Method for establishing wheel track prediction model of dirt runway based on the action of large transport aircraft

Abstract

The invention discloses a method for establishing a wheel rut prediction model of a dirt runway based on the action of a large transport aircraft, comprising the following steps: studying the surface characteristics of the flatness of an emergency airport pavement, analyzing the entrapment state of an aircraft wheel and the stress condition of an aircraft when passing on the pavement, establishing a vibration equation, and calculating the allowable depression depth and ridge height of the emergency airport pavement; analyzing the passability of the soil pavement of the emergency airport, and proposing a calculation method for the allowable wheel rut depth for ensuring the passability of the soil pavement; and proposing a wheel rut prediction model for the soil pavement of the emergency airport. By studying the structure of the soil pavement of the emergency airport, the surface characteristics of the pavement, etc., a wheel rut prediction model suitable for the soil pavement of the emergency airport is obtained, which is used to guide the construction of the soil pavement of the emergency airport, and has important strategic significance for giving full play to the performance of large transport aircraft and greatly improving the long-range mobility and strategic projection capabilities of the air force.

Description

Technical Field

[0001] The invention relates to the technical field of aircraft runway monitoring, and in particular to a method for establishing a wheel track prediction model for a dirt runway based on the action of a large transport aircraft. Background Art

[0002] Modern warfare dominated by information technology is characterized by strong suddenness, fast tempo, high intensity and huge material consumption. Countries around the world are striving to strengthen the rapid response and deployment capabilities of their armies so that they can quickly deliver troops, weapons and equipment to the frontline areas, thereby taking the initiative in the war and controlling the war situation. In order to achieve the above strategic goals, continuously improving the long-range mobility and strategic delivery capabilities of the air force is the fastest and most efficient measure and way. Therefore, in a sense, the size of a country's air transport capacity has gradually become one of the key factors in determining the outcome of a war.

[0003] The Air Force is the main force in gaining air superiority, and airports, as important battlefield facilities to ensure aircraft takeoff, landing and taxiing, are the support for aviation units to take off and fight in wartime and the base for flight training in peacetime. Under the conditions of informationized local wars, permanent airports are often the primary targets for countries to launch surprise attacks in order to gain air superiority, as they are too exposed. Therefore, countries around the world attach great importance to the planning and construction of emergency airports, which are airports that are quickly built according to the development of the war situation and the needs of emergency tasks for emergency takeoff and landing of aircraft in a short period of time. The construction of emergency airports is a major aspect of the Air Force's battlefield preparations, but in the face of the requirements of modern high-tech warfare, the relative lag in the research of pavement structures and materials suitable for rapid construction of airports has always been a key "bottleneck" problem restricting the generation of emergency combat effectiveness of the Air Force.

[0004] As the main component of the airport, the airport pavement is an important carrier of combat aircraft. Whether the emergency airport can fully play its role in wartime depends to a large extent on the reasonable design of the pavement structure and the rapid construction of pavement materials. Due to the great difference between emergency airports and permanent airports, traditional pavement materials and structural types are not suitable for the rapid construction and use requirements of emergency airports. Emergency airports are often built in an emergency situation according to the development of the situation and the needs of rescue and disaster relief tasks. They have the characteristics of fast construction speed, small number of take-offs and landings, and short use time. In view of the performance characteristics of emergency airports that can be quickly constructed and used in short-term emergency situations, one of the currently recognized and feasible methods for rapid pavement construction is to conduct on-site reinforcement of local soil and construct earth pavement, which can greatly save materials and time, thereby speeding up the construction of emergency airports.

[0005] Therefore, during the construction of temporary airports, the bearing capacity of the treated earth pavement often determines the take-off and landing quality and transportation efficiency of transport aircraft during operation. Therefore, after the construction of the earth pavement is completed, it is necessary to simulate and evaluate the bearing performance of the earth pavement, that is, the wheel ruts of the transport aircraft on the pavement, and then determine whether the earth pavement is suitable for large transport aircraft based on the simulation results. However, there is no record of this technology in the prior art. Summary of the invention

[0006] In view of the above-mentioned problems, the present invention aims to provide a method for establishing a wheel rut prediction model for a dirt runway based on the action of large transport aircraft. By studying the structure of the earth pavement of an emergency airport and its combination, the surface characteristics of the pavement, and the structural design method, a wheel rut prediction model suitable for the earth pavement of an emergency airport is obtained. The model can be used to guide the construction of the earth pavement of an emergency airport, which has important strategic significance for giving full play to the performance of large transport aircraft and greatly enhancing the long-range mobility and strategic delivery capabilities of the Air Force.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] The method for establishing a wheel track prediction model for a dirt runway based on the action of a large transport aircraft includes the following steps:

[0009] Step 1: Study the surface characteristics of the flatness of the emergency airport pavement, analyze the wheel sinking state and the stress of the landing gear when the aircraft passes on the pavement, establish the vibration equation when the aircraft passes through the uneven pavement, and calculate and analyze the allowable depression depth and bulge height of the emergency airport pavement;

[0010] Step 2: Analyze the passability of the soil pavement of the emergency airport, obtain the calculation formula of the rolling friction coefficient of the wheels on the soil pavement, and derive the calculation method of the allowable wheel track depth to ensure the passability of the soil pavement;

[0011] Step 3: Analyze the types and causes of wheel ruts, select wheel rut control indicators and prediction methods, and derive a wheel rut prediction model suitable for emergency airport soil pavement.

[0012] Preferably, the specific process of establishing the vibration equation when the aircraft passes through an uneven road surface in step 1 includes:

[0013] S1. Analyze the force of the aircraft when passing on the normal road surface:

[0014] S1.1 Assume that when an aircraft is traveling on an ideally smooth and flat runway, it is vertically subjected to the combined effects of its own weight, the lift of the wing, and the reaction force of the runway. The lift generated by the wing is:

[0015] Where: R yis the lift generated by the aircraft wing; ρ is the density of the air on the runway; C y is the lift coefficient of the aircraft (related to the pitch angle and the wing); S is the lift area of ​​the wing; v is the aircraft speed;

[0016] S1.2 Then, the runway reaction force is:

[0017]

[0018] S1.3 When the aircraft reaches takeoff speed, the lift generated by the wings is equal to the weight of the aircraft, that is, Where v0 is the aircraft's takeoff speed, the runway reaction force calculation formula is:

[0019]

[0020] S2. Analyze the force on the aircraft when it passes on an uneven road surface:

[0021] S2.1 When an aircraft passes an obstacle on an uneven pavement, the control equation of the motion system composed of the aircraft and the pavement can be expressed as:

[0022]

[0023] Where: m1 and m2 are the mass of the landing gear and the mass of the aircraft borne by a single landing gear; k1 and k2 are the elastic coefficients of the tire and the aircraft spring respectively; C1 and C2 are the damping of the tire and the aircraft buffer respectively; y1 and y2 are the absolute vertical displacements of m1 and m2 respectively; y(t) is the displacement interference function representing the road surface flatness;

[0024] S2.2 Ignore the damping effect of wheels, tires and fuselage buffers, that is, assume that C1 and C2 are both 0. At the same time, the mass of the main landing gear m1 is very small compared to the mass of the aircraft fuselage m2, so ignore the mass of the main landing gear, that is, assume that m1 = 0, then Equation 4 can be simplified to:

[0025]

[0026] Formula (5) can be further simplified as:

[0027]

[0028] S2.3 Solve the differential equation of equation (6) and let And add the initial condition t = 0, y2 = 0, Then the solution is:

[0029]

[0030] S3. Calculate the vibration dynamic load coefficient of the aircraft when it passes on an uneven road surface:

[0031] S3.1 From the solution process of formula (7), it can be seen that the vibration acceleration of the aircraft is not only related to the mechanical properties of the aircraft itself, but also to the interference function y(t) of the uneven surface of the pavement. According to the principle of mechanics, when the length-to-depth ratio of the concave or pit size is the same, the dynamic response generated by the cosine is the largest. Therefore, the cosine function is used as the curve function of the concave for analysis, and then:

[0032]

[0033] Where: l is the length of the pavement depression parallel to the runway centerline; h is the maximum vertical depth of the pavement depression;

[0034] S3.2 Order Then formula (8) is:

[0035]

[0036] Substituting formula (9) into formula (7), we can obtain the following through integral transformation:

[0037]

[0038] S3.3 Assume that when an aircraft passes over an uneven road surface, the ratio of the vibration acceleration to the gravity acceleration is the vibration dynamic load coefficient, denoted as K1, and its calculation formula is:

[0039]

[0040] S3.4 Substitute the load factor in formula (3) when the aircraft is not vibrating into Adding K1 calculated by formula (11) to the total dynamic load coefficient of the main landing gear when the aircraft experiences vertical vibration is:

[0041]

[0042] Preferably, the specific process of calculating and analyzing the allowable depression depth of the emergency airport pavement in step 1 includes:

[0043] S1. Analyze the maximum allowable depth of the pavement surface when the aircraft passes through the pavement surface:

[0044] S1.1 During the design and production of aircraft landing gear, in order to prevent the landing gear components from fatigue damage or even breakage too quickly, the aircraft dynamic load coefficient is introduced. The dynamic load coefficient K d ,Right now:

[0045]

[0046] S1.2 Take 1.25 as the allowable dynamic load coefficient value, that is, K d=1.25, substitute it into formula (13), take cosωt-cosαt=1, and we get:

[0047]

[0048] S2. Analyze the maximum allowable depth of the pavement surface depression when the aircraft passes through the pavement surface while ensuring the quality of the ride and the integrity of instrument control and cargo loading:

[0049] S2.1 When the aircraft passes through uneven areas, in order to ensure the integrity of flight personnel, instruments and cargo, the vibration dynamic load coefficient K1 is introduced. When K1 = 0.4:

[0050]

[0051] Let t′ = αt, equation (15) can be transformed into:

[0052]

[0053] Where: K1(t) is a function that changes with time, and only its maximum value is considered here;

[0054] S2.2 First determine The value is related to the value of ω / α. According to calculations, the value of ω / α is between 0.05 and 0.6. When the aircraft's taxiing speed v>v0 / 3, ω / α<0.2, then The maximum value of is approximately equal to 2, then the maximum vibration dynamic load coefficient K1′ is:

[0055]

[0056] At this time, the maximum depth h2 of the concave surface of the road surface is:

[0057]

[0058] S3. Analyze the process of the aircraft passing through the pavement surface, and solve the maximum allowable depth of the pavement surface depression while ensuring that the aircraft does not jump when taxiing at high speed:

[0059] S3.1 When the aircraft passes through an uneven surface, in order to ensure that the aircraft does not jump during high-speed taxiing, the vibration dynamic load coefficient K′1 is introduced:

[0060]

[0061] S3.2 For the rolling distance area where jumping may occur, the maximum depth of the depression h3 on the pavement surface shall meet the following requirements:

[0062]

[0063] S4. Combining formulas (14), (18) and (21), the allowable depth of road surface depressions or potholes in different areas can be calculated, namely:

[0064]

[0065] Preferably, the specific process of calculating and analyzing the allowable uplift height of the emergency airport pavement in step 1 includes:

[0066] S1. The vibration equation when the aircraft passes through the raised part of the pavement surface is the same as that of the concave part, and both can be expressed by formula (5). The pavement interference function of the raised part can still be expressed by the cosine function, but it is different from the interference function corresponding to the concave part by a positive or negative sign:

[0067]

[0068] S2. Order Then formula (23) becomes

[0069]

[0070] After integral transformation, solving the equation we can get:

[0071]

[0072]

[0073] S3. Equations (25) and (26) show that the interference function and vibration acceleration of the raised part of the pavement surface differ only by a positive or negative sign from those of the depressed part, and the calculated results are the same; therefore, the dynamic response of the raised part and the depressed part or pothole to the aircraft is the same, and the maximum allowable height value of the raised part is the same as the maximum allowable depth value of the depressed part.

[0074] Preferably, the specific process of obtaining the calculation formula of the rolling friction coefficient of the wheel on the soil road surface in step 2 includes:

[0075] S1. When the aircraft wheel moves on the soil road surface, the sum of the horizontal components of the soil's radial reaction force on the rigid wheel is balanced with the horizontal traction force F, and the sum of the vertical components of the radial reaction force is balanced with the wheel load P. k Phase equilibrium, we can get:

[0076]

[0077]

[0078] Where: σ is the bearing capacity coefficient of the soil, which is equal to the radial reaction force of the soil at a depth of 1 cm on the wheel surface, MPa; μ is a parameter related to soil quality, which is between 0.34 and 0.98, with an average of 0.67; h1 is the depth of the rigid wheel pressed into the soil; h2 is the recoverable deformation height; b is the spoke width of the rigid wheel; d is the diameter of the rigid wheel;

[0079] S2. From equations (29) and (30), the rolling friction coefficient f is:

[0080]

[0081] S3. For plastic soil, since its recoverable elastic deformation is small, h2 = 0, H = h1, and equations (30) and (31) can be simplified to:

[0082]

[0083]

[0084] Substituting formula (32) into formula (33), we can obtain:

[0085]

[0086] S4. Since d′=αd, α is the conversion coefficient, and its value is related to the soil bearing capacity coefficient σ and the tire pressure of the machine, the calculation formula for the wheel track depth and rolling friction coefficient when the pneumatic machine wheel rolls on the soil road surface is:

[0087]

[0088]

[0089] S5. When the soil is in a fluid or plastic state, the parameters related to the soil are close to zero, that is, μ = 0, then equations (35) and (36) can be further simplified as:

[0090]

[0091]

[0092] S6. By performing mechanical experiments according to the design, the bearing capacity coefficient σ can be obtained, and the calculated σ is substituted into formula (38) to obtain the rolling friction coefficient f value. The solution equation of the bearing capacity coefficient σ is:

[0093]

[0094] Preferably, the process of proposing the calculation method of the allowable wheel track depth for ensuring the passability of the soil road surface described in step 2 includes:

[0095] S1. When the aircraft can start and taxi on the soil road surface, analyze the limiting conditions of the wheel track depth H1 and soil bearing capacity coefficient σ1 for the aircraft to start and taxi on the soil road surface:

[0096] S1.1 When the aircraft starts taxiing on the soil surface, the relative thrust Φ of the engine is greater than the rolling friction coefficient f of the wheel. q , take f q =1.4f, then:

[0097] Φ>f q =1.4f (40)

[0098] S1.2 Substituting equation (40) into equations (37)-(39) respectively, the constraints on the wheel track depth H1 and soil bearing capacity coefficient σ1 that ensure the aircraft can start taxiing on the soil road surface are obtained as follows:

[0099]

[0100]

[0101] S2. When the aircraft reaches the take-off speed within the length of the soil runway, analyze the limiting conditions of the wheel track depth H2 and the soil bearing capacity coefficient σ2 for the aircraft to start taxiing on the soil surface:

[0102] The aircraft glides at high speed within a limited length of the soil runway and reaches a take-off speed v0. Assume that when the aircraft glides on the soil runway, the average rolling friction coefficient f h =0.5f, then the wheel track depth H2 and the soil bearing capacity coefficient σ2 must meet the following conditions respectively:

[0103]

[0104]

[0105] Where: S is the length of the emergency airport soil runway, m; ΔS is the distance from the aircraft starting position to the end of the soil runway, m; i is the average longitudinal slope of the soil runway, which takes a positive value when the aircraft takes off along the slope and a negative value when the aircraft takes off against the slope;

[0106] S3. When the aircraft can taxi safely on the soil road surface, the limiting conditions of the wheel track depth H3 and the soil bearing capacity coefficient σ3 for the aircraft to start taxiing on the soil road surface are analyzed:

[0107] When an aircraft glides at high speed on a soil road surface, the wheel track depth H3 generated by the repeated action of the aircraft satisfies:

[0108] H3<0.07d (45)

[0109] At this time, the bearing capacity coefficient σ3 of the corresponding soil should satisfy:

[0110]

[0111] S4. From the above analysis, it can be seen that in order to ensure the trafficability of aircraft on soil pavement, the above three conditions must be met at the same time, that is, the maximum wheel track depth and the minimum bearing capacity coefficient of the soil produced by the repeated action of the aircraft on the pavement should meet the following conditions:

[0112]

[0113]

[0114] Preferably, the process of establishing the wheel rut prediction model of the emergency airport soil pavement described in step 3 includes:

[0115] S1. Assume that the pavement wheel track equation under aircraft load is in the form of:

[0116] N=f(ε,μ) (52)

[0117] Where: N is the number of times the load can be repeated; ε is the vertical compressive strain on the top surface of the soil foundation; μ is other related variables;

[0118] S2. Based on the cumulative damage principle and combined with formula (52), a wheel rutting prediction model for the critical state of wheel rutting damage on soil pavement under the action of various types of transport machine loads is established:

[0119]

[0120] Where: n i is the estimated number of repeated load actions for the i-th aircraft; N i is the number of load repetitions allowed for the i-th aircraft; ε i is the vertical compressive strain on the top surface of the soil foundation under the action of the i-th aircraft; E s is the soil resilience modulus (MPa).

[0121] The beneficial effects of the present invention are as follows: the present invention discloses a method for establishing a wheel track prediction model of a dirt runway based on the action of a large transport aircraft. Compared with the prior art, the present invention has the following improvements:

[0122] (1) The present invention designs a method for establishing a wheel rut prediction model for a dirt runway based on the action of a large transport aircraft. By studying the structure and combination of the soil pavement of an emergency airport, the surface characteristics of the pavement, and the structural design method, a wheel rut prediction model suitable for the soil pavement of an emergency airport is obtained. On the one hand, during the construction of the emergency airport, the wheel rut prediction model can be used to design the pavement structure according to the wheel rut deformation and damage mode of the soil pavement of the emergency airport, and an earth pavement of the emergency airport that meets the needs can be designed. This has important strategic significance for giving full play to the performance of large transport aircraft and greatly improving the long-range mobility and strategic delivery capabilities of the Air Force. It also has great contemporary significance for the development of special models of new military transport aircraft and the provision of corresponding technical indicators.

[0123] (2) On the other hand, the use of this wheel track prediction model to standardize the construction of emergency airport earth pavement is not only of great military significance for improving the layout of my country's airport network during wartime, effectively improving the rapid mobility of troops and the survivability of aviation forces, and thus enhancing emergency combat effectiveness; it also has great practical significance for the implementation of non-war military operations in peacetime (such as earthquake relief and post-disaster reconstruction, anti-terrorism and peacekeeping operations, and international humanitarian rescue operations). BRIEF DESCRIPTION OF THE DRAWINGS

[0124] Figure 1 The present invention is a flow chart of a method for establishing a wheel track prediction model for a dirt runway based on the action of a large transport aircraft.

[0125] Figure 2 The figure is a relationship diagram between the wheel mark size of an aircraft and the plane size of the road surface depression according to the present invention.

[0126] Figure 3 This is a diagram of the wheel being trapped in the present invention.

[0127] Figure 4 This is a simplified model diagram of aircraft vibration according to the present invention.

[0128] Figure 5 It is a relationship diagram between the vibration acceleration of the fuselage and the depression depth of the present invention.

[0129] Figure 6 This is a relationship diagram between the dynamic load coefficient and the depression depth of the present invention.

[0130] Figure 7 This is a force state diagram of the rigid wheel of the present invention. DETAILED DESCRIPTION

[0131] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0132] The surface smoothness of an airport pavement is an important indicator for characterizing the surface characteristics of the pavement. The so-called pavement smoothness refers to the deviation of the airport pavement surface from the ideal plane. The smoothness plays an important role in the numerical characteristics of the dynamic characteristics, driving stability and dynamic load of the aircraft when the aircraft passes on the pavement. In order to ensure the safe taxiing of the aircraft on the pavement, it is necessary to study and analyze the passability of the soil pavement and propose the allowable wheel track depth range. At the same time, establishing a wheel track prediction model corresponding to the wheel track damage mode is an important part of the airport pavement mechanics-empirical design method.

[0133] See attached Figure 1-7 The method for establishing the wheel track prediction model of the earth runway based on the action of the large transport aircraft shown in the figure includes:

[0134] Step 1: Study the surface characteristics of the flatness of the emergency airport pavement, analyze the wheel sinking state and the stress of the landing gear when the aircraft passes on the pavement, establish the vibration equation when the aircraft passes through the uneven pavement, and calculate and analyze the allowable depression depth and bulge height of the emergency airport pavement;

[0135] Step 2: Analyze the passability of the soil pavement of the emergency airport, obtain the calculation formula of the rolling friction coefficient of the wheels on the soil pavement, and derive the calculation method of the allowable wheel track depth to ensure the passability of the soil pavement;

[0136] Step 3: Analyze the types and causes of wheel ruts, select wheel rut control indicators and prediction methods, and derive a wheel rut prediction model suitable for emergency airport soil pavement. Using this wheel rut prediction model, the pavement structure design can be carried out according to the wheel rut deformation and damage mode of the emergency airport soil pavement.

[0137] Preferably, the specific process of step one includes:

[0138] Practice has shown that the surface of an airport pavement cannot be an ideal plane. The flatness of the pavement affects the stability, safety and comfort of the aircraft passing on the pavement. When the aircraft passes through the unevenness of the pavement, random vibration and impact load will be generated, which will not only cause damage to the aircraft landing gear and wear of the parts, but also cause severe turbulence of the aircraft fuselage, resulting in a vertical acceleration, affecting the pilot's correct interpretation of instruments, aircraft control, passenger ride quality and cargo integrity. In particular, when the aircraft is taxiing on an uneven pavement, due to the different force conditions on the left and right landing gear wheels, the aircraft will have longitudinal and lateral swings, seriously endangering flight safety and mission completion. At the same time, the excitation dynamic load generated when the aircraft passes through the uneven pavement will also accelerate the wear, damage and deformation of the airport pavement.

[0139] 1. Analyze the stuck state of the wheel and the stuck state of the emergency airport pavement:

[0140] The geometric size of depressions or potholes on uneven surfaces is an important factor affecting the dynamic response of aircraft when passing through. When the size of the depression on the pavement surface is much smaller than the size of the aircraft tire, the aircraft will pass through the pavement quickly at high speed, and the dynamic response is very small, or even negligible. When the size of the depression is larger, the aircraft tire will be partially or completely sunken into the depression, and the aircraft will produce a larger dynamic response. Therefore, it is necessary to analyze the relationship between the geometric size of the depression or pothole on the pavement surface and the size of the aircraft tire ground contact, and to conduct in-depth research on the state of the wheel sinking into the depression or pothole on the pavement surface.

[0141] S1. Assume that the length of the wheel footprint of the aircraft landing gear is a1 and the width is b1; and the length of the plane dimension of the depression or pit on the pavement surface is a2 (parallel to the centerline of the runway) and the width is b2. The relationship between the wheel footprint of the aircraft and the depression on the pavement can be roughly divided into the following nine situations: Figure 2 As shown;

[0142] S2. According to Figure 2 The geometric relationship between the wheel marks of aircraft and the depressions on the pavement surface can be analyzed to find that the states of the wheels sinking into the depressions on the pavement surface can be roughly divided into three types: suspended state, semi-sinking state and fully sinking state. Figure 3 (a)-(c) As shown; Based on the landing gear parameters of the aircraft passing on the earthen pavement of the emergency airport, the wheel mark size is compared with the geometric size of the depression on the pavement, so that the wheel's sinking state can be known, and then the allowable depth or height of the unevenness can be calculated;

[0143] S3. When the aircraft is gliding on the pavement at high speed, the dynamic response of the suspended state to the aircraft is very small and can be ignored. In the fully sunken state, the aircraft landing gear experiences vertical turbulence and severe vibration, which is the focus of surface property research. The semi-sunken state can be regarded as a special form of the fully sunken state. According to the research conclusions of relevant literature and engineering practice, the probability of an aircraft passing through depressions or ridges at the same time within a short distance is small when the aircraft is passing through two depressions or ridges in succession with a large distance between them. Considering the effect of damping, the dynamic response generated by the aircraft at this time can ignore the mutual superposition effect. Therefore, the dynamic response generated by the aircraft passing through a single depression or ridge position will be mainly studied and analyzed.

[0144] 2. Establish the vibration equation when the aircraft passes through an uneven road surface:

[0145] S1. Analyze the force of the aircraft when passing on the normal road surface:

[0146] S1.1 Assume that when an aircraft is traveling on an ideally smooth and flat runway, it is vertically subjected to the combined effects of its own weight, the lift of the wing, and the reaction force of the runway. The lift generated by the wing is: (1)

[0148] Where: R y is the lift generated by the aircraft wing; ρ is the density of the air on the runway; C y is the lift coefficient of the aircraft (related to the pitch angle and the wing); S is the lift area of ​​the wing; v is the aircraft speed;

[0149] S1.2 Then, the runway reaction force is:

[0150]

[0151] S1.3 Considering that when the aircraft reaches takeoff speed, the lift generated by the wing is equal to the aircraft's own weight, that is, Where v0 is the aircraft's takeoff speed, the runway reaction force calculation formula can be converted to:

[0152]

[0153] S2. Analyze the force on the aircraft when it passes on an uneven road surface:

[0154] Large ridges or depressions on the pavement surface caused by factors such as aircraft loads, construction factors, and natural conditions can be called obstacles. These obstacles are not allowed for permanent airport pavements, and should also be strictly restricted for emergency airports. Whether it is a ridge or a depression, the dynamic response caused by it to the aircraft has certain similarities. Therefore, we first conduct a vibration analysis of the aircraft passing through the depression in the pavement, and establish a simplified vibration model of the aircraft passing through the depression. Its basic assumptions are as follows: (1) The pavement does not produce bending changes under the action of the wheel load, that is, the pavement is regarded as a rigid body;

[0155] (2) The aircraft wheels pass through the concave part of the road surface at a constant speed; (3) Only the influence of the main landing gear wheels of the aircraft is considered; when the aircraft passes through the uneven road surface with concave or grooves, the wheels will move along the concave surface, and the aircraft and landing gear will vibrate. For this reason, the aircraft can be simplified into a two-degree-of-freedom system, such as Figure 4 As shown;

[0156] S2.1 shows that when an aircraft passes an obstacle on an uneven pavement, the control equation of the motion system composed of the aircraft and the pavement can be expressed as:

[0157]

[0158] Where: m1 and m2 are the mass of the landing gear and the mass of the aircraft borne by a single landing gear; k1 and k2 are the elastic coefficients of the tire and the aircraft spring respectively; C1 and C2 are the damping of the tire and the aircraft buffer respectively; y1 and y2 are the absolute vertical displacements of m1 and m2 respectively; y(t) is the displacement interference function representing the road surface flatness;

[0159] S2.2 Considering that the damping effect of the wheels, tires and fuselage buffers occurs with a certain time lag during the rapid passage of the aircraft on the pavement, the damping effect can be ignored, that is, C1 and C2 are both set to 0. At the same time, the mass of the main landing gear m1 is very small compared to the mass of the aircraft fuselage m2, so the mass of the main landing gear is ignored, that is, m1 = 0, and equation 4 can be simplified to:

[0160]

[0161] Formula (5) can be further simplified as:

[0162]

[0163] S2.3 Solve the differential equation of equation (6) and let And add the initial condition t = 0, y2 = 0, Then the solution is:

[0164]

[0165] S3. Calculate the vibration dynamic load coefficient of the aircraft when it passes on an uneven road surface:

[0166] S3.1 From the solution process of formula (7), it can be seen that the vibration acceleration of the aircraft is not only related to the mechanical properties of the aircraft itself, but also to the interference function y(t) of the uneven surface of the pavement. The interference function is determined by the geometric shape and size of the uneven surface of the pavement. The geometric shape of the uneven surface of the pavement (such as ridges, depressions or potholes) is roughly similar to triangles, arcs, sine and cosine curves. According to the principle of mechanics, when the length-to-depth ratio of the depression or pothole size is the same, the dynamic response generated by the cosine is the largest. Therefore, the cosine function is used as the curve function of the depression for analysis, then:

[0167]

[0168] Where: l is the length of the pavement depression parallel to the runway centerline; h is the maximum vertical depth of the pavement depression;

[0169] S3.2 Order Then formula (8) is:

[0170]

[0171] Substituting formula (9) into formula (7), we can obtain the following through integral transformation:

[0172]

[0173] S3.3 Assume that when an aircraft passes over an uneven road surface, the ratio of the vibration acceleration to the gravity acceleration is the vibration dynamic load coefficient, denoted as K1, and its calculation formula is:

[0174]

[0175] S3.4 Substitute the load factor in formula (3) when the aircraft is not vibrating into Adding K1 calculated by formula (11) to the total dynamic load coefficient of the main landing gear when the aircraft experiences vertical vibration is:

[0176]

[0177] 3. Calculate and analyze the allowable depression depth of the emergency airport pavement:

[0178] When an aircraft passes through a depression or pothole on the pavement surface, in order to ensure the safety and stability of the aircraft's passage, strict restrictions should be placed on the maximum depth of the depression. The following will study and analyze the maximum allowable depth of the pavement surface depression from three aspects:

[0179] S1. Analyze the maximum allowable depth of the pavement surface when the aircraft passes through the pavement surface:

[0180] S1.1 During the design and production of aircraft landing gear, strict restrictions are placed on the dynamic load coefficient to prevent the landing gear components from fatigue damage or even breakage too quickly. When the aircraft passes through uneven areas, the vertical vibration causes the impact on the aircraft main landing gear, which is mainly reflected by the comprehensive dynamic load coefficient K of the aircraft under vibration. In order to control the dynamic response of the vibration to the aircraft landing gear within the allowable range, the comprehensive dynamic load coefficient K of the aircraft under vibration shall not exceed the specified value of the aircraft dynamic load coefficient. The dynamic response analysis of the aircraft to the pavement is a relatively complex issue. The dynamic load coefficient K is usually introduced in the airport pavement design. d , convert the dynamic load into static load, and then calculate the stress, strain and displacement of the pavement structure according to the static analysis method. The dynamic load coefficient K d The influence of power and lift when the aircraft passes on the pavement is comprehensively considered, reflecting the power effect and lift of the aircraft. The effect of the aircraft's comprehensive dynamic load coefficient K on the pavement must also comply with the dynamic load coefficient K introduced in the airport pavement design. d The requirements are:

[0181]

[0182] S1.2 In the design of emergency airport soil pavement, considering its characteristics of rapid construction and short-term use, the dynamic load coefficient value range of airport cement concrete pavement design is taken as 1.25, that is, K d =1.25, substitute it into formula (13), take cosωt-cosαt=1, and we get:

[0183]

[0184] S2. Analyze the maximum allowable depth of the pavement surface depression when the aircraft passes through the pavement surface while ensuring the quality of the ride and the integrity of instrument control and cargo loading:

[0185] S2.1 The impact of vertical vibration caused by the aircraft passing through uneven areas on the integrity of flight personnel, instruments and cargo can be expressed by the vibration dynamic load coefficient K1. On airport runways with specified unevenness requirements, the vertical acceleration at the pilot's position should not exceed the index value recommended by the aviation medicine department. For the vertical acceleration standard, Boeing has obtained three standards of 0.25g, 0.55g and 0.80g based on the fatigue life of the aircraft. From the perspective of ergonomics, when the vertical acceleration at the center of gravity of the aircraft is used as an evaluation index of comfort, the research results show that when the vertical acceleration is greater than 0.4g, the flight personnel and aircraft passengers will feel uncomfortable, which in turn affects the ride quality. At present, the US military uses the 0.4g standard to limit the flatness requirements of airport pavements. For this reason, the 0.4g vertical acceleration is used as the standard to limit the maximum depth of airport pavement depressions, then:

[0186]

[0187] Let t′ = αt, equation (15) can be transformed into:

[0188]

[0189] Where: K1(t) is a function that changes with time, and only its maximum value is considered here;

[0190] S2.2 First determine The value is related to the value of ω / α. According to calculations, the value of ω / α is between 0.05 and 0.6. When the aircraft's taxiing speed v>v0 / 3, ω / α<0.2, then The maximum value of is approximately equal to 2, then the maximum vibration dynamic load coefficient K1′ is:

[0191]

[0192] At this time, the maximum depth h2 of the concave surface of the road surface is:

[0193]

[0194] S3. Analyze the process of the aircraft passing through the pavement surface, and solve the maximum allowable depth of the pavement surface depression while ensuring that the aircraft does not jump when taxiing at high speed:

[0195] When the aircraft is taxiing on the runway at high speed, the lift of the aircraft is increasing with the increase of taxiing speed, while the pressure on the ground is decreasing. If the aircraft passes through the uneven surface of the runway and the comprehensive dynamic load coefficient K is less than 0, the aircraft may jump. The jumping phenomenon of the aircraft before taking off on the soil runway is much more obvious than when taking off on a cement or asphalt concrete runway. At this time, if K1=0.4, then the aircraft will jump when the taxiing speed reaches v≥0.78v0; assuming that the aircraft's takeoff taxiing stage is a uniformly accelerated motion with an acceleration of a, the aircraft starts to taxi from the starting line until it reaches the takeoff speed and leaves the runway. The total taxiing distance is Then, when the aircraft's takeoff taxiing speed increases from v = 0.78v0 to the ground speed v0, the aircraft's taxiing distance on the runway can be calculated by formula (19):

[0196]

[0197] The calculation results of formula (19) show that the taxiing distance where the aircraft may experience jumping phenomenon during taxiing is about 40% of the entire taxiing distance, which will seriously endanger the safe taxiing of the aircraft. Therefore, it is necessary to strictly limit the range where the jumping phenomenon may occur to avoid the aircraft from jumping at a large angle of attack before reaching the take-off speed. Relevant literature research shows that it is more appropriate to limit the area where the jumping phenomenon may occur to 25% of the entire taxiing distance. At this time, the vibration dynamic load coefficient of the aircraft is K1=0.25. Since K1 is small, the negative value of the comprehensive dynamic load coefficient K is also small, and the duration is short. The aircraft only experiences slight jumping phenomenon or even no jumping phenomenon, which has little impact on the taxiing safety of the aircraft. Therefore, in order to prevent the aircraft from jumping during takeoff and landing taxiing and affecting the taxiing safety of the aircraft, the maximum vibration dynamic load coefficient K1′ should also be limited as follows:

[0198]

[0199] S3.2 Then, for the rolling distance area where jumping may occur, the maximum depth of the depression h3 in the pavement surface must satisfy:

[0200]

[0201] S4. Combining formulas (14), (18) and (21), the allowable depth of road surface depressions or potholes in different areas can be calculated, namely:

[0202]

[0203] 4. Calculate and analyze the allowable uplift height of the emergency airport pavement:

[0204] S1. The vibration equation of an aircraft passing through a raised area on the pavement surface is the same as that of a depressed area, and both can be expressed by equation (5). The pavement interference function of the raised area can still be expressed by the cosine function, but it differs from the interference function corresponding to the depressed area by a positive or negative sign:

[0205]

[0206] S2. Order Then formula (23) becomes

[0207]

[0208] After integral transformation, solving the equation we can get:

[0209]

[0210]

[0211] S3. Equations (25) and (26) show that the interference function and vibration acceleration of the raised part of the pavement surface differ only by a positive or negative sign from those of the depressed part, and the calculated results are the same; therefore, the dynamic response of the raised part and the depressed part or pothole to the aircraft is the same, and the maximum allowable height value of the raised part is the same as the maximum allowable depth value of the depressed part.

[0212] Preferably, the specific process of step 2 includes:

[0213] 1. Analyze the passability of soil pavement:

[0214] S1. Most modern aircraft use jet engines, with high taxiing speeds. In addition, the aircraft are large in size, have heavy wheel loads, and high tire pressures, which poses a challenge to the trafficability of earthen pavements. How to ensure the safety of modern large transport aircraft taxiing on earthen pavements during takeoff and landing is a hot topic in the current airport engineering field. Therefore, it is necessary to conduct in-depth research on the trafficability of aircraft taxiing safely on earthen pavements;

[0215] S2. The passability of a dirt pavement refers to the ability of an aircraft to start on the spot on the dirt pavement under the action of the engine thrust and to reach the take-off speed within the specified taxiing distance. At the same time, under the repeated action of the aircraft, the depth of the wheel tracks formed on the surface of the airport dirt pavement shall not affect the safe taxiing of the aircraft, and the wheel tracks shall be well repaired and smooth. The passability of the dirt pavement varies for different aircraft models, landing gear configurations and soil conditions. The passability of the dirt pavement at an emergency airport mainly depends on the following factors: (1) the configuration of the aircraft landing gear, the size of the tires and the tire pressure; (2) the thrust of the aircraft engine and the lift of the wings; and (3) the soil conditions and soil moisture of the emergency airport.

[0216] 2. Obtain the formula for calculating the rolling friction coefficient of the wheel on the soil road surface

[0217] The trafficability of the soil pavement of the emergency airport is mainly reflected in the rolling friction coefficient of the aircraft wheels on the soil pavement and the corresponding movement resistance. After the aircraft repeatedly acts on the soil pavement, especially when the aircraft passes on the taxiway, the aircraft wheel track often forms a channelized traffic distribution and is easy to form deeper wheel tracks, which increases the rolling friction resistance of the wheels, thereby affecting the safety of the aircraft starting and taxiing on the soil pavement. Therefore, it is necessary to study and analyze the formation mechanism of the wheel tracks on the pavement surface under the action of aircraft load and the rolling friction coefficient of the wheels on the soil pavement.

[0218] The tires of the aircraft are pneumatic tires, and when the wheels roll on the soil road surface, they will produce compression deformation. The smaller the rigidity of the soil road surface, the smaller the deformation of the aircraft tire; conversely, the greater the rigidity of the soil road surface, the greater the deformation of the aircraft tire. In order to facilitate calculation and analysis, the aircraft wheel can be simplified and assumed to be a rigid wheel, that is, the wheel will not deform under the action of the road surface reaction force. The force state of a rigid wheel when sliding on a soil road surface is as follows: Figure 7 As shown in the figure, F is the horizontal traction force, P k is the vertical wheel load. When the wheel slides on the soil road surface, the depth of the rigid wheel pressed into the soil is h1. Since the soil has a certain elasticity, a part of the soil is deformed after the rigid wheel passes and rebounds. If the height of this part of the recoverable deformation is h2, then the wheel track depth formed by the repeated action of the aircraft on the soil road surface is:

[0219] H=h1-h2 (27)

[0220] After the rigid wheel is pressed into the soil, the reaction force of the soil on the wheel is expressed by the radial reaction force q on the surface of the wheel pressed into the soil. The radial reaction force q can be calculated according to formula (28):

[0221] q=σh μ (28)

[0222] Where: σ is the bearing capacity coefficient of the soil, which is equal to the radial reaction force of the soil at a depth of 1 cm on the wheel surface, MPa; h is the depth of the calculation point, cm; μ is a parameter related to the soil quality, which is between 0.34 and 0.98, with an average of 0.67;

[0223] S1. According to the principle of force balance, Figure 5 As shown in the force state of the rigid wheel sliding on the soil road surface, the horizontal component of the soil's radial reaction force on the rigid wheel is balanced with the horizontal traction force F, and the vertical component of the radial reaction force is balanced with the wheel load P. k Phase balance, we can get the horizontal traction F and wheel load P k The calculation formula is:

[0224]

[0225]

[0226] Where: b is the spoke width of the rigid wheel; d is the diameter of the rigid wheel;

[0227] S2. From equations (29) and (30), the rolling friction coefficient f is:

[0228]

[0229] S3. For plastic soil, since its recoverable elastic deformation is small, h2 = 0, H = h1, and equations (30) and (31) can be simplified to:

[0230]

[0231]

[0232] Substituting formula (32) into formula (33), we can obtain:

[0233]

[0234] S4. The above calculations and analyses all assume that aircraft tires are rigid wheels. However, for pneumatic wheels, B.Φ Babkov, a road safety expert at the Moscow Highway Institute, believes that a rigid tire with a diameter of d′ (d′>d) can be used to replace a pneumatic tire with a diameter of d when rolling on a soil road surface. The relationship between d′ and d satisfies: d′=αd, where α is a conversion factor, and its value is related to the bearing capacity coefficient σ of the soil and the tire pressure. According to Babkov's research conclusions, the calculation formula for the wheel track depth and rolling friction coefficient when a pneumatic wheel rolls on a soil road surface is:

[0235]

[0236]

[0237] S5. Experimental studies have shown that when the soil is in a fluid or plastic state, the parameters related to the soil are close to zero, that is, μ = 0, then equations (35) and (36) can be further simplified to:

[0238]

[0239]

[0240] S6. According to formula (38), in order to determine the bearing capacity coefficient σ of the soil, a traction vehicle can be used on site to tow an aircraft (or an aircraft load simulation vehicle) through a dynamometer, and slide uniformly on the soil surface, and the tension T is measured by the dynamometer, and then the bearing capacity coefficient σ is calculated according to formula (38). Substituting the calculated σ into formula (38), the rolling friction coefficient f value can be obtained. The solution equation of the bearing capacity coefficient σ is:

[0241]

[0242] 3. The calculation method of the allowable wheel track depth to ensure the passability of soil road surface is proposed:

[0243] In order to ensure smooth takeoff, landing and safe taxiing of aircraft on earth pavements, the following three conditions must be met: (1) the earth pavement has sufficient bearing capacity to enable the aircraft to start taxiing on the spot; (2) the aircraft can reach takeoff speed within the taxiing distance of the runway; (3) the pavement surface has a good degree of flatness, and the depth of the wheel tracks formed does not affect the safe taxiing of the aircraft. The following analyzes these three aspects one by one:

[0244] S1. When the aircraft can start and taxi on the soil road surface, analyze the limiting conditions of the wheel track depth H1 and soil bearing capacity coefficient σ1 for the aircraft to start and taxi on the soil road surface:

[0245] S1.1 In order to ensure that the aircraft can be started on the soil road surface, the relative thrust Φ of the engine must be greater than the rolling friction coefficient f of the wheel when the aircraft starts. q , experimental studies have shown that the rolling friction coefficient of the aircraft starting machine wheel is f q It must be greater than the rolling friction coefficient f of the aircraft in a uniform gliding state. Usually, f q :f=1.1~1.7:1, in order to ensure that the aircraft can start on the soil road surface, take f q =1.4f, then:

[0246] Φ>f q =1.4f (40)

[0247] S1.2 Substituting equation (40) into equations (37)-(39) respectively, the constraints on the wheel track depth H1 and soil bearing capacity coefficient σ1 that ensure the aircraft can start taxiing on the soil road surface are obtained as follows:

[0248]

[0249]

[0250] S2. When the aircraft reaches the take-off speed within the length of the soil runway, analyze the limiting conditions of the wheel track depth H2 and the soil bearing capacity coefficient σ2 for the aircraft to start taxiing on the soil surface:

[0251] In order to ensure that the aircraft can glide at high speed within the limited length of the soil runway until it reaches the take-off speed v0, it is assumed that when the aircraft glides on the soil surface, the average rolling friction coefficient f h =0.5f, then the wheel track depth H2 and the soil bearing capacity coefficient σ2 must meet the following conditions respectively:

[0252]

[0253]

[0254] Where: S is the length of the emergency airport soil runway, m; ΔS is the distance from the aircraft starting position to the end of the soil runway, m; i is the average longitudinal slope of the soil runway, which takes a positive value when the aircraft takes off along the slope and a negative value when the aircraft takes off against the slope;

[0255] S3. When the aircraft can taxi safely on the soil road surface, the limiting conditions of the wheel track depth H3 and the soil bearing capacity coefficient σ3 for the aircraft to start taxiing on the soil road surface are analyzed:

[0256] In order to ensure the stability and safety of the aircraft when taxiing at high speed on the soil road surface, the wheel track depth value H3 generated by the repeated action of the aircraft on the road surface when the aircraft taxis at high speed satisfies:

[0257] H3<0.07d (45)

[0258] At this time, the bearing capacity coefficient σ3 of the corresponding soil should satisfy:

[0259]

[0260] S4. From the above analysis, it can be seen that in order to ensure the trafficability of aircraft on soil pavement, the three conditions of S1, S2 and S3 must be met at the same time, that is, the maximum wheel track depth and the minimum bearing capacity coefficient of the soil produced by the repeated action of the aircraft on the pavement should meet the following conditions:

[0261]

[0262]

[0263] Preferably, the specific process of step three includes:

[0264] 1. On the soil pavement of the emergency airport, the factors that affect the design length of the runway are mainly the rolling friction coefficient f and the slope i of the runway. When the aircraft takes off on the soil pavement, the greater the wheel track depth, the greater the rolling friction coefficient of the aircraft wheels, and the corresponding aircraft's runway distance to reach the take-off speed is extended, so the design length of the soil runway is required to increase. The longitudinal slope of the runway affects the magnitude of the horizontal component of the aircraft load. When the aircraft glides down the slope, the aircraft load component is consistent with the direction of the engine thrust, which is conducive to the aircraft's takeoff and can shorten the design length of the runway. In addition, the factors that affect the design length of the runway include the aircraft landing gear configuration, take-off angle of attack, landing approach altitude and speed, etc. According to the analysis of the above factors, combined with the take-off and landing performance of the aircraft and the requirements for the rapid construction of the emergency airport, it is preliminarily determined that the length of the earth runway is about 1200 to 1800m. When calculating and analyzing here, the average value is taken as 1500m, and the distance between the aircraft starting position and the end of the runway is set to 100m. Although designing the earth runway as a longitudinal slope is conducive to reducing the taxiing length of the aircraft, it will also increase the amount of earthwork construction accordingly. For this reason, the longitudinal slope is only considered when there is enough time. In order to meet the strong timeliness requirements, the longitudinal slope is not considered in the calculation and analysis, that is, the longitudinal slope i = 0. The calculation parameters of the transport aircraft (type 1, type 2 and type 3) are sorted out, as shown in Table 4:

[0265] Table 4: Calculation parameters for takeoff of transport aircraft on soil surface

[0266]

[0267] According to the calculation parameters in the above table, according to formulas (47) and (48), the corresponding maximum allowable wheel track depth and minimum soil bearing capacity coefficient when each model passes smoothly on the soil road surface are calculated, as shown in Table 5:

[0268] Table 5: Maximum wheel track depth for transporters and minimum soil bearing capacity coefficient

[0269]

[0270] From the calculation results listed in the above table, it can be seen that for model 1, only when the wheel rut depth is less than 6.3cm and the soil bearing capacity coefficient is greater than 0.60MPa; for model 2, only when the wheel rut depth is less than 7.4cm and the soil bearing capacity coefficient is greater than 0.69MPa; for model 3, only when the wheel rut depth is less than 9.1cm and the soil bearing capacity coefficient is greater than 0.47MPa can it pass smoothly and land safely on the emergency airport soil pavement. From the analysis of the above calculation results, it can be seen that: model 3 has the lowest take-off and landing requirements for the emergency airport soil pavement, because it has a landing gear device with adjustable tire pressure and has relatively excellent take-off and landing performance on the simple airport soil pavement; model 1 has the highest requirement for wheel rut depth, because the wheel diameter of this type of aircraft is the smallest; model 2 has the highest requirement for the bearing capacity of the soil pavement, because the tire pressure of this type of aircraft is the highest, reaching 7.5 +0.5 ×98kpa. When the emergency airport needs to support the above three types of transport aircraft at the same time, the value must be determined according to the highest requirements of the three types of aircraft;

[0271] From the above analysis, it can be seen that the wheel size will directly affect the limit requirement of the maximum wheel track depth, while the tire pressure determines the bearing capacity requirement of the earth road surface. In order to improve the aircraft's performance on the earth road surface, the measures that can be taken for the design of future large transport aircraft are to increase the wheel size and reduce the tire pressure.

[0272] 2. Rutting prediction of airport soil pavement:

[0273] S1. Analysis of wheel rut types and causes:

[0274] The PCI survey results of the American Society of Civil Engineers (ASCE) and the Federal Aviation Administration (FAA) show that wheel rutting deformation is one of the most common forms of damage to flexible pavements at airports. The U.S. military's "Joint Airfield Rapid Construction" program (JRAC) also shows that the main form of damage to the unpaved surface structure of simple airports is concentrated in the wheel rutting, and wheel rutting damage should be used as the main control standard. The formation of wheel rutting on the soil pavement of emergency airports will greatly reduce the pavement's traffic performance and shorten the pavement's service life, and even cause safety accidents during aircraft taxiing. The impact of wheel rutting on the safe passage of aircraft on soil pavements is mainly manifested in the following aspects: (1) Wheel rutting affects the traffic performance of soil pavements. Deep wheel rutting makes it difficult for aircraft to start on the spot, which prolongs the taxiing distance for the aircraft to reach takeoff speed, thereby affecting the runway. (1) The wheel ruts affect the smoothness of the pavement surface, reducing the taxiing comfort and ride quality of the aircraft, and may even affect the safe operation of the aircraft or cause damage to the landing gear; (2) The wheel ruts will reduce the thickness of the pavement structure layer on the wheel track, thereby reducing the overall strength of the pavement structure layer and causing other forms of pavement damage such as dents, potholes and cracks; (3) The wheel ruts make the pavement prone to water accumulation on rainy days and snow accumulation and ice on snowy days, which in turn reduces the pavement's anti-skid performance and affects the normal take-off and landing and high-speed taxiing of aircraft.

[0275] The wheel rutting deformation of flexible pavement at airports is mainly caused by the accumulation of permanent deformation of each structural layer of the pavement (soil base, subbase / cushion, base layer and surface layer). For the proposed structural type of emergency airport soil pavement "functional surface layer + fiber reinforced stabilized soil base / subbase + compacted soil base", the wheel rutting produced on the pavement under the action of aircraft load is mainly caused by the accumulation of plastic deformation of the base / subbase and soil base; it is generally believed that according to the formation mechanism of wheel rutting on flexible pavement at airports, the wheel rutting types can be divided into: structural wheel rutting, wear wheel rutting, unstable wheel rutting and compacted wheel rutting. Among them, unstable wheel rutting mainly occurs on asphalt concrete pavement, which is caused by the lateral flow deformation of asphalt mixture caused by high temperature; the other three types of wheel rutting may appear in the structure of emergency airport soil pavement.

[0276] (1) Structural wheel tracks: Due to the lack of overall rigidity of the soil pavement structure, the soil deformation caused by repeated aircraft loads and the vertical permanent deformation of the pavement structure layer are transmitted to the surface layer. This type of wheel track is mainly distributed on the wheel track belt, is often wide and has a concave subsidence deformation.

[0277] (2) Compacted wheel tracks: These are formed during the rapid construction of emergency airports due to insufficient compaction of the soil base or poor uniformity of the solidified / stabilized materials in the structural layer. Under the action of aircraft loads, the pavement structure undergoes compaction deformation. This type of wheel track is mainly distributed in areas such as aprons, taxiways, and runway ends where aircraft loads last for a long time and vertical loads are large.

[0278] (3) Wear-type wheel tracks: These are formed due to the continuous wear of the pavement surface caused by the dual effects of the aircraft landing gear wheel load and natural environmental factors. This type of wheel track is more likely to occur when the aircraft is braking or turning.

[0279] For the soil pavement of emergency airport, due to the thin soil base, local vertical deformation often occurs under the action of large transport aircraft loads, and the permanent deformation of the soil base is reflected in the pavement surface layer, resulting in deep wheel tracks on the pavement. In this process, structural wheel tracks and compaction wheel tracks are mainly produced. Among them, structural wheel tracks occupy a dominant position and need to be controlled by wheel track design indicators; compaction wheel tracks can be prevented by controlling construction quality and improving pavement material performance; and wear wheel tracks can be improved by laying functional surface layers and spreading wear-resistant and anti-skid aggregates. In summary, it can be seen that selecting reasonable wheel track control indicators for emergency airport soil pavement, establishing a scientific wheel track prediction model and deriving the corresponding soil pavement structure design method are of great significance to reducing the impact and harm of wheel tracks, improving the guarantee quality of soil pavement, extending the service life of pavement and enhancing the traffic performance of soil pavement.

[0280] S2. Wheel track control index and prediction method:

[0281] Under the long-term and repeated effects of aircraft loads, the soil pavement of the emergency airport will continue to produce a lot of permanent deformation (plastic deformation) causing wheel rutting damage on the pavement, which in turn affects the safety of aircraft traffic and the performance of the pavement structure. Therefore, wheel rutting damage has become a controlled damage mode in the mechanical-empirical design method of flexible pavement structures at airports in various countries. Limiting the amount of permanent deformation produced by the pavement structure and preventing wheel rutting damage on the pavement are key considerations in the design of flexible pavement structures at airports.

[0282] At present, in the design methods of flexible pavement structures at airports in various countries, two indicators, permanent deformation and vertical strain on the top surface of the soil subgrade, are generally used to control the wheel tracks generated on the pavement. Among them, the permanent deformation indicator is to study the elastic and plastic deformation properties of the pavement structure layer materials, analyze the stress and strain state of the pavement structure through experimental research, consider the permanent deformation of each structural layer of the pavement, and then establish the corresponding permanent deformation prediction equation, and then accumulate the calculated permanent deformation. The vertical compressive strain on the top surface of the soil subgrade controls the permanent deformation of the pavement through the vertical compressive strain or stress on the top surface of the soil subgrade. The cumulative damage method can be used to linearly superimpose the wheel track damage caused by different aircraft.

[0283] Among the above two indicators, the permanent deformation of each component of the pavement structure layer can be estimated by the layered strain summation method, which requires a large number of indoor material tests and long-term observations of outdoor test sections and structural analysis. The method of using the vertical compressive strain on the top surface of the soil subgrade to control the wheel rutting of the pavement structure has strong practicality. This method is simple, convenient and easy to implement. At the same time, the cumulative damage method based on the Miner principle is a linear cumulative damage theory. For all kinds of damage that use the vertical compressive strain on the top surface of the soil subgrade as a design control indicator, linear superposition can be performed; for the permanent deformation indicator, since the permanent deformation of the pavement structure layer does not develop linearly, the cumulative damage method is not compatible with the permanent deformation indicator, and the use of the cumulative damage method for linear superposition will produce a large error. From the above analysis, it can be seen that since the vertical compressive strain index on the top surface of the soil subgrade meets the requirements of practical design, the flexible pavement design methods of airports in various countries all use this index to control and estimate the deformation of the pavement wheel rutting. For this reason, the vertical compressive strain on the top surface of the soil subgrade is selected as the control index to limit the wheel rutting damage of the pavement structure.

[0284] In recent years, with the continuous development of elastic layered system theory and numerical simulation technology, many mechanical-empirical methods have emerged in the design of airport pavement structures. The vertical compressive strain index of the top surface of the subgrade has been widely used and developed in the design of airport flexible pavements. For example, the elastic layered system method of the UFC of the US military, the LEDFAA of the FAA, the APSDS of Australia, and the PAVER of the Netherlands all use the vertical compressive strain of the top surface of the subgrade to control the wheel rutting damage of the airport flexible pavement. These methods believe that when the subgrade undergoes a large deformation, the pavement structure will produce corresponding permanent deformation, that is, the pavement will be damaged by wheel rutting; in 1962, Dormon and Pettie established an empirical relationship between the vertical compressive strain of the top surface of the subgrade and the number of repeated actions of the standard axle load by back-calculating the pavement structure, as shown in formula (49). This wheel rutting equation has become the most widely used model in the current mechanical-empirical design method of airport flexible pavements:

[0285] ε z =aN -b (49)

[0286] Where: ε z is the vertical compressive strain on the top surface of the soil foundation; N is the number of repeated load actions; a and b are empirical regression coefficients;

[0287] The pavement structure design method based on the elastic layered system theory established by the U.S. Army Corps of Engineers (UFC) also uses the vertical compressive strain of the top surface of the soil subgrade as the design indicator for controlling the pavement wheel tracks. The wheel track equation established by UFC is obtained by fitting the model test data, and the allowable number of repeated actions of aircraft loads is expressed as a function of the vertical compressive strain of the top surface of the soil subgrade, such as Formula 50. In order to reflect the destructive effect of the soil subgrade, the equation takes into account the influence of the soil subgrade rebound modulus. When the vertical compressive strain of the top surface of the soil subgrade is constant, the number of repeated actions on the pavement decreases as the soil subgrade rebound modulus continues to decrease. This reflects that when the strength of the soil subgrade decreases, the pavement structure often produces an effect of increased permanent deformation.

[0288]

[0289] in:

[0290]

[0291] In the above two formulas: N is the number of times the load can be repeated; ε z is the vertical compressive strain on the top surface of the soil foundation; E S is the modulus of resilience of the soil base;

[0292] In the LEDFAA series of programs developed by the FAA of the United States based on the elastic layered system, the pavement wheel rutting equation is also characterized by the relationship between the number of repeated load actions and the maximum vertical compressive strain on the top surface of the subgrade. In the LEDFAA1.2 developed by the FAA, for a given vertical compressive strain on the top surface of the subgrade, the wheel rutting equation for determining the number of repeated aircraft load actions that the pavement can withstand before wheel rutting damage occurs is the same as the formulas (50) and (51) used by the UFC of the United States Army Corps of Engineers mentioned above.

[0293] 3. Establishment of wheel track prediction model for soil pavement of emergency airport

[0294] S1. Under the repeated action of transport aircraft wheel loads, the emergency airport soil pavement will continuously produce wheel rutting deformation. At this time, a soil pavement wheel rutting prediction model can be established based on the cumulative damage principle to predict the critical state of wheel rutting damage on the soil pavement. To this end, it can be assumed that the pavement wheel rutting equation under aircraft load is in the form of:

[0295] N=f(ε,μ) (52)

[0296] Where: N is the number of times the load can be repeated; ε is the vertical compressive strain on the top surface of the soil foundation; μ is other related variables;

[0297] S2. Most of the emergency airport pavement design methods of foreign militaries are based on the CBR empirical method, while there are few studies on permanent deformation of airport pavements in China. In particular, for typical structures of emergency airport soil pavements, no special wheel rutting damage tests have been carried out, and there is a lack of sufficient experimental data to support theoretical research. At present, foreign research on airport flexible pavement structure design theory and wheel rutting prediction equations has been relatively mature and complete, and many research results and application experience have been achieved. Faced with the lack of theoretical research on emergency airport pavement structure design in China, the existing permanent airport and emergency airport design specifications cannot effectively guide the soil pavement structure design, and there is no corresponding wheel rutting damage model for reference. A better solution is to combine the current status and trends of airport flexible pavement structure design research, learn and introduce the current more mature airport flexible pavement structure design method system abroad,

[0298] Based on the cumulative damage principle and combined with the wheel rut equation of formula (52), a wheel rut prediction model under the critical state of wheel rut damage on the soil pavement under the load of various transport aircraft is established as shown in formula (53); for the wheel rut deformation damage on the soil pavement of the emergency airport, this wheel rut prediction model can be used to guide the structural design of the soil pavement of the emergency airport:

[0299]

[0300] Where: n i is the estimated number of repeated load actions for the i-th aircraft; N i is the number of load repetitions allowed for the i-th aircraft; ε i is the vertical compressive strain on the top surface of the soil foundation under the action of the i-th aircraft; E s is the soil resilience modulus (MPa).

[0301] Example 1: Calculate the allowable depression depth for a certain type of aircraft:

[0302] Since the vibration characteristics of an aircraft passing through a pavement depression are closely related to the performance parameters of the aircraft itself, it is necessary to first collect relevant parameters such as the aircraft's mass, the elastic coefficients of the tires and landing gear. The relevant parameters of a certain type of aircraft are shown in Table 1-2:

[0303] Table 1: Parameters of a certain type of aircraft

[0304]

[0305] Table 2: Elastic coefficients of aircraft main wheels and main landing gear

[0306]

[0307] When the aircraft takes off at the maximum takeoff weight, the wheel load is the largest and the aircraft landing gear is in the most unfavorable state. From formula (11), we can know that the vibration acceleration of the fuselage is proportional to the natural angular frequency ω, and from It can be seen that ω is inversely proportional to the mass, so it can be concluded that the smaller the mass, the greater the vibration acceleration of the aircraft fuselage, that is, when the aircraft is at the minimum mass (empty mass) for takeoff, the vibration of the fuselage is the strongest. For this reason, the minimum mass (empty mass) of the aircraft is selected for calculation. At the same time, by It can be seen that the aircraft taxiing speed v will also have a great influence on the vibration acceleration. Therefore, 0.2, 0.5 and 0.8 times the take-off speed representing the aircraft's low-speed taxiing, medium-speed taxiing and high-speed taxiing are selected for calculation;

[0308] The takeoff speed of this type of aircraft is v0 = 97.2 m / s, and the length of the dent is l = 3.0 m. According to the relevant parameters given in Table 2, the relationship between the fuselage vibration acceleration and the dent depth is calculated by formula (11), as follows: Figure 5 As shown; According to formula (12), the relationship between the comprehensive dynamic load coefficient of the aircraft's minimum take-off mass (empty mass) and the depth of the depression is calculated, as shown in Figure 6 As shown;

[0309] Depend on Figure 2 It can be seen that when the aircraft is taxiing on the pavement at various speeds, the vibration acceleration of the fuselage increases with the increase of the pavement depression depth. When the depression depth is constant, the vibration acceleration decreases with the increase of the aircraft taxiing speed, and the greater the depth, the greater the increase in the vibration acceleration at each speed. Figure 3 It can be seen that when the depression depth is 0, the dynamic load coefficient is the load coefficient when the aircraft is not vibrating, and its value is only related to the lift of the aircraft. When the taxiing speed is 0.2v0, 0.5v0, and 0.8v0, the corresponding load coefficient K is 0.96, 0.75, and 0.36 respectively. Corresponding to the vibration acceleration of the fuselage, the dynamic load coefficient of the aircraft increases with the increase of the depression depth of the pavement, and decreases with the increase of the taxiing speed of the aircraft.

[0310] According to the above analysis, in order to ensure the safety and stability of aircraft passage and reduce the vibration and turbulence caused by the aircraft passing through the depression or potholes on the pavement surface, it is necessary to strictly limit the maximum depth of the pavement depression. From the three aspects of limiting the impact of vibration on the aircraft landing gear, ensuring the quality of the ride and ensuring the safety of instrument control and cargo loading, and preventing the aircraft from jumping when taxiing at high speed, the maximum depression depth limit value of this type of aircraft can be calculated according to formula (22), as shown in Table 3:

[0311] Table 3: Maximum concave depth limit values

[0312]

[0313] Note: When the aircraft is taxiing at high speed, the dynamic load coefficient generally does not exceed 0.25.

[0314] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for establishing a wheel track prediction model for a dirt runway based on the action of a large transport aircraft, characterized in that: The following steps are involved: Step 1: Study the surface characteristics of the flatness of the emergency airport pavement, analyze the wheel sinking state and the stress of the landing gear when the aircraft passes on the pavement, establish the vibration equation when the aircraft passes through the uneven pavement, and calculate and analyze the allowable depression depth and bulge height of the emergency airport pavement; Step 2: Analyze the passability of the soil pavement of the emergency airport, obtain the calculation formula of the rolling friction coefficient of the wheels on the soil pavement, and derive the calculation method of the allowable wheel track depth to ensure the passability of the soil pavement; Step 3: Analyze the types and causes of wheel ruts, select wheel rut control indicators and prediction methods, and derive a wheel rut prediction model suitable for emergency airport soil pavement; where: The specific process of establishing the vibration equation when the aircraft passes through an uneven road surface as described in step 1 includes: S1. Analyze the force of the aircraft when passing on the normal road surface: S1.1 Assume that when an aircraft is traveling on an ideally smooth and flat runway, it is vertically subjected to the combined effects of its own weight, the lift of the wing, and the reaction force of the runway. The lift generated by the wing is: Where: R y is the lift generated by the aircraft wing; ρ is the density of the air on the runway; C y is the lift coefficient of the aircraft; S is the lift area of ​​the wing; v is the passing speed of the aircraft; S1.2 Then, the runway reaction force is: S1.3 When the aircraft reaches takeoff speed, the lift generated by the wings is equal to the weight of the aircraft, that is, Where v0 is the aircraft's takeoff speed, the runway reaction force calculation formula is: S2. Analyze the force on the aircraft when it passes on an uneven road surface: S2.1 When an aircraft passes an obstacle on an uneven pavement, the control equation of the motion system composed of the aircraft and the pavement can be expressed as: Where: m1 and m2 are the mass of the landing gear and the mass of the aircraft borne by a single landing gear; k1 and k2 are the elastic coefficients of the tire and the aircraft spring respectively; C1 and C2 are the damping of the tire and the aircraft buffer respectively; y1 and y2 are the absolute vertical displacements of m1 and m2 respectively; y(t) is the displacement interference function representing the road surface flatness; S2.2 Ignore the damping effect of wheels, tires and fuselage buffers, that is, assume that C1 and C2 are both 0. At the same time, the mass of the main landing gear m1 is very small compared to the mass of the aircraft fuselage m2, so ignore the mass of the main landing gear, that is, assume that m1 = 0, then Equation 4 can be simplified to: Formula (5) can be further simplified as: S2.3 Solve the differential equation of equation (6) and let And add the initial condition t = 0, y2 = 0, Then the solution is: S3. Calculate the vibration dynamic load coefficient of the aircraft when it passes on an uneven road surface: S3.1 From the solution process of formula (7), it can be seen that the vibration acceleration of the aircraft is not only related to the mechanical properties of the aircraft itself, but also to the interference function y(t) of the uneven surface of the pavement. According to the principle of mechanics, when the length-to-depth ratio of the concave or pit size is the same, the dynamic response generated by the cosine is the largest. Therefore, the cosine function is used as the curve function of the concave for analysis, and then: Where: l is the length of the pavement depression parallel to the runway centerline; h is the maximum vertical depth of the pavement depression; S3.2 Order Then formula (8) is: Substituting formula (9) into formula (7), we can obtain the following through integral transformation: S3.3 Assume that when an aircraft passes over an uneven road surface, the ratio of the vibration acceleration to the gravity acceleration is the vibration dynamic load coefficient, denoted as K1, and its calculation formula is: S3.4 Substitute the load factor in formula (3) when the aircraft is not vibrating into Adding K1 calculated by formula (11) to the total dynamic load coefficient of the main landing gear when the aircraft experiences vertical vibration is: The specific process of calculating and analyzing the allowable depression depth of the emergency airport pavement described in step 1 includes: S1. Analyze the maximum allowable depth of the pavement surface when the aircraft passes through the pavement surface: S1.1 During the design and production of aircraft landing gear, in order to prevent the landing gear components from fatigue damage or even breakage too quickly, the aircraft dynamic load coefficient is introduced. The dynamic load coefficient K d ,Right now: S1.2 Take 1.25 as the allowable dynamic load coefficient value, that is, K d =1.25, substitute it into formula (13), take cosωt-cosαt=1, and we get: S2. Analyze the maximum allowable depth of the pavement surface depression when the aircraft passes through the pavement surface while ensuring the quality of the ride and the integrity of instrument control and cargo loading: S2.1 When the aircraft passes through uneven areas, in order to ensure the integrity of flight personnel, instruments and cargo, the vibration dynamic load coefficient K1 is introduced. When K1 = 0.4: Let t′ = αt, equation (15) can be transformed into: Where: K1(t) is a function that changes with time, and only its maximum value is considered here; S2.2 First determine The value is related to the value of ω / α. According to calculations, the value of ω / α is between 0.05 and 0.

6. When the aircraft's taxiing speed v>v0 / 3, ω / α<0.2, then The maximum value of is approximately equal to 2, then the maximum vibration dynamic load coefficient K1′ is: At this time, the maximum depth h2 of the concave surface of the road surface is: S3. Analyze the process of the aircraft passing through the pavement surface, and solve the maximum allowable depth of the pavement surface depression while ensuring that the aircraft does not jump when taxiing at high speed: S3.1 When the aircraft passes through an uneven surface, in order to ensure that the aircraft does not jump during high-speed taxiing, the vibration dynamic load coefficient K1′ is introduced: S3.2 For the rolling distance area where jumping may occur, the maximum depth of the depression h3 on the pavement surface shall meet the following requirements: S4. Combining formulas (14), (18) and (21), the allowable depth of road surface depressions or potholes in different areas can be calculated, namely: The specific process of calculating and analyzing the allowable uplift height of the emergency airport pavement described in step 1 includes: S1. The vibration equation when the aircraft passes through the raised part of the pavement surface is the same as that of the concave part, and both can be expressed by formula (5). The pavement interference function of the raised part can still be expressed by the cosine function, but it is different from the interference function corresponding to the concave part by a positive or negative sign: S2. Order Then formula (23) becomes After integral transformation, solving the equation we can get: S3. Equations (25) and (26) show that the interference function and vibration acceleration of the ridged part of the pavement surface differ only by a positive or negative sign from those of the concave part, and the calculation results are the same; therefore, the dynamic response of the ridge and the concave part or the pothole to the aircraft is the same, and the maximum allowable height value of the ridge is the same as the maximum allowable depth value of the concave part; The specific process of obtaining the calculation formula of the rolling friction coefficient of the wheel on the soil road surface described in step 2 includes: S1. When the aircraft wheel moves on the soil road surface, the sum of the horizontal components of the soil's radial reaction force on the rigid wheel is balanced with the horizontal traction force F, and the sum of the vertical components of the radial reaction force is balanced with the wheel load P. k Phase equilibrium, we can get: Where: σ is the bearing capacity coefficient of the soil, which is equal to the radial reaction force of the soil at a depth of 1 cm on the wheel surface, MPa; μ is a parameter related to soil quality, which is between 0.34 and 0.98, with an average of 0.67; h1 is the depth of the rigid wheel pressed into the soil; h2 is the recoverable deformation height; b is the spoke width of the rigid wheel; d is the diameter of the rigid wheel; S2. From equations (29) and (30), the rolling friction coefficient f is: S3. For plastic soil, since its recoverable elastic deformation is small, h2 = 0, H = h1, and equations (30) and (31) can be simplified to: Substituting formula (32) into formula (33), we can obtain: S4. Since d′=αd, α is the conversion coefficient, and its value is related to the soil bearing capacity coefficient σ and the tire pressure of the machine, the calculation formula for the wheel track depth and rolling friction coefficient when the pneumatic machine wheel rolls on the soil road surface is: S5. When the soil is in a fluid or plastic state, the parameters related to the soil are close to zero, that is, μ = 0, then equations (35) and (36) can be further simplified as: S6. By performing mechanical experiments according to the design, the bearing capacity coefficient σ can be obtained, and the calculated σ is substituted into formula (38) to obtain the rolling friction coefficient f value. The solution equation of the bearing capacity coefficient σ is: The process of proposing the calculation method of the allowable wheel track depth to ensure the passability of the soil road surface described in step 2 includes: S1. When the aircraft can start and taxi on the soil road surface, analyze the limiting conditions of the wheel track depth H1 and soil bearing capacity coefficient σ1 for the aircraft to start and taxi on the soil road surface: S1.1 When the aircraft starts taxiing on the soil surface, the relative thrust Φ of the engine is greater than the rolling friction coefficient f of the wheel. q , take f q =1.4f, then: Φ>f q =1.4f (40) S1.2 Substituting equation (40) into equations (37)-(39) respectively, the constraints on the wheel track depth H1 and soil bearing capacity coefficient σ1 that ensure the aircraft can start taxiing on the soil road surface are obtained as follows: S2. When the aircraft reaches the take-off speed within the length of the soil runway, analyze the limiting conditions of the wheel track depth H2 and the soil bearing capacity coefficient σ2 for the aircraft to start taxiing on the soil surface: The aircraft glides at high speed within a limited length of the soil runway and reaches a take-off speed v0. Assume that when the aircraft glides on the soil runway, the average rolling friction coefficient f h =0.5f, then the wheel track depth H2 and the soil bearing capacity coefficient σ2 must meet the following conditions respectively: Where: S is the length of the emergency airport soil runway, m; ΔS is the distance from the aircraft starting position to the end of the soil runway, m; i is the average longitudinal slope of the soil runway, which takes a positive value when the aircraft takes off along the slope and a negative value when the aircraft takes off against the slope; S3. When the aircraft can taxi safely on the soil road surface, the limiting conditions of the wheel track depth H3 and the soil bearing capacity coefficient σ3 for the aircraft to start taxiing on the soil road surface are analyzed: When an aircraft glides at high speed on a soil road surface, the wheel track depth H3 generated by the repeated action of the aircraft satisfies: H3<0.07d (45) At this time, the bearing capacity coefficient σ3 of the corresponding soil should satisfy: S4. From the above analysis, it can be seen that in order to ensure the trafficability of aircraft on soil pavement, the above three conditions must be met at the same time, that is, the maximum wheel track depth and the minimum bearing capacity coefficient of the soil produced by the repeated action of the aircraft on the pavement should meet the following conditions: The process of establishing the wheel track prediction model of the emergency airport soil pavement described in step 3 includes: S1. Assume that the pavement wheel track equation under aircraft load is in the form of: N=f(ε,μ) (52) Where: N is the number of times the load can be repeated; ε is the vertical compressive strain on the top surface of the soil foundation; μ is other related variables; S2. Based on the cumulative damage principle and combined with formula (52), a wheel rutting prediction model for the critical state of wheel rutting damage on soil pavement under the action of various types of transport machine loads is established: Where: n i is the estimated number of repeated load actions for the i-th aircraft; N i is the number of load repetitions allowed for the i-th aircraft; ε i is the vertical compressive strain on the top surface of the soil foundation under the action of the i-th aircraft; E s is the soil resilience modulus (MPa).

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