method comprises the steps of carrying out a first treatment on the surface of the (6) Lateral soil resistance p after segment ring is deformed under various loads k . After the excavation of the foundation pit is completed, the additional confining pressure of the tunnel lining after the tunnel deformation is stabilized, which is calculated by the method of the invention, is shown in fig. 4 (b). And superposing the initial confining pressure and the additional confining pressure to obtain a final tunnel lining confining pressure value, and researching the internal force and deformation response of the tunnel lining by applying the final confining pressure value to a common correction usage method or a finite element analysis model.
Examples
Taking a left line tunnel crossing a subway No. 1 line on Hangzhou Yanan road-kernel and road-crossing road channel one-term engineering as an example: foundation pit plane excavation dimension l=11.4m, b=14.83 m, and excavation depth d=8.2m. The buried depth h=15.3m of the axis of the shield tunnel below, the outer diameter D=6.2m of the lining of the shield tunnel and the ring width D t =1.2m; the segment rings are connected by 16M 30 longitudinal bolts. The buried depth of the underground water level is about 1m, the fluctuation of the water level in the construction process is small, and the change of the underground water level is not considered in calculation. Soil layer distribution and corresponding parameters are shown in table 1. Calculating residual stress coefficient alpha when excavating and unloading foundation pit 0 ＝0.3。
Table 1: soil layer distribution and physical and mechanical parameters
Obtaining soil body related calculation parameters by adopting weighted average methodAnd (3) taking the value: the soil gravity gamma (kN/m) 3 ) The method comprises the steps of carrying out a first treatment on the surface of the Cohesion C (kPa); internal friction angle Φ (°); poisson's ratio of soil μ. And the horizontal distance l between the tunnel section to be calculated and the excavation center of the foundation pit along the y-axis direction.
According to the method of the invention, the additional confining pressure p of the tunnel lining after deformation stabilization is obtained ar (,l)。
Fig. 5 is a comparison chart of confining pressure before and after excavation of a foundation pit. According to the working condition of the embodiment, the method can be used for calculating the tunnel confining pressure before and after the foundation pit is excavated, and the section of the position l=0m below the excavation center is taken as an example, as shown in fig. 5. Before the foundation pit is excavated, the calculated shield tunnel surrounding pressure is small, large and left and right symmetrically distributed as the water and soil pressure increases along with the increase of the depth. The apex is 0 deg., and the angle increases clockwise. The change of the peripheral pressure is smaller in the range of 0-90 degrees and is between 218.46kPa and 234.56 kPa. The confining pressure is gradually increased between 90 degrees and 150 degrees, and the confining pressure is maximum near 150 degrees and is about 272.45kPa. In the implementation, the foundation pit is positioned right above the tunnel, and the tunnel lining confining pressures calculated by the theoretical method are still symmetrically distributed. As shown in fig. 5, after the foundation pit is excavated, the tunnel confining pressure below the excavation center (i=0m) is significantly reduced. The confining pressure unloading effect caused by foundation pit excavation mainly acts near the arch crown and the arch bottom of the lining of the tunnel below. Wherein the unloading effect of the tunnel vault (0 deg.) is most pronounced, the confining pressure is reduced from 218.46kPa before excavation to 161.92kPa, by 25.88%.
Fig. 6 shows additional confining pressure acting on the segment lining ring at different distances from the excavation center along the shield tunnel direction. As shown, the additional confining pressure is negative, i.e. the excavation of the foundation pit mainly causes the confining pressure of the tunnel lining below to be reduced. The additional confining pressure influence area is mainly near the arch crown and the arch bottom, and the absolute value of the additional confining pressure at the arch waist is smaller. The absolute value of the additional confining pressure at the lining vault of the tunnel below the excavation center of the foundation pit (l=0m) is the maximum, which is 56.54kPa. As the horizontal distance from the excavation center increases, the absolute value of the additional confining pressure acting on the underlying shield tunnel lining decreases. And near the lower part of the excavation area, the absolute value of the additional confining pressure acting on the upper half part of the shield tunnel lining is larger than that of the lower half part. As the distance from the excavated area increases, the difference in additional confining pressure between the upper and lower parts of the lining gradually decreases until the additional confining pressures at the dome and the dome bottom are substantially equivalent, at-22.42 kPa and-21.12 kPa, respectively, at a distance of 7.2m (l=7.2m) from the excavation center. As the distance from the excavation center increases further, the absolute value of the additional load on the tunnel lining will translate into a lower, larger, smaller profile.
In actual engineering, confining pressure change data on shield tunnel lining are difficult to obtain, and in order to verify the reliability of the method, the initial confining pressure calculated by the theoretical method and additional confining pressure caused by excavation of the foundation pit above the initial confining pressure are used as load combination for structural stress analysis in a finite element model. The deformation of the segment rings at different positions can be obtained through calculation, and the actual measurement values of the additional convergence deformation of the horizontal directions of the segments of each ring pipe are compared. Fig. 7 is a comparison of the measured values of the horizontal additional convergence deformation of the tunnel below caused by the excavation of the foundation pit in this case and the calculation results. Positive values indicate horizontal compression of shield tunnel segment rings, radial convergence deformation of the arch, and the unit is mm. As shown in FIG. 7, the horizontal convergence deformation values at each position of the lower tunnel calculated by the method of the invention and the change rule of the horizontal convergence deformation values along the longitudinal direction of the tunnel are basically consistent with the actual measurement values, and the reliability of the calculation result of the method of the invention is verified.
Claims (1)
1. The method for predicting the additional confining pressure change of the lower shield tunnel caused by foundation pit excavation is characterized by comprising the following steps:
(1) Establishing a coordinate system at the center o of the foundation pit, wherein an x-axis is perpendicular to the axis of the tunnel, a y-axis is parallel to the axis of the tunnel, and a z-axis takes a vertical downward direction as a positive direction;
(2) According to the coordinate system established in the step 1, calculating the unloading of the bottom excavation surface of the foundation pit caused by the excavation of the foundation pit above, and obtaining the vertical additional stress and the horizontal additional stress distribution on the cross section of the shield tunnel below caused by the unloading of the bottom excavation surface of the foundation pit, wherein the method specifically comprises the following sub-steps:
(2.1) unloading of the excavation surface at the bottom of the foundation pit is uniformly distributed load vertically upwards at the bottom of the foundation pit, and calculating unloading p at the bottom of the foundation pit:
p＝(1-α 0 )γd (1)
wherein: gamma is the soil weight, and a weighted average value of soil layers excavated above the foundation pit bottom is taken; d is the excavation depth of the foundation pit; alpha 0 Is the residual stress coefficient;
(2.2) calculating to obtain vertical additional stress sigma on the cross section of the lower shield tunnel under excavation unloading of the foundation pit by taking the excavation surface of the foundation pit bottom as an integral area according to Mindlin stress solution az (θ, l) and horizontal additional stress σ ax (θ, l) are respectively:
wherein: θ is the position angle of the calculation point on the cross section of the shield tunnel below, the angle is increased clockwise by taking the vault of the tunnel as 0 degrees; b is the excavation size of the foundation pit along the x-axis direction; l is the excavation size of the foundation pit along the y-axis direction; h is the tunnel burial depth; d is the outer diameter of the shield tunnel below; a is the horizontal distance between the center of the foundation pit and the tunnel axis, and l is the y coordinate value corresponding to any point on the tunnel axis in the coordinate system; x is x 1 As a first integral variable, y 1 Sigma, the second integral variable zz For Mindlin vertical stress solution, sigma xz Is Mindlin horizontal stress solution;
(3) According to the on-site monitoring data of the longitudinal deformation of the tunnel, the vertical displacement of the tunnel is combined to obtain the distribution of the resultant force of the action between the vertical rings of the segment, and the method specifically comprises the following sub-steps:
(3.1) measuring the total vertical displacement w (l) of the tunnel along the longitudinal direction, measuring the displacement caused by the corner between segment rings, and calculating the vertical inter-ring shearing force Q between the segment ring at the l position and the segment ring at the previous segment L (l) Vertical inter-ring shearing force Q between the segment ring and the following segment ring R (l)：
Q L (l)＝(1-j)[w(l-D t )-w(l)]×k sl (4)
Q R (l)＝(1-j)[w(l)-w(l-D t )]×k sl (5)
Wherein j is the ratio of the displacement amount caused by the rotation angle between adjacent segment rings to the total vertical displacement, D t Is the width of the segment ring, k sl For the inter-ring shear stiffness of the tunnel, Q L (l) Upward acting in the direction of action, Q R (l) The action direction is downward positive;
(3.2) according to Q L (l) And Q R (l) Obtaining the acting force F between the vertical rings of the segment on the segment ring at the position l sz (l)：
F sz (l)＝Q R (l)-Q L (l) (6)
(4) The vertical additional stress sigma on the cross section of the lower shield tunnel obtained according to the step (2.2) az (θ, l) and horizontal additional stress σ ax (theta, l) calculating additional load distribution in all directions of different parts on the lining of the lower shield tunnel:
wherein p is az (theta, l) is vertical additional load of the upper half lining of the lower shield tunnel, p' ax (theta, l) is the horizontal additional load of the left lining of the lower shield tunnel,
horizontal additional load for lining the right side of the lower shield tunnel;
and then, according to additional load distribution in each direction of different parts on the lower shield tunnel lining, an additional confining pressure change model of the lower shield tunnel lining is established:
wherein F is sx To apply a force between the rings in the horizontal direction, F sz Acting as a resultant force between the rings in the vertical direction, deltaq R The unloading amount is the vertical counter force of the arch bottom;
(5) Selecting a calculated section to be analyzed of the lower shield tunnel according to the evaluation requirement, and introducing additional load on the tunnel lining at the position of the calculated section obtained in the step (4) and the combined force of the actions between the vertical rings of the pipe piece at the position of the calculated section obtained in the step (3) into the additional confining pressure change model of the tunnel lining of the lower shield tunnel established in the step (4) to obtain combined force F of the actions between the horizontal rings at the position of the calculated section sx Unloading quantity delta q of arch bottom vertical counterforce R ；
(6) According to the distribution of additional loads in different directions of different parts on the lining of the lower shield tunnel and the unloading quantity deltaq of the vertical counter force of the arch bottom R Obtaining the additional confining pressure p of the lining of the lower shield tunnel after deformation stabilization ar (θ,l)：
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| CN112597674B (en) * | 2020-12-05 | 2022-07-08 | 福建工程学院 | Method for determining lateral pipeline transverse additional internal force caused by foundation pit excavation |
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