Shield tunneling machine jacking force calculation method considering influence of gradient and curvature radius

Abstract

The invention provides a shield tunneling machine jacking force calculation method considering gradient and curvature radius influences. The method comprises the steps that friction resistance between a shield shell and surrounding soil is calculated; calculating the front resistance of the cutterhead; calculating the friction force between the duct piece and the shield tail, the resistance of a traction trailer and the penetration resistance of a notch ring; calculating the resistance caused by the self weight of the shield tunneling machine along the axial component of the tunnel during upslope tunneling; the turning thrust difference of the shield tunneling machine is calculated; and calculating the jacking force of the shield tunneling machine according to the frictional resistance between the shield shell and the surrounding soil body, the front resistance of the cutter head, the friction force between the duct piece and the shield tail, the resistance of the traction trailer, the penetration resistance of the notch ring, the resistance caused by the self weight of the shield tunneling machine along the axial component of the tunnel, and the turning thrust difference of the shield tunneling machine. According to the method, the influence of the slope and curvature radius conditions on the jacking force of the shield tunneling machine is considered, two key subitem resistances are added, the calculation accuracy of the jacking force of the shield tunneling machine is improved, and the technical defect that the slope and the curvature radius are ignored in an existing calculation method is overcome.

Description

Technical Field

[0001] The invention relates to the technical field of underground drilling, and in particular to a method for calculating the top thrust of a shield machine taking into account the influence of slope and curvature radius. Background Art

[0002] The shield machine is an underground excavation and drilling equipment that integrates optical, mechanical, electrical, hydraulic, sensor and information technologies, and has the functions of excavating and cutting soil, transporting soil and ballast, assembling tunnel linings, measuring and guiding deviation correction, etc. During the tunnel excavation and drilling process of the shield machine, due to the dynamic adjustment of the shield machine's posture, the shield excavation parameters of the large slope and small radius section are significantly different from those of the straight and flat slope section. If the shield construction is still considered according to the straight and flat slope section, it will cause an imbalance between the shield excavation face support force and the front soil pressure, aggravate the impact of the construction on the surrounding strata, increase the risk of the shield deviating from the tunnel design axis, and further aggravate the uneven force on the segments. The current calculation method cannot solve the problem of selecting shield excavation parameters for large slopes and small radii. Summary of the invention

[0003] The purpose of the present invention is to overcome the deficiencies in the above-mentioned prior art and to provide a method for calculating the top thrust of a shield machine taking into account the influence of slope and curvature radius, which solves the problem that the current calculation method cannot solve the problem of selecting shield excavation parameters with large slope and small radius.

[0004] In order to solve the above problems, the present invention provides a method for calculating the top thrust of a shield machine taking into account the influence of slope and curvature radius, which is characterized by comprising the following steps:

[0005] Step 1: According to the friction calculation model between the shield shell and the surrounding soil, the vertical soil pressure and the lateral soil pressure acting on the shield shell are calculated, and the sum of the vertical soil pressure and the lateral soil pressure in the radial direction of the shield is obtained as the radial soil pressure. The friction coefficient between the shield shell and the surrounding soil is selected to calculate the friction resistance between the shield shell and the surrounding soil;

[0006] Step 2: According to the calculation model of the front earth pressure of the cutter disc and the micro-element force of the soil in the soil bin, the front earth pressure of the cutter disc and the frictional resistance between the inner wall of the soil bin and the soil are calculated respectively, and the front resistance of the cutter disc is calculated according to the front earth pressure of the cutter disc and the frictional resistance between the inner wall of the soil bin and the soil;

[0007] Step 3, calculating the friction between the segment and the shield tail, the resistance of the tractor trailer, and the penetration resistance of the cutout ring;

[0008] Step 4, calculating the resistance caused by the weight of the shield machine along the tunnel axis during uphill excavation;

[0009] Step 5: Calculate the torque of the shield shell soil pressure increment and the cutter head soil pressure increment on the rotation center according to the soil pressure change around the shield shell and the cutter head respectively, and calculate the shield machine turning thrust difference according to the soil pressure increment of the shield shell and the cutter head on the rotation center.

[0010] Step 6, calculating the top thrust of the shield machine according to the friction resistance between the shield shell and the surrounding soil, the front resistance of the cutterhead, the friction between the pipe segment and the shield tail, the resistance of the tractor trailer and the penetration resistance of the cutter ring, the resistance caused by the weight of the shield machine along the tunnel axis, and the shield machine turning thrust difference;

[0011] The above-mentioned method for calculating the top thrust of a shield machine taking into account the influence of slope and curvature radius is characterized in that in the step 1:

[0012] When the shield machine is excavating in a curved section, due to the geometric characteristics of the curve, the squeezing force of the inner soil on the shield shell is significantly greater than that on the outer side, so the friction between the shield shell and the soil on the inner side of the curve is also greater than that on the outer side; therefore, the friction between the shield shell and the surrounding soil should be calculated according to the inner side and the outer side of the curve, and the friction resistance between the shield shell and the surrounding soil can be calculated by multiplying the radial soil pressure acting on the shield shell and the friction coefficient between the shield shell and the surrounding soil; the soil pressure acting on the shield shell can be divided into vertical soil pressure and lateral soil pressure according to the direction, and the sum of the vertical soil pressure and the lateral soil pressure in the radial direction of the shield is the radial soil pressure. Since the soil pressure is different between the upper and lower parts of the shield machine, it should be divided into two parts for calculation; specifically including:

[0013] 101. Calculate the vertical earth pressure dP on the microelement of the upper part of the shield e1 and lateral earth pressure dq e1 :

[0014] dP e 1 ′ = c [ h N + l sin β + R D ( 1 − sin i ) cos β ]

[0015] dq e 1 ′ = K 0 dP e 1 ′ = ( 1 − sin f i ) c [ h N + l sin β + R D ( 1 − sin i ) cos β ]

[0016] Where: K0 is the static earth pressure coefficient, ; γ is the soil density, unit is kN / m 3 ;h N is the distance between the top of the cutter head and the ground surface, in m; R D is the cutter head radius, in m; β is the tunneling slope of the shield machine, in о ; φ i is the internal friction angle of soil, in units о ; θ is the angle between the calculation point and the horizontal line of the cutter head, unit о ; l is the distance between the calculated microelement and the cutter head surface, unit: m;

[0017] According to the vertical earth pressure dP on the upper part of the shield e1 and lateral earth pressure dq e1 , calculate the earth pressure on the upper part of the microelement per unit length of the radial contact surface between the shield and the soil :

[0018] d s i 1 = dP e 1 ′ sin i + dq e 1 ′ cos i = c [ h N + l sin β + R D ( 1 − sin i ) cos β ] ⋅ [ sin i + ( 1 − sin f i ) cos i ]

[0019] 102. Calculate the vertical earth pressure dP on the microelement of the lower half of the shield e2 and lateral earth pressure dq e2 :

[0020] dP e 2 ′ = c [ h N + l sin β + R D ( 1 − sin i ) cos β ] + W π R D L

[0021] dq e 2 ′ = K 0 dP e 2 ′ = ( 1 − sin f i ) { c [ h N + l sin β + R D ( 1 − sin i ) cos β ] + W π R D L }

[0022] Where: W is the weight of the shield machine, unit is kN.

[0023] According to the vertical earth pressure dP on the microelement of the lower half of the shield e2 and lateral earth pressure dq e2 , calculate the earth pressure on the upper part of the microelement per unit length of the radial contact surface between the shield and the soil :

[0024] d s i 2 = dP e 2 ′ sin i + dq e 2 ′ cos i = { c [ h N + l sin β + R D ( 1 − sin i ) cos β ] + W π R D L } ⋅ [ sin i + ( 1 − sin f i ) cos i ] ;

[0025] 103. Calculate the friction forces df1 and df2 on the inner and outer upper parts of the shield shell:

[0026] df 1 = ndf 1 = n h [ h N + 0 . 5 L sin β + R D ( 1 − sin i ) cos β ] [ sin i + ( 1 − sin f i ) cos i ]

[0027] df 2 = h [ h N + 0 . 5 L sin β + R D ( 1 − sin i ) cos β ] [ sin i + ( 1 − sin f i ) cos i ]

[0028] Where: n is the difference coefficient of friction between the inner and outer sides of the curve, which is calculated and analyzed based on engineering monitoring data to obtain n=1.1; η is the friction coefficient between the shield and the surrounding soil, which is generally ;

[0029] 104. Calculate the friction forces df3 and df4 on the inner and outer lower half of the shield:

[0030] df 3 = or { c [ h N + 0 . 5 L sin β + R D ( 1 − sin i ) cos β ] + W π R D L } [ sin i + ( 1 − sin f i ) cos i ]

[0031] df 4 = ndf 3 = n or { c [ h N + 0 . 5 L sin β + R D ( 1 − sin i ) cos β ] + W π R D L } ⋅ [ sin i + ( 1 − sin f i ) cos i ]

[0032] 105. Calculate the friction resistance F1 between the shield and the surrounding soil:

[0033] ;

[0034] The above-mentioned method for calculating the top thrust of a shield machine taking into account the influence of slope and curvature radius is characterized in that the front earth pressure of the cutterhead in step 2 is the vertical earth pressure p e and lateral earth pressure q e The resultant force in the normal direction of the cutterhead and the soil bin pressure σ α Equal in size and opposite in direction;

[0035] The calculation method of the front resistance of the cutter disc includes:

[0036] 201. Calculate the vertical earth pressure dP on the microelement of the upper half of the cutterhead e1 and lateral earth pressure dq e1 :

[0037] dP e 1 = c [ h N + ( R D − r sin i ) cos β ]

[0038] dq e 1 = K 0 dP e 1 = ( 1 − sin f ) c [ h N + ( R D − r sin i ) cos β ]

[0039] According to the vertical earth pressure dP on the microelement of the upper half of the cutterhead e1 and lateral earth pressure dq e1 , calculate the earth pressure on the upper part of the cutter head :

[0040] d s α 1 = dP e 1 sin β + dq e 1 cos β = c [ h N + ( R D − r sin i ) cos β ] ⋅ [ sin β + ( 1 − sin f ) cos β ]

[0041] 202. Calculate the vertical earth pressure dP on the microelement of the lower half of the cutterhead e2 and lateral earth pressure dq e2 :

[0042] dP e 2 = c [ h N + ( R D − r sin i ) cos β ] + W π R D L

[0043] dq e 2 = K 0 dP e 2 = ( 1 − sin f ) { c [ h N + ( R D − r sin i ) cos β ] + W π R D L }

[0044] According to the vertical earth pressure dP on the microelement of the lower half of the cutterhead e2 and lateral earth pressure dqe2 , calculate the earth pressure on the upper part of the cutter head :

[0045] d s α 2 = dP e 2 sin β + dq e 2 cos β = { c [ h N + ( R D − r sin i ) cos β ] + W π R D L } ⋅ [ sin β + ( 1 − sin f ) cos β ]

[0046] 203. Calculate the front earth pressure dF on the microelement on the cutterhead surface 2-1 :

[0047]

[0048] According to the front earth pressure dF on the cutterhead surface microelement 2-1 , integrate both sides of the equation according to the upper and lower parts of the cutterhead, consider the influence of the cutterhead opening rate, and calculate the soil pressure F on the front of the cutterhead 2-1 :

[0049]

[0050] Where: is the cutter disc opening rate.

[0051] 204. Calculate the soil microelement force in the soil bin:

[0052]

[0053] According to the force of the soil microelement in the soil bin, the axial stress σ along the tunnel axis is l The size of the soil bin pressure σ α Equal, so according to the cutter head upper and lower parts of the equation on both sides of the integration, calculate the friction between the soil bin inner wall and the soil F 2-2 :

[0054]

[0055] Where: l ch is the length of the earth pressure chamber, in m; v is the Poisson’s ratio of the soil.

[0056] 205. Calculate the front resistance F2 of the cutter disc:

[0057] F 2 = F 2 − 1 + F 2 − 2 = ( ∫ 0 R D ∫ 0 π d s α 1 rd i dr + ∫ 0 R D ∫ π 2 π d s α 2 rd i dr ) [ ( 1 − oh ch ) + ( e 2 tan f R D v 1 − v l ch − 1 ) ] .

[0058] The above-mentioned method for calculating the top thrust of a shield machine taking into account the influence of slope and curvature radius is characterized in that in the step three:

[0059] The calculation formulas for the friction force F3 between the segment and the shield tail, the resistance F4 of the tractor trailer, and the penetration resistance F5 of the cut ring are as follows:

[0060]

[0061] Where n4 is the number of segments in the tail shield; W s is the deadweight of each ring of segments, in kN; D0 is the outer diameter of the segments, in m; b w is the contact length between each shield tail sealing brush and the pipe ring, in m; p T is the pressure of the shield tail seal brush, in kPa; n5 is the number of layers of the shield tail seal brush; μ3 is the friction coefficient between the shield tail seal brush and the pipe segment; μ2 is the rolling friction coefficient between the rear supporting trailer wheel and the supply surface or the steel wheel and the track; W p is the deadweight of the trailer, in kN; D is the outer diameter of the front shield, in m; D i is the inner diameter of the front shield, in m; P3 is the average soil pressure of the stratum where the cut ring is inserted, in kPa; t is the depth of the cut ring inserted into the stratum, in m; P m It is the average earth pressure acting on the shield, in kPa.

[0062] The above-mentioned method for calculating the top thrust of a shield machine considering the influence of slope and curvature radius is characterized in that, in step 4, when excavating uphill, the resistance F caused by the weight of the shield machine along the tunnel axis is s The calculation is done using the following formula:

[0063]

[0064] The above-mentioned method for calculating the top thrust of a shield machine considering the influence of slope and curvature radius is characterized in that, in the step 5, the turning thrust difference is that when the shield cylinder is pushed forward, the force arms of the left thrust and the right thrust are the same, so the torque M generated when the shield machine pushes forward one ring of segments is the difference between the left thrust and the right thrust, wherein:

[0065] The torque M can be obtained by the sum of the torque M1 of the shield shell soil pressure increment on the rotation center during the shield rotation process and the torque M2 of the cutterhead soil pressure increment on the rotation center, specifically including:

[0066] 501. Calculate the shield shell soil pressure increment Δσ:

[0067]

[0068] In the formula, k t is the soil spring constant, in kN / m; S is the horizontal displacement of the soil around the shield, in m; E s is the elastic modulus of soil, in kPa; E p is the elastic modulus of the shield machine, in kPa; I p is the moment of inertia of the shield machine, in m 4 ;

[0069] According to the shield earth pressure increment Δσ, find its relative to the rotation center O q The total torque M1:

[0070]

[0071] In the formula, the turning angle of the shield machine when advancing one ring of segments is , δ g Unit: rad; l is the width of each ring segment, unit: m; R is the radius of curvature of the tunnel, unit: m; L q is the length of the front shield, in m;

[0072] 502. Calculate the horizontal displacement S' and the cutterhead soil pressure increment Δσ' of any point on the cutterhead:

[0073]

[0074] ;

[0075] According to the soil pressure increment Δσ´ of the cutter head, calculate its relative pressure to the rotation center O q The total torque M2:

[0076] ;

[0077] 503. Calculate the turning thrust difference F6 of the shield machine:

[0078] .

[0079] The above-mentioned method for calculating the top thrust of a shield machine taking into account the influence of slope and curvature radius is characterized in that the top thrust F is calculated according to the following formula:

[0080] .

[0081] Compared with the prior art, the present invention takes into account the influence of slope and curvature radius conditions on the top thrust of the shield machine, adds two key sub-resistances: the resistance caused by the shield's own weight along the tunnel axis and the turning thrust difference, improves the traditional top thrust calculation formula, makes the calculation result close to the actual situation, can effectively guide the top thrust design of the shield machine, improves the calculation accuracy of the top thrust of the shield machine, and makes up for the technical defect of ignoring the slope and curvature radius in the existing calculation method.

[0082] The invention is further described in detail below through the accompanying drawings and examples. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] The drawings constituting a part of the present application are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0084] Figure 1 A schematic diagram of a calculation model for the friction between the shield shell and the surrounding soil of a shield machine top thrust calculation method taking into account the influence of slope and curvature radius of the present invention;

[0085] Figure 2 A schematic diagram of shield shell friction force partitioning of a shield machine top thrust calculation method considering the influence of slope and curvature radius of the present invention;

[0086] Figure 3 A schematic diagram of a cutterhead earth pressure calculation model of a shield machine top thrust calculation method considering the influence of slope and curvature radius of the present invention;

[0087] Figure 4 A schematic diagram of the force of the soil microelement in the soil bin of a shield machine top thrust calculation method considering the influence of slope and curvature radius of the present invention;

[0088] Figure 5 A schematic diagram of the change of soil pressure around the shield shell of a shield machine top thrust calculation method considering the influence of slope and curvature radius of the present invention;

[0089] Figure 6 A schematic diagram of the shield shell earth pressure increment of a shield machine top thrust calculation method considering the influence of slope and curvature radius of the present invention;

[0090] Figure 7 The present invention is a schematic diagram of the cutterhead soil pressure change of a shield machine top thrust calculation method taking into account the influence of slope and curvature radius. DETAILED DESCRIPTION

[0091] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present invention and its application or use. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0092] This embodiment provides a method for calculating the top thrust of a shield machine taking into account the influence of slope and curvature radius, comprising the following steps:

[0093] Step 1: According to the friction calculation model between the shield shell and the surrounding soil, calculate the vertical soil pressure and lateral soil pressure acting on the shield shell, and obtain the sum of the two components in the radial direction of the shield as the radial soil pressure. Select the friction coefficient between the shield shell and the surrounding soil, and calculate the friction resistance between the shield shell and the surrounding soil.

[0094] Furthermore, when the shield machine is excavating in a curved section, due to the geometric characteristics of the curve, the squeezing force of the inner soil on the shield shell is significantly greater than that on the outer side, so the friction between the shield shell and the soil on the inner side of the curve is also greater than that on the outer side. Therefore, the friction between the shield shell and the surrounding soil should be calculated according to the inner and outer sides of the curve, and the friction resistance between the shield shell and the surrounding soil can be calculated by multiplying the radial soil pressure acting on the shield shell by the friction coefficient between the shield shell and the surrounding soil. The soil pressure acting on the shield shell can be divided into vertical soil pressure and lateral soil pressure according to the direction. The sum of the two components in the radial direction of the shield is the radial soil pressure. Since the soil pressure is different between the upper and lower parts of the shield machine, it should be divided into two parts for calculation;

[0095] Calculate the vertical earth pressure dP on the microelement of the upper part of the shield e1 and lateral earth pressure dq e1 :

[0096] dP e 1 ′ = c [ h N + l sin β + R D ( 1 − sin i ) cos β ]

[0097] dq e 1 ′ = K 0 dP e 1 ′ = ( 1 − sin f i ) c [ h N + l sin β + R D ( 1 − sin i ) cos β ]

[0098] Where: K0 is the static earth pressure coefficient, ; γ is the soil density, unit is kN / m 3 ;h N is the distance between the top of the cutter head and the ground surface, in m; R D is the cutter head radius, in m; β is the tunneling slope of the shield machine, in о ; φ i is the internal friction angle of soil, in units о ; θ is the angle between the calculation point and the horizontal line of the cutter head, unit о ; l is the distance between the calculated microelement and the cutter head surface, unit: m;

[0099] According to the vertical earth pressure dP on the upper part of the shield e1 and lateral earth pressure dq e1 , calculate the earth pressure on the upper part of the microelement per unit length of the radial contact surface between the shield and the soil :

[0100] d s i 1 = dP e 1 ′ sin i + dq e 1 ′ cos i = c [ h N + l sin β + R D ( 1 − sin i ) cos β ] ⋅ [ sin i + ( 1 − sin f i ) cos i ]

[0101] Calculate the vertical earth pressure dP on the microelement of the lower half of the shield e2 and lateral earth pressure dq e2 :

[0102] dP e 2 ′ = c [ h N + l sin β + R D ( 1 − sin i ) cos β ] + W π R D L

[0103] dq e 2 ′ = K 0 dP e 2 ′ = ( 1 − sin f i ) { c [ h N + l sin β + R D ( 1 − sin i ) cos β ] + W π R D L }

[0104] Where: W is the weight of the shield machine, unit is kN.

[0105] According to the vertical earth pressure dP on the microelement of the lower half of the shield e2 and lateral earth pressure dq e2 , calculate the earth pressure on the upper part of the microelement per unit length of the radial contact surface between the shield and the soil :

[0106] d s i 2 = dP e 2 ′ sin i + dq e 2 ′ cos i = { c [ h N + l sin β + R D ( 1 − sin i ) cos β ] + W π R D L } ⋅ [ sin i + ( 1 − sin f i ) cos i ]

[0107] Calculate the friction forces df1 and df2 on the inner and outer shield upper parts of the curve:

[0108] df 1 = ndf 1 = n h [ h N + 0 . 5 L sin β + R D ( 1 − sin i ) cos β ] [ sin i + ( 1 − sin f i ) cos i ]

[0109] df 2 = h [ h N + 0 . 5 L sin β + R D ( 1 − sin i ) cos β ] [ sin i + ( 1 − sin f i ) cos i ]

[0110] Where: n is the difference coefficient of friction between the inner and outer sides of the curve, which is calculated and analyzed based on engineering monitoring data to obtain n=1.1; η is the friction coefficient between the shield and the surrounding soil, which is generally .

[0111] Calculate the friction forces df3 and df4 on the inner and outer shield lower parts of the curve:

[0112] df 3 = or { c [ h N + 0 . 5 L sin β + R D ( 1 − sin i ) cos β ] + W π R D L } [ sin i + ( 1 − sin f i ) cos i ]

[0113] df 4 = ndf 3 = n or { c [ h N + 0 . 5 L sin β + R D ( 1 − sin i ) cos β ] + W π R D L } ⋅ [ sin i + ( 1 − sin f i ) cos i ]

[0114] Calculate the friction resistance F1 between the shield and the surrounding soil:

[0115]

[0116] Step 2: According to the calculation model of the front earth pressure of the cutter disc and the micro-element force of the soil in the soil bin, the front earth pressure of the cutter disc and the frictional resistance between the inner wall of the soil bin and the soil are calculated respectively, and the front resistance of the cutter disc is calculated according to the front earth pressure of the cutter disc and the frictional resistance between the inner wall of the soil bin and the soil.

[0117] Furthermore, the calculation method of the front resistance of the cutter disc includes:

[0118] The soil pressure in front of the cutterhead is the vertical soil pressure p e and lateral earth pressure q e The resultant force in the normal direction of the cutterhead and the soil bin pressure σ α Equal in size and opposite in direction;

[0119] Calculate the vertical earth pressure dP on the microelement of the upper part of the cutterhead e1 and lateral earth pressure dq e1 :

[0120] dP e 1 = c [ h N + ( R D − r sin i ) cos β ]

[0121] dq e 1 = K 0 dP e 1 = ( 1 − sin f ) c [ h N + ( R D − r sin i ) cos β ]

[0122] According to the vertical earth pressure dP on the upper part of the cutterhead e1 and lateral earth pressure dq e1 , calculate the earth pressure on the upper part of the cutter head :

[0123] d s α 1 = dP e 1 sin β + dq e 1 cos β = c [ h N + ( R D − r sin i ) cos β ] ⋅ [ sin β + ( 1 − sin f ) cos β ]

[0124] Calculate the vertical earth pressure dP on the microelement of the lower half of the cutterhead e2 and lateral earth pressure dq e2 :

[0125] dP e 2 = c [ h N + ( R D − r sin i ) cos β ] + W π R D L

[0126] dq e 2 = K 0 dP e 2 = ( 1 − sin f ) { c [ h N + ( R D − r sin i ) cos β ] + W π R D L }

[0127] The vertical earth pressure dP of the microelement under the cutterhead is e2 and lateral earth pressure dq e2 , calculate the earth pressure on the upper part of the cutter head :

[0128] d s α 2 = dP e 2 sin β + dq e 2 cos β = { c [ h N + ( R D − r sin i ) cos β ] + W π R D L } ⋅ [ sin β + ( 1 − sin f ) cos β ]

[0129] Calculate the positive earth pressure dF on the cutterhead surface 2-1 :

[0130]

[0131] According to the positive earth pressure dF on the cutterhead surface 2-1 , integrate both sides of the equation according to the upper and lower parts of the cutterhead, consider the influence of the cutterhead opening rate, and calculate the soil pressure F on the front of the cutterhead 2-1 :

[0132]

[0133] Where: is the cutter disc opening rate.

[0134] Calculate the micro-element force of soil in the soil bin:

[0135]

[0136] According to the force of the soil microelement in the soil bin, the axial stress σ along the tunnel axis is l The size of the soil bin pressure σ α Therefore, the frictional resistance F between the inner wall of the soil bin and the soil is calculated by integrating the two sides of the equation for the upper and lower parts of the cutter head. 2-2 :

[0137]

[0138] Where: l ch is the length of the earth pressure chamber, in m; v is the Poisson’s ratio of the soil.

[0139] Calculate the front resistance F2 of the cutter head:

[0140] F 2 = F 2 − 1 + F 2 − 2 = ( ∫ 0 R D ∫ 0 π d s α 1 rd i dr + ∫ 0 R D ∫ π 2 π d s α 2 rd i dr ) [ ( 1 − oh ch ) + ( e 2 tan f R D v 1 − v l ch − 1 ) ]

[0141] Step three: calculate the friction between the segment and the shield tail, the resistance of the tractor trailer, and the penetration resistance of the cut ring.

[0142] Furthermore, the calculation formulas for the friction force F3 between the segment and the shield tail, the resistance F4 of the tractor trailer, and the penetration resistance F5 of the cut ring are:

[0143]

[0144] Where n4 is the number of segments in the tail shield; W s is the deadweight of each ring of segments, in kN; D0 is the outer diameter of the segments, in m; b w is the contact length between each shield tail sealing brush and the pipe ring, in m; p T is the pressure of the shield tail seal brush, in kPa; n5 is the number of layers of the shield tail seal brush; μ3 is the friction coefficient between the shield tail seal brush and the pipe segment; μ2 is the rolling friction coefficient between the rear supporting trailer wheel and the supply surface or the steel wheel and the track; Wp is the deadweight of the trailer, in kN; D is the outer diameter of the front shield, in m; D i is the inner diameter of the front shield, in m; P3 is the average soil pressure of the stratum where the cut ring is inserted, in kPa; t is the depth of the cut ring inserted into the stratum, in m; P m It is the average earth pressure acting on the shield, in kPa.

[0145] Step 4: Calculate the resistance caused by the shield machine's deadweight along the tunnel axis when excavating uphill.

[0146] Furthermore, when tunneling uphill, the resistance F caused by the weight of the shield machine along the tunnel axis is s The calculation is done using the following formula:

[0147]

[0148] Step 5: According to the changes in soil pressure around the shield shell and the cutter head, the torques of the shield shell soil pressure increment and the cutter head soil pressure increment on the rotation center are calculated respectively, and the turning thrust difference of the shield machine is calculated according to the torque of the shield shell and the cutter head soil pressure increment on the rotation center.

[0149] Furthermore, since the force arms of the left and right thrusts are the same when the shield cylinder is advancing, the torque M generated when the shield machine advances one ring of segments is the difference between the left and right thrusts, where:

[0150] The torque M can be obtained by the sum of the torque M1 of the shield shell soil pressure increment on the rotation center and the torque M2 of the cutterhead soil pressure increment on the rotation center during the shield rotation process, where:

[0151] Calculate the shield earth pressure increment Δσ:

[0152]

[0153] In the formula, k t is the soil spring constant, in kN / m; S is the horizontal displacement of the soil around the shield, in m; E s is the elastic modulus of soil, in kPa; E p is the elastic modulus of the shield machine, in kPa; I p is the moment of inertia of the shield machine, in m 4 .

[0154] According to the shield earth pressure increment Δσ, find its relative to the rotation center O q The total torque M1:

[0155]

[0156] In the formula, the turning angle of the shield machine when advancing one ring of segments is , δ g Unit: rad; l is the width of each ring segment, unit: m; R is the radius of curvature of the tunnel, unit: m; L q is the length of the front shield, in m;

[0157] Calculate the horizontal displacement S' and the cutterhead soil pressure increment Δσ' at any point on the cutterhead:

[0158]

[0159]

[0160] According to the increment of cutterhead soil pressure Δσ´, find its relative to the rotation center O q The total torque M2:

[0161]

[0162] Calculate the shield machine turning thrust difference F6:

[0163]

[0164] Step six, calculate the top thrust of the shield machine based on the friction resistance between the shield shell and the surrounding soil, the front resistance of the cutterhead, the friction between the pipe segment and the shield tail, the resistance of the tractor trailer and the penetration resistance of the cutter ring, the turning thrust difference, the resistance caused by the shield machine's own weight along the tunnel axis, and the shield machine's turning thrust difference.

[0165] Furthermore, the thrust force F is calculated according to the following formula:

[0166]

[0167] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating the top thrust of a shield machine taking into account the influence of slope and curvature radius, characterized in that: The steps include: Step 1: According to the friction calculation model between the shield shell and the surrounding soil, the vertical soil pressure and the lateral soil pressure acting on the shield shell are calculated, and the sum of the vertical soil pressure and the lateral soil pressure in the radial direction of the shield is obtained as the radial soil pressure. The friction coefficient between the shield shell and the surrounding soil is selected to calculate the friction resistance between the shield shell and the surrounding soil; Step 2: According to the calculation model of the front earth pressure of the cutter disc and the micro-element force of the soil in the soil bin, the front earth pressure of the cutter disc and the frictional resistance between the inner wall of the soil bin and the soil are calculated respectively, and the front resistance of the cutter disc is calculated according to the front earth pressure of the cutter disc and the frictional resistance between the inner wall of the soil bin and the soil; Step 3, calculating the friction between the segment and the shield tail, the resistance of the tractor trailer, and the penetration resistance of the cutout ring; Step 4, calculating the resistance caused by the weight of the shield machine along the tunnel axis during uphill excavation; Step 5: Calculate the torque of the shield shell soil pressure increment and the cutter head soil pressure increment on the rotation center according to the soil pressure change around the shield shell and the cutter head respectively, and calculate the shield machine turning thrust difference according to the soil pressure increment of the shield shell and the cutter head on the rotation center. Step 6: Calculate the top thrust of the shield machine based on the friction resistance between the shield shell and the surrounding soil, the front resistance of the cutterhead, the friction between the pipe segment and the shield tail, the resistance of the tractor trailer and the penetration resistance of the cutter ring, the resistance caused by the weight of the shield machine along the tunnel axis, and the turning thrust difference of the shield machine.

2. A shield machine top thrust calculation method considering the influence of slope and curvature radius as claimed in claim 1, characterized in that: In the step 1: When the shield machine is excavating in a curved section, due to the geometric characteristics of the curve, the squeezing force of the inner soil on the shield shell is significantly greater than that on the outer side, so the friction between the shield shell and the soil on the inner side of the curve is also greater than that on the outer side; therefore, the friction between the shield shell and the surrounding soil should be calculated according to the inner side and the outer side of the curve, and the friction resistance between the shield shell and the surrounding soil can be calculated by multiplying the radial soil pressure acting on the shield shell and the friction coefficient between the shield shell and the surrounding soil; the soil pressure acting on the shield shell can be divided into vertical soil pressure and lateral soil pressure according to the direction, and the sum of the vertical soil pressure and the lateral soil pressure in the radial direction of the shield is the radial soil pressure. Since the soil pressure is different between the upper and lower parts of the shield machine, it should be divided into two parts for calculation; specifically including:

101. Calculate the vertical earth pressure on the microelement of the upper part of the shield and lateral earth pressure : Where: K0 is the static earth pressure coefficient, ; γ is the bulk density of soil layer; h N is the distance between the top of the cutterhead and the ground surface; R D is the cutter head radius; β is the tunneling slope of the shield machine; φ i is the internal friction angle of the soil; θ is the angle between the calculation point and the horizontal line of the cutterhead; l is the distance between the calculation microelement and the cutterhead surface; According to the vertical earth pressure on the upper part of the shield and lateral earth pressure , calculate the earth pressure on the upper part of the microelement per unit length of the radial contact surface between the shield and the soil : Where: θ is the angle between the calculation point and the horizontal line of the cutterhead; 102. Calculate the vertical earth pressure on the microelement of the lower half of the shield and lateral earth pressure : Where: γ is the soil bulk density; h N is the distance between the top of the cutterhead and the ground surface; l is the distance between the calculation microelement and the cutterhead surface; β is the tunneling slope of the shield machine; R D is the radius of the cutterhead; θ is the angle between the calculation point and the horizontal line of the cutterhead; W is the weight of the shield machine, is pi, L is the length of the shield; According to the vertical earth pressure on the microelement of the lower half of the shield and lateral earth pressure , calculate the earth pressure on the upper part of the microelement per unit length of the radial contact surface between the shield and the soil : Where: θ is the angle between the calculation point and the horizontal line of the cutterhead; 103. Calculate the friction forces df1 and df2 on the inner and outer upper parts of the shield shell: Where: n is the difference coefficient of friction between the inner and outer sides of the curve, which is calculated and analyzed based on engineering monitoring data to obtain n=1.1; η is the friction coefficient between the shield and the surrounding soil, which is generally ; 104. Calculate the friction forces df3 and df4 on the inner and outer lower half of the shield: Where: η is the friction coefficient between the shield and the surrounding soil, which is generally ; γ is the bulk density of soil layer; h N is the distance between the top of the cutterhead and the ground surface; β is the tunneling slope of the shield machine; R D is the radius of the cutterhead; θ is the angle between the calculation point and the horizontal line of the cutterhead; W is the weight of the shield machine; is pi, L is the length of the shield; 105. Calculate the friction resistance F1 between the shield and the surrounding soil: Where: f1 is the friction force on the upper half of the shield shell inside the curve; f2 is the friction force on the upper half of the shield shell outside the curve; f3 is the friction force on the lower half of the shield shell inside the curve; f4 is the friction force on the lower half of the shield shell outside the curve.

3. A shield machine top thrust calculation method considering the influence of slope and curvature radius as claimed in claim 1, characterized in that: The soil pressure on the front of the cutterhead in step 2 is the vertical soil pressure p e and lateral earth pressure q e The resultant force in the normal direction of the cutterhead and the soil bin pressure σ α Equal in size and opposite in direction; The calculation method of the front resistance of the cutter head includes:

201. Calculate the vertical earth pressure dP on the microelement of the upper half of the cutterhead e1 and lateral earth pressure dq e1 : Where: γ is the soil bulk density; h N is the distance between the top of the cutterhead and the ground surface; β is the tunneling slope of the shield machine; R D is the radius of the cutterhead; θ is the angle between the calculation point and the horizontal line of the cutterhead; K0 is the static earth pressure coefficient, ; According to the vertical earth pressure dP on the microelement of the upper half of the cutterhead e1 and lateral earth pressure dq e1 , calculate the earth pressure on the upper part of the cutter head : Where: β is the tunneling slope of the shield machine; 202. Calculate the vertical earth pressure dP on the microelement of the lower half of the cutterhead e2 and lateral earth pressure dq e2 : Where: γ is the soil bulk density; h N is the distance between the top of the cutterhead and the ground surface; l is the distance between the calculation microelement and the cutterhead surface; β is the tunneling slope of the shield machine; R D is the radius of the cutterhead; θ is the angle between the calculation point and the horizontal line of the cutterhead; W is the weight of the shield machine; K0 is the static earth pressure coefficient, ; According to the vertical earth pressure dP on the microelement of the lower half of the cutterhead e2 and lateral earth pressure dq e2 , calculate the earth pressure on the upper part of the cutter head : Where: β is the tunneling slope of the shield machine; 203. Calculate the front earth pressure dF on the microelement on the cutterhead surface 2-1 : According to the front earth pressure dF on the cutterhead surface microelement 2-1 , integrate both sides of the equation according to the upper and lower parts of the cutterhead, consider the influence of the cutterhead opening rate, and calculate the soil pressure F on the front of the cutterhead 2-1 : Where: is the cutter head opening rate; 204. Calculate the soil microelement force in the soil bin: Where: R D is the cutter head radius; σ l is the axial stress; According to the force of the soil microelement in the soil bin, the axial stress σ along the tunnel axis is l The size of the soil bin pressure σ α Equal, so according to the cutter head upper and lower parts of the equation on both sides of the integration, calculate the friction between the soil bin inner wall and the soil F 2-2 : Where: l ch is the length of the earth pressure chamber, in m; v is the Poisson’s ratio of the soil; 205. Calculate the front resistance F2 of the cutter disc: Where: F 2-1 is the soil pressure on the front of the cutterhead; F 2-2 It is the frictional resistance between the inner wall of the soil bin and the soil.

4. A shield machine top thrust calculation method considering the influence of slope and curvature radius as claimed in claim 1, characterized in that: In the step three: The calculation formulas for the friction force F3 between the segment and the shield tail, the resistance F4 of the tractor trailer, and the penetration resistance F5 of the cut ring are as follows: Where n4 is the number of segments in the tail shield; W s is the deadweight of each ring of segments; D0 is the outer diameter of the segments; b w is the contact length between each shield tail sealing brush and the pipe ring; p T is the pressure of the shield tail sealing brush; n5 is the number of layers of the shield tail sealing brush; μ3 is the friction coefficient between the shield tail sealing brush and the pipe segment; μ2 is the rolling friction coefficient between the rear supporting trailer wheel and the supply surface or the steel wheel and the track; W p is the weight of the trailer; D is the outer diameter of the front shield; D i is the inner diameter of the front shield; P3 is the average soil pressure of the stratum where the cut ring is inserted; t is the depth of the cut ring inserted into the stratum; P m is the average earth pressure acting on the shield.

5. A shield machine top thrust calculation method considering the influence of slope and curvature radius as claimed in claim 1, characterized in that: When excavating uphill in step 4, the resistance F caused by the weight of the shield machine along the tunnel axis s The calculation is done using the following formula: Where W is the weight of the shield machine; β is the tunneling slope of the shield machine; W p It is the deadweight of the trailer to be equipped later.

6. A method for calculating the top thrust of a shield machine taking into account the influence of slope and curvature radius as claimed in claim 1, characterized in that: In step 5, the turning thrust difference is that when the shield cylinder is advancing, the force arms of the left thrust and the right thrust are the same, so the torque M generated when the shield machine advances one ring of segments is the difference between the left thrust and the right thrust, where: The torque M can be obtained by the sum of the torque M1 of the shield shell soil pressure increment on the rotation center during the shield rotation process and the torque M2 of the cutterhead soil pressure increment on the rotation center, specifically including:

501. Calculate the shield earth pressure increment : In the formula, k t is the soil spring constant; S is the horizontal displacement of the soil around the shield; E s is the elastic modulus of soil; E p is the elastic modulus of the shield machine; I p is the inertia moment of the shield machine; R D is the cutter head radius; According to the shield earth pressure increment Find its rotation center O q The total torque M1: In the formula, the turning angle of the shield machine when advancing one ring of segments is , δ g Unit: rad; l is the width of each ring segment, unit: m; R is the radius of curvature of the tunnel, unit: m; L q is the length of the front shield, in m; 502. Calculate the horizontal displacement of any point on the cutter head and cutterhead earth pressure increment : ； According to the cutterhead soil pressure increment Find its rotation center O q The total torque M2:

503. Calculate the turning thrust difference F6 of the shield machine: Where M1 is the shield earth pressure increment relative to the rotation center O q The total torque; M2 is the increment of the cutter head earth pressure on the rotation center O q of total torque.

7. A method for calculating the top thrust of a shield machine taking into account the influence of slope and curvature radius as claimed in claim 1, characterized in that: The thrust force F is calculated according to the following formula: Where, F1 is the friction resistance between the shield shell and the surrounding soil; F2 is the front resistance of the cutterhead; F3 is the friction between the segment and the shield tail; F4 is the resistance of the traction trailer; F5 is the penetration resistance of the cut ring; and F6 is the turning thrust difference of the shield machine.

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