Shield soil cabin pressure control method in air pressure auxiliary tunneling mode

Abstract

The invention is suitable for the technical field of earth pressure balance shield tunnel safe tunneling, and provides a shield soil cabin pressure control method in an air pressure auxiliary tunneling mode, which comprises the following steps: according to the volume percentages of gas, solid and liquid phases, pore water pressure and air pressure of foam improved muck, considering the compressibility and the unsaturation of the foam improved muck; obtaining the vertical effective stress distribution of the muck in the soil cabin; determining gas-soil mixing pressure distribution in the soil cabin according to the height of a gas-soil interface in the soil cabin; according to the rotating speed of the spiral conveyor, the shield tunneling speed and the air pressure loss amount in the soil cabin, determining air-soil mixed pressure distribution at the next moment; by adjusting the tunneling speed of the shield tunneling machine and the rotating speed of the screw conveyor, the gas-soil mixed pressure resultant force in the soil cabin is between the active soil pressure resultant force and the passive soil pressure resultant force of the excavated stratum. The control precision of the air-soil mixing pressure in the shield soil cabin in the air pressure auxiliary tunneling mode can be improved.

Description

Technical Field

[0001] The present application belongs to the technical field of safe excavation of earth pressure balance shield tunnels, and in particular relates to a method for controlling the pressure of a shield soil compartment in a pneumatically assisted excavation mode. Background Art

[0002] The air-pressure-assisted excavation mode of an earth pressure balance shield (EPB) is a new shield construction method proposed by the Chinese tunnel engineering community. During EPB shield excavation, the chamber pressure is controlled by adjusting the propulsion speed, screw conveyor speed, and chamber pressure to achieve a balance between chamber pressure and water-soil pressure, thereby ensuring the stability of the excavation interface. However, as the strata change, excavation parameters such as the propulsion speed, screw conveyor speed, and shield chamber pressure must be continuously adjusted to maintain a dynamic balance between the air-soil mixed pressure and water-soil pressure at the excavation interface. In the air-pressure-assisted excavation mode, air pressure and soil coexist within the shield chamber. The air-soil pressure distribution characteristics of the chamber are related to the permeability of the soil and are also affected by the gas permeability of the excavated stratum. Under the dynamic effects of gas infiltration, groundwater seepage, and soil migration, controlling the shield chamber pressure with the goal of balancing water-soil pressure at the excavation face is extremely complex. The key lies in accurately calculating the air-soil mixed pressure distribution within the shield chamber, taking into account air pressure losses.

[0003] Although numerous studies based on field data have initially revealed the relationship between tunneling parameters such as chamber pressure, screw speed, and tunneling speed and the ground, these studies often rely on data rather than physical models to explain the relationship between these construction parameters and the air-soil mixed pressure at the tunneling interface. This results in low control accuracy for the air-soil mixed pressure in the shield chamber. Summary of the Invention

[0004] The embodiment of the present application provides a method for controlling the shield soil chamber pressure in a pneumatically assisted excavation mode, which can solve the problem of low control accuracy of the air-soil mixed pressure in the shield sealed chamber.

[0005] The present application provides a method for controlling the pressure of a shield soil compartment in a pneumatically assisted tunneling mode, comprising:

[0006] The changes in the volume percentages of the gas, solid, and liquid phases of the slag, as well as the pore water and pore air pressures, are obtained. Taking into account the compressibility and unsaturated characteristics of the foam-modified slag, the friction between the slag and the sealed cabin shell, the slag's permeability, and the slag's deadweight are also obtained at the current moment. The sealed cabin is the shield machine's sealed cabin, and the permeability is caused by water and gas infiltrating the slag.

[0007] According to the friction force between the soil and the sealed bulkhead, the penetration force and the deadweight of the soil, and the force balance of the soil in the sealed cabin, the vertical effective stress distribution equilibrium equation of the foam-improved soil in the soil cabin is established.

[0008] According to the established vertical effective stress distribution of the foam-improved slag in the soil cabin and the height of the air-soil interface in the soil cabin at the current moment, the resultant pressure of the air-soil mixture in the soil cabin at the current moment is determined;

[0009] Based on the unsaturated soil gas permeability test, the permeability coefficients of the stratum and foam-improved soil are measured to determine the air pressure loss in the sealed cabin at the current moment;

[0010] The resultant pressure of the air-soil mixture in the sealed cabin at the next moment is obtained based on the screw conveyor speed, shield machine excavation speed, the air-soil mixture pressure in the sealed cabin at the current moment, and the air pressure loss in the sealed cabin at the construction site.

[0011] Obtain the active earth pressure resultant and the passive earth pressure resultant of the stratum;

[0012] By adjusting the shield machine's excavation speed and the screw machine's rotation speed, the combined pressure of the air-soil mixture in the soil chamber is adjusted to be between the combined pressure of the active and passive earth pressures of the stratum in front of the excavation face, thereby ensuring the stability of the excavation stratum.

[0013] Alternatively, the groundwater penetration capacity can be calculated as:

[0014]

[0015] Among them, F1 represents the groundwater permeability, γ w Indicates the weight of water, i 渣土 It represents the hydraulic gradient when water infiltrates into the soil. P represents the shield sealed cabin pressure, P 标态 represents standard atmospheric pressure, H represents the height of the soil-air interface in the sealed cabin, B represents the length of the sealed cabin, D represents the cutterhead diameter of the shield machine, z represents the height of the slag from the bottom of the sealed cabin, and Δz represents the average thickness of the slag in the vertical direction when performing discrete solution;

[0016] The calculation formula for gas permeability is:

[0017]

[0018] P(z)=10(P 标态 +i 渣土 z)

[0019]

[0020]

[0021] Among them, F2 represents the gas permeability of the soil, P(z) is the average pore gas pressure at height z after the mm water column is converted to Pa, φ 等效固相，渣土 (z) represents the volume percentage of the solid phase of the slag at position z in the sealed cabin when considering the improved compressibility of the slag, φ等效液相，渣土 (z) represents the volume percentage of the liquid phase of the slag at position z in the sealed cabin when considering the improved compressibility of the slag, u 地层 represents the pore water pressure, ρ represents the density of the slag, ω represents the moisture content of the slag, G s Indicates the relative density of the soil particles. u(z) represents the pore water and gas pressure;

[0022] The calculation formula of the friction between the slag in the sealed cabin and the sealed cabin shell is:

[0023]

[0024] Among them, F3 represents the friction force, μ represents the friction coefficient between the slag and the sealed bulkhead shell,

[0025] σ z (z)=u(z)+σ′ z (z)=f(u(z))

[0026]

[0027] u(z) represents the pore water and gas pressure, σ' z (z) represents the vertical effective stress, σ z (z) represents the vertical stress of the soil in the sealed cabin at the current moment, and f represents σ z The relationship between (z) and u(z), u w (z) pore water pressure, P(z) represents the pore gas pressure;

[0028] The calculation formula for the deadweight of slag soil is:

[0029]

[0030] Among them, F4 represents the deadweight, G s Indicates the relative density of soil particles.

[0031] Optionally, based on the friction force between the soil and the sealed bulkhead, the penetration force, and the deadweight of the soil, and the force balance of the soil in the sealed cabin, the vertical effective stress distribution equilibrium equation of the foam-improved soil in the soil cabin is established, including:

[0032] Based on the movement of the entire slag in the sealed cabin, the relationship is constructed:

[0033]

[0034] Based on the relationship, φ 等效固相，渣土 The expression of (z), φ 等效液相，渣土 The expression of (z), σ z(z)=f(u(z)) to solve the vertical effective stress and obtain the vertical stress σ of the slag in the sealed cabin at the current moment z (z).

[0035] Optionally, the resultant pressure of the air-soil mixture in the sealed cabin at the current time t is:

[0036]

[0037] Among them, F 密封舱 (t) represents the combined pressure of the air-soil mixture in the sealed cabin at the current moment, P(t)S(t) represents the gas pressure in the sealed cabin at the current moment, represents the soil pressure in the sealed cabin at the current moment, P(t) represents the air pressure in the shield sealed cabin at the current moment, and S(t) represents the area of ​​air pressure acting on the top of the soil layer in the sealed cabin at the current moment;

[0038]

[0039] H(t) represents the height of the soil-air interface in the sealed cabin at the current moment, N represents the number of layers when the soil is discretely solved, and σ z (H(t)-iΔz) represents the vertical stress at the current position H(t)-iΔz, i=1,2,…,N;

[0040]

[0041] v 土层，输走 is the volume rate of the soil in the sealed cabin transported out by the screw conveyor, v 土层，输走 η represents the earth discharge efficiency of the shield machine, ω 螺旋机转速 (t) represents the screw speed of the shield machine at the current moment, A s V represents the effective soil discharge area of ​​the shield machine's screw machine, l represents the shield machine's screw pitch; 土层，进入 is the volume rate of the formation entering the sealed cabin during the shield advancement process, V 推进 (t) represents the tunneling speed of the shield machine at the current moment;

[0042]

[0043] Optionally, based on the unsaturated soil gas permeability test, the permeability coefficients of the stratum and the foam-improved soil are measured to determine the air pressure loss in the sealed cabin at the current moment. Based on the screw conveyor speed, shield machine excavation speed, air-soil mixed pressure in the sealed cabin at the current moment, and air pressure loss in the sealed cabin, the resultant air-soil mixed pressure in the sealed cabin at the next moment is obtained, including:

[0044] By formula Calculate the height of the soil-air interface in the sealed cabin at the next moment H(t+Δt);

[0045] By formula Calculate the shield sealed cabin pressure P(t+dt) at the next moment;

[0046] The air pressure loss q(t) in the sealed cabin at the current moment is calculated by the formula q(t)=q1(t)+q2(t);

[0047] P 标态 q1(t+Δt)=P 标态 q1(t)+P 标态 k sq1 i 地层 S(t)Δt

[0048]

[0049] The gas-soil mixed pressure force F in the sealed cabin at the next moment is calculated by the following formula 密封舱 (t+Δt):

[0050]

[0051] Where t represents the current moment, Δt represents the time difference between the next moment and the current moment, q1(t) represents the cumulative amount of gas flowing into the formation at the current moment, q2(t) represents the cumulative amount of gas flowing into the pores of the soil in the sealed cabin at the current moment, q1(t+Δt) represents the cumulative amount of gas flowing into the formation at the next moment, and k sq1 Indicates the permeability coefficient of the formation, h represents the buried depth of the cutter head of the shield machine, q2(t+Δt) represents the cumulative amount of gas flowing into the pores of the soil in the sealed cabin at the next moment, and k sq2 Indicates the permeability coefficient of slag.

[0052] Optionally, the calculation formula for the resultant active earth pressure of the stratum is:

[0053]

[0054] Among them, F 主动土压力 represents the active earth pressure of the stratum, k 主动 represents the active earth pressure coefficient, represents the internal friction angle of the excavated stratum, γ i represents the weight of the i-th layer of soil in the excavation stratum, i represents the top burial depth of the shield machine cutterhead, h i represents the top height of the i-th soil layer, c i It represents the cohesion of the i-th layer of soil in the excavation stratum.

[0055] Optionally, the formula for calculating the resultant passive earth pressure is:

[0056]

[0057] Among them, F 被动土压力 represents the resultant passive earth pressure of the stratum, k 被动 represents the passive earth pressure coefficient,

[0058] Optional, F 主动土压力 ≤F 密封舱 (t+Δt)≤F 被动土压力 , H min ≤H(t+Δt)≤H max ;H min Indicates the preset minimum airtight cabin soil-air interface height, H max Indicates the height of the soil-air interface in the preset maximum sealed cabin.

[0059] Optionally, adjust the shield machine's tunneling speed and screw machine speed, including:

[0060] If F 密封舱 (t+Δt) <F 主动土压力 , then reduce the shield machine's excavation speed, increase the shield machine's screw speed and the shield machine's sealed cabin pressure;

[0061] If F 密封舱 (t+Δt)>F 被动土压力 , then increase the shield machine's excavation speed, reduce the shield machine's screw speed and the shield machine's sealed cabin pressure;

[0062] If H(t+Δt>H max , then reduce the shield machine's excavation speed and increase the shield machine's screw speed;

[0063] If H(t+Δt) <H min , then increase the shield machine's excavation speed and reduce the shield machine's screw speed.

[0064] Optionally, the control method further includes:

[0065] The shield sealed cabin pressure P(t) at the current moment is calculated using the following formula:

[0066]

[0067] Where t0 represents the time of the last air pressure replenishment, S(t0+jΔt) represents the effective area of ​​the air pressure chamber in the jth time period from t0 to t divided by Δt intervals during the refined solution, and H(t0+jΔt) represents the height of the soil interface in the jth time period from t0 to t divided by Δt intervals.

[0068] The above solution of the present application has the following beneficial effects:

[0069] In an embodiment of the present application, by comprehensively considering multiple factors of excavation parameters such as gas and liquid infiltration, slag movement, excavation speed, and screw machine speed, a physical model of the pressure distribution in the sealed cabin is constructed. Starting from the essence of the stress state change of the slag in the sealed cabin, the permeability of the seepage field to the slag, the resistance of the sealed cabin wall shell to the slag, and the air pressure loss caused by gas infiltration are considered to accurately calculate the gas-soil mixed pressure in the sealed cabin, so as to accurately detect whether the stratum force meets the stratum force balance condition (that is, the resultant force of the gas-soil mixed pressure in the soil cabin is between the active soil pressure resultant and the passive soil pressure resultant of the stratum in front of the excavation face). When the force balance condition is not met, the excavation speed of the shield machine, the screw machine speed and the sealed cabin air pressure are adjusted in time, thereby achieving precise control of the support force of the sealed cabin and improving the control accuracy of the support force of the shield sealed cabin.

[0070] Other beneficial effects of the present application will be described in detail in the subsequent specific implementation section. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments or descriptions of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0072] Figure 1 This is a flow chart of a shield soil compartment pressure control method in a pneumatically assisted excavation mode provided in an embodiment of the present application;

[0073] Figure 2 A schematic diagram of the forces acting on the slag in a sealed cabin according to an embodiment of the present application;

[0074] Figure 3 A flowchart for adjusting the excavation speed, screw machine speed, and sealed cabin air pressure provided in one embodiment of the present application;

[0075] Figure 4 A schematic diagram of a sealed cabin pressure distribution calculation model provided in one embodiment of the present application. DETAILED DESCRIPTION

[0076] In the following description, specific details such as specific system structures and techniques are provided for purposes of illustration rather than limitation to facilitate a thorough understanding of the embodiments of the present application. However, it will be apparent to those skilled in the art that the present application may be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid obscuring the description of the present application with unnecessary detail.

[0077] It should be understood that when used in the present specification and the appended claims, the term "comprising" indicates the presence of described features, integers, steps, operations, elements and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or collections thereof.

[0078] It will also be understood that the term "and / or" used in this specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.

[0079] As used in this specification and the appended claims, the term "if" can be interpreted as "when" or "upon" or "in response to determining" or "in response to detecting," depending on the context. Similarly, the phrase "if it is determined" or "if [described condition or event] is detected" can be interpreted as meaning "upon determination" or "in response to determining" or "upon detection of [described condition or event]" or "in response to detecting [described condition or event]," depending on the context.

[0080] In addition, in the description of the present application specification and the appended claims, the terms "first", "second", "third", etc. are only used to distinguish the descriptions and cannot be understood as indicating or implying relative importance.

[0081] References to "one embodiment" or "some embodiments" in this specification mean that a particular feature, structure, or characteristic described in conjunction with that embodiment is included in one or more embodiments of the present application. Thus, phrases such as "in one embodiment," "in some embodiments," "in other embodiments," and "in other embodiments" appearing in various places in this specification do not necessarily refer to the same embodiment, but rather mean "one or more but not all embodiments," unless otherwise specifically emphasized. The terms "including," "comprising," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0082] In response to the current problem of low control accuracy of the support force of the shield sealed cabin, an embodiment of the present application provides a shield soil cabin pressure control method in an air pressure-assisted excavation mode. By comprehensively considering multiple factors such as gas and liquid infiltration, slag movement, and excavation parameters, a physical model of the sealed cabin pressure distribution is constructed. Starting from the essence of the stress state change of the slag in the sealed cabin, the permeability, the resistance of the sealed cabin wall shell to the slag, and the air pressure loss caused by gas infiltration are considered to accurately calculate the gas-soil mixed pressure in the sealed cabin. This can accurately detect whether the stratum force meets the stratum force balance condition (that is, the resultant force of the gas-soil mixed pressure in the soil cabin is between the active soil pressure resultant and the passive soil pressure resultant of the stratum in front of the excavation face). When the force balance condition is not met, the excavation speed of the shield machine, the screw machine speed and the sealed cabin air pressure are adjusted in time, thereby achieving precise control of the support force of the sealed cabin and improving the control accuracy of the support force of the shield sealed cabin.

[0083] The shield soil compartment pressure control method in the air pressure assisted excavation mode provided in this application is exemplarily described below with reference to specific embodiments.

[0084] To facilitate understanding of the shield soil compartment pressure control method in the air pressure-assisted excavation mode provided in this application, the relevant parameters involved in the following embodiments are first explained.

[0085] Direct parameters (input parameters): soil parameters: density ρ (g / cm 3 ), moisture content w, particle relative density G s , cohesion c (kPa), internal friction angle Pore ​​water pressure u 地层 (kPa); Shield machine parameters: cutterhead diameter D (m), cutterhead top burial depth h (m), tunneling speed v 推进 (m / s), screw pitch l (m), soil discharge efficiency η, effective soil discharge area A of the screw machine s (m 2 ), screw machine speed ω 螺旋机转速 (rad / s), shield chamber pressure P (kPa), chamber length B (m), foam injection ratio FIR, foam expansion ratio FER, height of air-soil interface in shield chamber at the beginning of tunneling H0 (m); gas permeability coefficient k of the formation sq1 (m / s), permeability coefficient k of slag sq2 .

[0086] Indirect parameter: Volume percentage of gas, solid and liquid phases in the formation: φ 固相，地层 ,φ 液相，地层 ,φ 气相，地层 ; Volume percentage of gas, solid and liquid phases of slag in the screw conveyor: φ 固相，改良渣土 ,φ 液相，改良渣土 ,φ 气相，改良渣土; Volume percentage of gas, solid and liquid phases of slag at different positions and times in the sealed cabin: φ 等效固相，渣土 ,φ 等效液相，渣土 ,φ 等效气相，渣土 and vertical stress σ z (Pa) and pore water pressure u (Pa); the volume velocity v of the formation entering the shield sealed chamber 土层，进入 (m 3 / s), soil transportation rate v 土层，输走 (m 3 / s); the height of the soil-air layer interface in the sealed cabin H (m), the horizontal cross-sectional area at the soil-air layer interface in the sealed cabin S (m 2 ), the equivalent volume Q(m 3 ), air loss q(m 3 ); Gas infiltration hydraulic gradient i 地层 The hydraulic gradient of soil infiltration i 渣土 .

[0087] Control target: The combined pressure of the air-soil mixture in the shield sealed cabin (i.e., the support force of the sealed cabin, which is also called the soil cabin) F 密封舱 (kN), active earth pressure F 主动土压力 (kN) and the passive earth pressure F 被动土压力 (kN), F 主动土压力 ≤F 密封舱 ≤F 被动土压力 .

[0088] The model control parameters are (output parameters): v 推进 、ω 螺旋机转速 、P.

[0089] Among them, φ 等效固相，渣土 ,φ 等效液相，渣土 ,φ 等效气相，渣土 The calculation process is:

[0090] As gas infiltrates the soil inside the sealed compartment, the stress state of the soil changes. Since the stress properties of the soil are closely related to the porosity, it is necessary to calculate the volume percentages of the three phases: gas, solid, and liquid.

[0091] Through the survey report, the ground parameters in front of the shield tunneling face are directly obtained, namely the density ρ, moisture content w, and relative density G of the slag. s , and then convert the volume percentages of soil gas, solid and liquid phases in the excavated stratum:

[0092]

[0093] Take the improved soil from the excavated ring car and measure the density, moisture content and relative density of the improved soil. 固相，地层 、φ 液相，地层 、φ 气相，地层 The volume percentages of the gas, solid, and liquid phases of the slag at the screw conveyor are converted using the calculation formula. The improvement effect of the same formation is mainly determined by the foam modifier addition parameters (foam injection ratio FIR, foam expansion ratio FER):

[0094] (φ 固相，改良渣土 ,φ 液相，改良渣土 ,φ 气相，改良渣土 )=J(FIR,FER)

[0095] Where: J(FIR, FER) represents the empirical formula obtained from the excavated ring soil and indoor tests.

[0096] The volume percentage of gas, solid and liquid phases of slag at different depths in the shield sealed cabin is equivalent to the three-phase φ 等效固相，渣土 ,φ 等效液相，渣土 ,φ 等效气相，渣土 The conversion is based on its pore pressure. Due to the infiltration of the gas from the pressure chamber into the soil in the sealed chamber, the gas mass and pressure in the soil pores at different depths vary, and the pore water pressure at different locations of the improved soil in the sealed chamber changes. Ignoring the compressibility of the solid and liquid phases in the soil layer in the sealed chamber, the actual volume of each phase per unit volume remains unchanged:

[0097] dV 固相，渣土 (z)=φ 固相，地层 dV

[0098] dV 液相，渣土 (z)=φ 液相，地层 dV

[0099] dV 气相，渣土 (z)=φ 气相，地层 dV

[0100] Where: V represents volume.

[0101] However, due to the increase in the number of moles of gas in the voids caused by gas infiltration, the pore gas volume under the same pressure can be calculated based on the ideal gas state equation:

[0102] u(z)φ 气相，地层 dV=u 地层 dV 等效气相，渣土 (z)

[0103]

[0104] Based on dV 固相，渣土 (z), dV 液相，渣土 (z), dV 气相，渣土(z),u(z)φ 气相，地层 dV vs. dV 等效气相，渣土 The expression of (z) can be used to obtain the equivalent three-phase at different positions:

[0105]

[0106]

[0107]

[0108] u(z) represents the pore water and air pressure, φ 等效固相，渣土 (z) represents the volume percentage of the solid phase of the slag at position z in the sealed cabin when considering the improved compressibility of the slag, φ 等效液相，渣土 (z) represents the volume percentage of the liquid phase of the slag at position z in the sealed cabin when considering the improved compressibility of the slag, u 地层 represents the pore water pressure, φ 等效气相，渣土 (z) represents the volume percentage of the slag gas phase at position z in the sealed cabin when the improved slag compressibility is considered.

[0109] Further obtain the equivalent porosity e 等效，渣土 (z):

[0110]

[0111] like Figure 1 As shown, the embodiment of the present application provides a method for controlling shield soil chamber pressure in a pneumatically assisted excavation mode, comprising:

[0112] Step 11: Obtain the changes in the volume percentages of the gas, solid, and liquid phases of the slag, the pore water pressure, and the pore air pressure. Considering the compressibility and unsaturated characteristics of the foam-modified slag, obtain the friction between the slag and the sealed cabin wall shell, the permeability of the slag, and the deadweight of the slag at the current moment.

[0113] The above-mentioned sealed cabin is the sealed cabin of the shield machine, also known as the soil bin, and the permeability is caused by water and gas infiltrating into the slag soil.

[0114] like Figure 2 As shown in Figure 1, the stress on the shield sealed cabin soil (i.e., the soil in the sealed cabin of the shield machine) during seepage is considered. Since the surface pore water pressure in the sealed cabin is higher than the pore water pressure at the screw machine, the soil is subjected to the seepage force caused by seepage, including groundwater permeability and gas permeability. The calculation formula for the groundwater permeability F1 is:

[0115]

[0116] Wherein, F1 represents the water penetration force, γ w Indicates the weight of water, i 渣土It represents the hydraulic gradient when water infiltrates into the soil. P represents the shield sealed cabin pressure, P 标态 represents standard atmospheric pressure, H represents the height of the soil-air interface in the sealed cabin, B represents the length of the sealed cabin, D represents the cutterhead diameter of the shield machine, z represents the height of the slag from the bottom of the sealed cabin, and Δz represents the average thickness of the slag in the vertical direction when performing discrete solution.

[0117] Slag is composed of three phases: solid, liquid, and gas. In addition to the liquid permeability, gas also has a permeability effect. The calculation formula for the gas permeability is:

[0118]

[0119] P(z)=10(P 标态 +i 渣土 z)

[0120] Wherein, F2 represents the gas permeability of the soil, P(z) is the average pore gas pressure at height z after the mm water column is converted to Pa, φ 等效固相，渣土 (z) represents the volume percentage of the solid phase of the slag at position z in the sealed cabin when considering the improved compressibility of the slag, φ 等效液相，渣土 (z) represents the volume percentage of the liquid phase of the slag at position z in the sealed cabin when the improved compressibility of the slag is considered.

[0121] Due to the overall downward movement of the slag, a friction force F3 exists between the slag and the sealed bulkhead shell. The friction coefficient μ between the slag and the sealed bulkhead shell can be approximately replaced by the friction angle tangent value measured in the triaxial shear test of the shield foam-improved slag. The effective stress of the improved slag is related to the pore water and air pressure. The bubbles and pore water in the slag both cause changes in the effective stress of the slag. The force on the shield pressure bulkhead shell is the sum of the horizontal effective stress and the pore water and air pressure. That is: x (z)=u(z)+Kσ' z (z), where K represents the lateral earth pressure coefficient, K = 1, σ x (z)=σ z (z), u(z) represents the pore water and air pressure, σ' z (z) represents the vertical effective stress, σ z (z)=f(u(z)),σ z (z) represents the vertical stress of the soil in the sealed cabin at the current moment, and f represents σ z The relationship between (z) and u(z).

[0122] It should be noted that the stress state of the slag in the sealed cabin is determined by the improved porosity ratio. The effective stress of the improved slag is related to the pore water and air pressure. Both the bubbles and pore water in the slag cause changes in the effective stress of the slag.

[0123]

[0124] u(z) represents the pore water and gas pressure, σ' z (z) represents the vertical effective stress, σ z (z) represents the vertical stress of the soil in the sealed cabin at the current moment, and f represents σ z The relationship between (z) and u(z), u w (z) pore water pressure, P(z) represents the pore gas pressure.

[0125] By taking in-situ soil, configuring improved soil with different improvement degrees, conducting permeability tests, and measuring the corresponding pore water pressure u(z) and soil pressure and porosity ratio, the vertical stress σ can be finally obtained. z The relationship between (z) and pore water pressure u(z): z (z) = f(u(z)), where f is an empirical formula obtained through indoor experiments.

[0126] In some embodiments of the present application, the friction force F3 is calculated as follows:

[0127]

[0128] The calculation formula for the deadweight of slag F4 is:

[0129]

[0130] Among them, F4 represents the weight of the slag, that is, the gravity of the slag.

[0131] Step 12: Based on the friction force between the slag in the sealed cabin and the sealed cabin shell, the penetration force and the deadweight of the slag, and the force balance of the slag in the sealed cabin, a vertical effective stress distribution equilibrium equation of the foam-improved slag in the soil cabin is established.

[0132] In some embodiments of the present application, the entire slag in the sealed cabin can be considered to be moving downward at a uniform speed. Therefore, based on the movement of the entire slag in the sealed cabin, the following relationship is constructed:

[0133]

[0134] Based on this relationship, φ 等效固相，渣土 The expression of (z), φ 等效液相，渣土 The expression of (z), σ z (z)=f(u(z)) to solve the vertical effective stress and obtain the vertical stress σ of the slag in the sealed cabin at the current moment z Specifically, by substituting the above expressions of F1, F2, F3, and F4 into this relational equation, we can obtain σ z (z), the solved σ zThe expression of (z) is the above vertical effective stress distribution equilibrium equation, σ z (z-Δz) represents the vertical stress at the z-Δz position.

[0135] Specifically, the above relationship is based on the formula σ z (z)=f(u(z)),φ 等效固相，渣土 The expression of (z), φ 等效液相，渣土 The expression of (z), φ 等效气相，渣土 The expression of (z) is converted into pore water pressure. Considering that the top of the soil layer in the sealed cabin is subjected to vertical uniform air pressure P, the soil layer in the sealed cabin is discretized and solved layer by layer from top to bottom to solve the pore water pressure field u(z). Then, based on φ 等效固相，渣土 The expression of (z), φ 等效液相，渣土(z) The expression of σ z (z)=f(u(z)) to solve the vertical effective stress and finally obtain the vertical stress field σ z (z).

[0136] Step 13: Determine the resultant pressure of the air-soil mixture in the soil cabin at the current moment based on the established vertical effective stress distribution of the foam-improved slag in the soil cabin and the height of the air-soil interface in the soil cabin at the current moment.

[0137] Step 14: Based on the unsaturated soil gas permeability test, the permeability coefficients of the stratum and the foam-improved soil are measured to determine the air pressure loss in the sealed cabin at the current moment.

[0138] Step 15, according to the screw conveyor speed at the construction site, the shield machine excavation speed, the air-soil mixed pressure of the sealed cabin at the current moment and the air pressure loss in the sealed cabin, obtain the air-soil mixed pressure resultant of the sealed cabin at the next moment.

[0139] In some embodiments of the present application, the support force of the sealed cabin is composed of gas pressure and soil pressure.

[0140] Specifically, the combined pressure F of the air-soil mixture in the sealed cabin at the current time t is 密封舱 (t) is:

[0141]

[0142] Among them, F 密封舱 (t) represents the combined pressure of the air-soil mixture in the sealed cabin at the current moment (i.e., the supporting force), P(t)S(t) represents the gas pressure in the sealed cabin at the current moment, represents the soil pressure in the sealed cabin at the current moment, P(t) represents the air pressure in the shield sealed cabin at the current moment, and S(t) represents the area of ​​air pressure acting on the top of the soil layer in the sealed cabin at the current moment;

[0143]

[0144] H(t) represents the height of the soil-air interface in the sealed cabin at the current moment, N represents the number of layers when the soil is discretely solved, and σ z (H(t)-iΔz) represents the vertical stress at the current position H(t)-iΔz, where i=1, 2,…, N.

[0145] It should be noted that, during the excavation process, the soil in the sealed cabin is replenished by the stratum in front and transported by the screw conveyor, which may cause the air pressure action area to change. Therefore, it is necessary to determine the volume rate v of the soil layer entering the sealed cabin. 土层，进入 and muck transportation efficiency 土层，输走 Decision. Specific, v 土层，输走 is the volume rate of the soil in the sealed cabin transported out by the screw conveyor, v 土层，进入 It is the volume rate at which the formation enters the sealed chamber during the shield tunneling process.

[0146] The volume rate of soil entering the sealed cabin during excavation v 土层，进入 From the excavation speed v 推进 Determined by the cutter head diameter D:

[0147]

[0148] Efficiency of soil transportation during excavation v 土层，输走 The shield adopts screw machine model (pitch l, effective discharge area A s ), soil discharge efficiency (related to the improved soil) η and screw machine speed ω 螺旋机转速 Decide:

[0149]

[0150] η represents the earth discharge efficiency of the shield machine, ω 螺旋机转速 (t) represents the screw speed of the shield machine at the current moment, A s It represents the effective soil discharge area of ​​the shield machine's screw machine, l represents the shield machine's screw pitch, v 推进 (t) represents the tunneling speed of the shield machine at the current moment.

[0151] Affected by the excavation speed and the screw machine speed, the soil interface in the sealed cabin fluctuates, and the increment of the pressure action area of ​​the air pressure cabin is:

[0152]

[0153] The change of interface height in the sealed cabin is:

[0154]

[0155] From the above S(t+Δt) and H(t+Δt), it can be seen that the support force of the sealed cabin can be precisely controlled by adjusting the screw speed and excavation speed of the shield machine.

[0156] During actual shield tunneling, air pressure is not continuously controlled. Instead, it loses a certain amount of pressure before returning to a specified value. Therefore, accurately calculating the air pressure loss q(t) helps determine when to re-pressurize. The air pressure loss q(t) includes the air pressure flowing into the formation q1(t) and the air pressure flowing into the soil pores within the sealed chamber q2(t).

[0157] Specifically, after calculating the support force of the sealed cabin at the current moment, the following steps can be used to determine the air pressure loss in the sealed cabin at the current moment according to the gas infiltration theory, and the support force F of the sealed cabin at the current moment can be used to determine the air pressure loss in the sealed cabin at the current moment. 密封舱 (t) and the air pressure loss in the sealed cabin at the current moment q(t), and obtain the support force F of the sealed cabin at the next moment 密封舱 (t+Δt):

[0158] By formula Calculate the height of the soil-air interface in the sealed cabin at the next moment H(t+Δt);

[0159] By formula Calculate the shield sealed cabin pressure at the next moment

[0160] The air pressure loss q(t) in the sealed cabin at the current moment is calculated by the formula q(t)=q1(t)+q2(t);

[0161] The amount of gas flowing into the formation q1(t) and the formation permeability coefficient k sq1 related:

[0162] P 标态 q1(t+Δt)=P 标态 q1(t)+P 标态 k sq1 i 地层 S(t)Δt

[0163] The amount of gas flowing into the pores of the soil in the sealed cabin q 2( t):

[0164]

[0165] The gas-soil mixed pressure force F in the sealed cabin at the next moment is calculated by the following formula 密封舱 (t+Δt):

[0166]

[0167] Where t represents the current moment, Δt represents the time difference between the next moment and the current moment, q1(t) represents the cumulative amount of gas flowing into the formation at the current moment, q2(t) represents the cumulative amount of gas flowing into the pores of the soil in the sealed cabin at the current moment, q1(t+Δt) represents the cumulative amount of gas flowing into the formation at the next moment, and k sq1 Indicates the permeability coefficient of the formation, h represents the buried depth of the cutter head of the shield machine, q2(t+Δt) represents the cumulative amount of gas flowing into the pores of the soil in the sealed cabin at the next moment, and k sq2 Indicates the permeability coefficient of slag.

[0168] It should be noted that when calculating i 渣土 When the slag movement at the screw conveyor is mainly linked with the conveyor belt, the gas penetration can be ignored. Therefore, the seepage path l = H, and the head difference can be approximated as PP 标态 , considering the unit conversion, we get

[0169] Step 16: Obtain the active earth pressure resultant and the passive earth pressure resultant of the stratum.

[0170] Specifically, the active earth pressure F 主动土压力 The calculation formula is:

[0171]

[0172] Among them, F 主动土压力 represents the active earth pressure resultant of the stratum, k 主动 represents the active earth pressure coefficient, represents the internal friction angle of the excavated stratum, γ i represents the weight of the i-th layer of soil in the excavation stratum, h represents the top burial depth of the shield machine cutterhead, h i represents the top height of the i-th soil layer, c i It represents the cohesion of the i-th layer of soil in the excavation stratum.

[0173] Resultant passive earth pressure F 被动土压力 The calculation formula is:

[0174]

[0175] Among them, F 被动土压力 represents the resultant passive earth pressure of the stratum, k 被动 represents the passive earth pressure coefficient,

[0176] Step 17, by adjusting the shield machine excavation speed and the screw machine speed, the air-soil mixed pressure in the soil chamber is adjusted to be between the active earth pressure and the passive earth pressure in the stratum ahead of the excavation face, thereby ensuring the stability of the excavation stratum.

[0177] In some embodiments of the present application, the above-mentioned conditions for ensuring the stability of the excavated stratum can be understood as the stratum force balance condition, and the stratum force balance condition is: F 主动土压力 ≤F 密封舱 (t+Δt)≤F 被动土压力 , H min ≤H(t+Δt)≤H max .

[0178] Among them, H min Indicates the preset minimum airtight cabin soil-air interface height, H max Indicates the height of the soil-air interface in the preset maximum sealed cabin.

[0179] like Figure 3 As shown in the figure, the specific implementation method of adjusting the shield machine's tunneling speed and the screw machine's speed is as follows:

[0180] If F 密封舱 (t+Δt) <F 主动土压力 , then reduce the shield machine's excavation speed, increase the shield machine's screw speed and the shield machine's sealed cabin pressure;

[0181] If F 密封舱 (t+Δt)>F 被动土压力 , then increase the shield machine's excavation speed, reduce the shield machine's screw speed and the shield machine's sealed cabin pressure;

[0182] If H(t+Δt)>H max , then reduce the shield machine's excavation speed and increase the shield machine's screw speed;

[0183] If H(t+Δt) <H min , then increase the shield machine's excavation speed and reduce the shield machine's screw speed.

[0184] It can be understood that the above adjustment refers to making appropriate adjustments based on the value at the current moment when the next moment is reached. For example, based on the shield sealed cabin air pressure at the current moment, the air pressure is appropriately increased to reach 5 to 6 atmospheres.

[0185] Since the pressurization process is not continuous, the above adjustment is performed periodically. In order to maintain the stability of the tunneling interface, the shield sealed chamber pressure P(t) at the current moment can be calculated by the following formula:

[0186]

[0187] Specifically, if the air pressure change P(t) is greater than the air pressure change threshold, the air pressure in the shield sealed cabin is increased.

[0188] Where t0 represents the time of the last air pressure replenishment, S(t0+jΔt) represents the effective area of ​​the air pressure chamber in the jth time period from t0 to t divided by Δt intervals during the refined solution, and H(t0+jΔt) represents the height of the soil interface in the jth time period from t0 to t divided by Δt intervals.

[0189] It should be noted that if the resultant active earth pressure of the stratum, the resultant passive earth pressure of the stratum and the support force of the sealed cabin meet the stratum force balance conditions at the next moment, there is no need to adjust the excavation speed, screw machine speed and shield sealed cabin air pressure, and the parameters at the current moment can be used as the recommended excavation parameters.

[0190] In summary, if Figure 4 As shown, when calculating the support force (i.e., effective support force) of the air-pressure-assisted shield sealed cabin, the present application comprehensively considers the three phases of the excavation stratum, the ideal gas state equilibrium equation, the empirical formula for slag improvement, the permeability, the resistance of the sealed cabin shell to the slag, and the vertical stress physical differential equation; when calculating the air pressure loss of the air-pressure-assisted shield, the infiltration of gas into the slag and the stratum is taken into account, so as to achieve more accurate calculation of the air pressure and more scientific determination of the air pressure replenishment time.

[0191] Most of the parameters in the mathematical model proposed in this application are based on the physical model rather than estimated through machine learning, so it is still persuasive in strata with less excavation data.

[0192] It is worth mentioning that this application constructs a physical model of the pressure distribution in the sealed cabin by comprehensively considering multiple factors of tunneling parameters such as gas and liquid infiltration, slag movement, tunneling speed, and screw machine speed. Starting from the essence of the stress state change of the slag in the sealed cabin, the penetration force of the seepage field on the slag and the resistance of the sealed cabin wall shell to the slag are accurately calculated, so as to accurately detect whether the formation force meets the formation force balance condition, and when the force balance condition is not met, the tunneling speed and screw machine speed of the shield machine are adjusted in time, thereby achieving precise control of the support force of the sealed cabin and improving the control accuracy of the support force of the shield sealed cabin.

[0193] Specifically, this application provides a physical model for the pressure distribution in the sealed chamber that comprehensively considers multiple factors, including stratum properties, tunneling speed, screw machine speed, and sealed chamber air pressure. Under the dynamic effects of "gas infiltration," "groundwater seepage," and "soil migration," the model considers that gas infiltration increases the number of gas moles in the pores of the soil within the sealed chamber, thereby increasing the soil pore pressure and excess pore water pressure. Based on the nature of the changes in the stress state of the soil within the sealed chamber, and taking into account the seepage field's penetration into the soil and the resistance of the sealed chamber's shell to the soil, the gas-soil mixed pressure within the sealed chamber is accurately calculated.

[0194] The above is a preferred embodiment of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles described in the present application. These improvements and modifications should also be regarded as the scope of protection of the present application.

Claims

1. A method for controlling the pressure of a shield soil compartment in a pneumatically assisted excavation mode, characterized in that: include: Obtain the change in volume percentage of gas, solid and liquid three phases of the slag, pore water pressure and pore gas pressure, consider the compressibility and unsaturated characteristics of the foam-modified slag, and obtain the friction between the slag and the sealed cabin wall shell, the permeability of the slag and the deadweight of the slag in the sealed cabin at the current moment; the sealed cabin is the sealed cabin of the shield machine, and the permeability is caused by water and gas infiltrating the slag; According to the friction between the slag in the sealed cabin and the sealed cabin wall shell, the penetration force and the deadweight of the slag, based on the force balance of the slag in the sealed cabin, a vertical effective stress distribution equilibrium equation of the foam-improved slag in the soil cabin is established; According to the established vertical effective stress distribution of foam-improved slag in the soil cabin and the height of the air-soil interface in the soil cabin at the current moment, the resultant pressure of the air-soil mixture in the soil cabin at the current moment is determined; According to the unsaturated soil gas permeability test, the gas permeability coefficients of the stratum and the foam-improved soil are measured to determine the gas pressure loss in the sealed cabin at the current moment; According to the screw conveyor speed, shield machine excavation speed, gas-soil mixed pressure of the sealed cabin at the current moment and the air pressure loss in the sealed cabin at the construction site, the gas-soil mixed pressure resultant of the sealed cabin at the next moment is obtained; Obtaining the active earth pressure resultant force and the passive earth pressure resultant force of the stratum; By adjusting the shield machine's excavation speed and the screw machine's rotation speed, the combined pressure of the air-soil mixture in the soil chamber is adjusted to be between the combined force of the active earth pressure and the combined force of the passive earth pressure in the stratum in front of the excavation face, thereby ensuring the stability of the excavation stratum.

2. The control method according to claim 1, characterized in that: The calculation formula for groundwater permeability is: Wherein, F1 represents the groundwater permeability, γ w Indicates the weight of water, i 渣土 It represents the hydraulic gradient when water infiltrates into the soil. P represents the shield sealed cabin pressure, P 标态 represents standard atmospheric pressure, H represents the height of the soil-air interface in the sealed cabin, B represents the length of the sealed cabin, D represents the cutter head diameter of the shield machine, z represents the height of the slag from the bottom of the sealed cabin, and Δz represents the average thickness of the slag in the vertical direction when performing discrete solution; The calculation formula for gas permeability is: P(z)=10(P 标态 +i 渣土 z) Wherein, F2 represents the gas permeability of the soil, P(z) is the average pore gas pressure at height z after mm water column is converted to Pa, φ 等效固相，渣土 (z) represents the volume percentage of the solid phase of the slag at position z in the sealed cabin when considering the improved compressibility of the slag, φ 等效液相，渣土 (z) represents the volume percentage of the liquid phase of the slag at position z in the sealed cabin when considering the improved compressibility of the slag, u 地层 is the pore water pressure, ρ represents the density of the slag, ω represents the moisture content of the slag, G s Indicates the relative density of the soil particles. u(z) represents the pore water and gas pressure; The calculation formula of the friction between the slag in the sealed cabin and the sealed cabin wall shell is: Wherein, F3 represents the friction force, μ represents the friction coefficient between the slag and the sealed bulkhead shell, σ z (z)=u(z)+σ′ z (z)=f(u(z)) u(z) represents the pore water and gas pressure, σ′ z (z) represents the vertical effective stress, σ z (z) represents the vertical stress of the slag in the sealed cabin at the current moment, and f represents σ z The relationship between (z) and u(z), u w (z) pore water pressure, P(z) represents pore gas pressure; The calculation formula of the deadweight of the slag is: Wherein, F4 represents the deadweight, G s Indicates the relative density of soil particles.

3. The control method according to claim 1, characterized in that: The vertical effective stress distribution equilibrium equation of the foam-improved slag in the soil cabin is established based on the friction between the slag in the sealed cabin and the sealed cabin wall shell, the penetration force and the deadweight of the slag, and based on the force balance of the slag in the sealed cabin, including: Based on the movement of the entire slag in the sealed cabin, the relationship is constructed: Based on the above relationship, φ 等效固相，渣土 The expression of (z), φ 等效液相，渣土 The expression of (z), σ z (z) = f(u(z)) to solve the vertical effective stress and obtain the vertical stress σ of the slag in the sealed cabin at the current moment z (z).

4. The control method according to claim 3, characterized in that: The combined pressure of the air-soil mixture in the sealed cabin at the current time t is: Among them, F 密封舱 (t) represents the combined pressure of the air-soil mixture in the sealed cabin at the current moment, P(t)S(t) represents the gas pressure in the sealed cabin at the current moment, represents the soil pressure in the sealed cabin at the current moment, P(t) represents the air pressure in the sealed cabin of the shield at the current moment, and S(t) represents the air pressure action area on the top of the soil layer in the sealed cabin at the current moment; H(t) represents the height of the soil-air interface in the sealed cabin at the current moment, N represents the number of layers when the soil is discretely solved, and σ z (H(t)-iΔz) indicates the vertical stress at the current position H(t)-iΔz, i=1, 2, ..., N; v 土层，输走 is the volume rate of the slag in the sealed cabin transported out by the screw conveyor, η represents the earth discharge efficiency of the shield machine, ω 螺旋机转速 (t) represents the screw speed of the shield machine at the current moment, A s represents the effective soil discharge area of ​​the shield machine's screw machine, l represents the screw pitch of the shield machine; v 土层，进入 is the volume rate of the formation entering the sealed chamber during the shield advancement process, v 推进 (t) represents the tunneling speed of the shield machine at the current moment; 5. The control method according to claim 4, characterized in that: According to the unsaturated soil gas permeability test, the permeability coefficients of the stratum and the foam-improved soil are measured, and the air pressure loss in the sealed cabin at the current moment is determined. According to the screw conveyor speed, shield machine excavation speed, air-soil mixed pressure in the sealed cabin at the current moment and air pressure loss in the sealed cabin at the construction site, the air-soil mixed pressure resultant of the sealed cabin at the next moment is obtained, including: By formula Calculate the height H(t+Δt) of the soil-air layer interface in the sealed cabin at the next moment; By formula Calculate the shield sealed cabin air pressure P(t+dt) at the next moment; The air pressure loss q(t) in the sealed cabin at the current moment is calculated by the formula q(t)=q1(t)+q2(t); P 标态 q1(t+Δt)=P 标态 q1(t)+P 标态 k sq1 i 地层 S(t)Δt The combined pressure F of the air-soil mixture in the sealed cabin at the next moment is calculated by the following formula: 密封舱 (t+Δt): Where t represents the current moment, Δt represents the time difference between the next moment and the current moment, q1(t) represents the cumulative amount of gas flowing into the formation at the current moment, q2(t) represents the cumulative amount of gas flowing into the pores of the slag in the sealed cabin at the current moment, q1(t+Δt) represents the cumulative amount of gas flowing into the formation at the next moment, and k sq1 The permeability coefficient of the formation is expressed as h represents the buried depth of the cutter head of the shield machine, q2(t+Δt) represents the cumulative amount of gas flowing into the pores of the soil in the sealed cabin at the next moment, and k sq2 Indicates the permeability coefficient of slag.

6. The control method according to claim 5, characterized in that: The calculation formula of the active earth pressure resultant of the stratum is: Among them, F 主动土压力 represents the active earth pressure resultant of the stratum, k 主动 represents the active earth pressure coefficient, represents the internal friction angle of the excavated stratum, γi represents the weight of the i-th layer of soil in the excavated stratum, h represents the burial depth of the top of the shield machine cutterhead, and h i represents the top height of the i-th soil layer, c i It represents the cohesion of the i-th layer of soil in the excavation stratum.

7. The control method according to claim 6, characterized in that: The calculation formula of the passive earth pressure resultant of the stratum is: Among them, F 被动土压力 represents the resultant passive earth pressure of the stratum, k 被动 represents the passive earth pressure coefficient, 8. The control method according to claim 7, characterized in that: F 主动土压力 ≤F 密封舱 (t+Δt)≤F 被动土压力 , H min ≤H(t+Δt)≤H max ;H min Indicates the preset minimum air-soil interface height in the sealed cabin, H max Indicates the height of the soil-air interface in the preset maximum sealed cabin.

9. The control method according to claim 8, characterized in that: The tunneling speed of the shield machine and the rotation speed of the screw machine are adjusted, including: If F 密封舱 (t+Δt) <F 主动土压力 , the tunneling speed of the shield machine is reduced, the screw speed of the shield machine and the air pressure of the shield sealed cabin are increased; If F 密封舱 (t+Δt)>F 被动土压力 , the tunneling speed of the shield machine is increased, and the screw speed of the shield machine and the air pressure of the shield sealed cabin are reduced; If H(t+Δt)>H max , then reduce the tunneling speed of the shield machine and increase the screw speed of the shield machine; If H(t+Δt)<H min , the excavation speed of the shield machine is increased and the screw speed of the shield machine is reduced.

10. The control method according to claim 9, characterized in that: The control method further comprises: The shield sealed cabin air pressure P(t) at the current moment is calculated by the following formula: Wherein, t0 represents the time of last air pressure replenishment, S(t0+jΔt) represents the effective area of ​​the air pressure chamber in the j-th time period from t0 to t divided by Δt intervals during refined solution, and H(t0+jΔt) represents the height of the soil layer interface in the j-th time period from t0 to t divided by Δt intervals.

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