CN105975720A - Structural layer thickness design method for mixed base course cement concrete pavement - Google Patents

Abstract

The invention discloses a structural layer thickness design method for a mixed base course cement concrete pavement. The structural layer thickness design method comprises the following steps that the comprehensive equivalent weight rebound modulus of a plate bottom foundation is calculated; the equivalent bending rigidity and the equivalent thickness of a mixed base course are calculated according to situations of a rigid base course and a semi-rigid subbase course and the rigid base course and a soft subbase course; load stress, load fatigue stress, a interlayer contact condition parameter, vertical contact rigidity, the maximum temperature stress, the temperature fatigue stress and the like are calculated according to the calculation results of the equivalent bending rigidity and the equivalent thickness through an elastic foundation doubling plate model; structural limiting state is checked, the situation that no limit breakage occurs is taken as a checking standard, and whether the drafted structural layer thickness meets requirements or not is determined. The problems of unnecessary waste and early serious damages caused by the unreasonable structural layer thickness design of the mixed base course cement concrete pavement can be effectively avoided, and the method has good social and economic benefits.

Description

A kind of Laminate construction thickness method for designing of composite base cement concrete pavement

Technical field

The invention belongs to road engineering technical field, relate to the Laminate construction thickness of a kind of composite base cement concrete pavement Method for designing.

Background technology

China is in early days to build cement concrete pavement, at present when road pavement structural bearing capacity requires higher, and cement Concrete road surface remains alternative primary structure form, abroad cement concrete pavement also because of length in service life by extensively General application.The build of cement concrete pavement can reduce the dependence to petroleum resources with application, makes full use of China's relative abundance Cement and fly ash material, drive local economic development.For high-grade highway, the design period of bituminous paving is 15 years, The design period of cement concrete pavement is 30 years, and the cost of investment of cement concrete pavement is relatively low, so building water Cement concrete road surface will produce significant social and economic effects.

In the application process of China's cement concrete pavement structure, traffic loading grade be extremely weigh or extra heavy situation more Common, according to existing " highway cement concrete pavement design specification JTG D40-2011 " (hereinafter referred to as specification), traffic loading When grade is for extremely weighing or be extra heavy, substrate type is only lean concrete, grinding coagulation soil, bituminous concrete, it is contemplated that Colophonium coagulation Tu Zuo basic unit cost is high, bearing capacity is limited, is typically chosen lean concrete, grinding coagulation soil is as base material, and sets cement Stabilization gravel or Lime-flyash treated aggregate underlayment, lean concrete, grinding coagulation soil rigidity more greatly rigid material, water Cement-stabilizing broken stone or Lime-flyash treated aggregate are semi-rigid material, and whole base layer structure is rigidity and semi-rigid material composition Composite base.Location such as level of ground water is higher, precipitation enriches, it is contemplated that cement stabilized macadam or Calx-flyash Scour resistance and the water stability of stabilization gravel are relatively poor, and underlayment may be used without dense bitumen stabilization gravel, whole basic unit Structure is rigidity and the composite base of flexible material composition.

Current specifications there is no rigid base's composite base cement with semi-rigid underlayment or with flexible underlayment composition mix The Laminate construction thickness method for designing of solidifying soil surface, whole pavement structure selects which kind of which kind of mechanical model and composite base use Mechanical model carries out the mechanical model of process annoying road work person, especially composite base, can for reference the most compound Slab, but composite plate model is primarily directed to basic unit and subbase course material character situation that is close and that all can process by thin plate, As basic unit and underlayment are rigid material or are stabilized with inorganic binder class material.For rigid base and semi-rigid underlayment Or with the composite base of flexible underlayment composition, rigid base typically uses lean concrete or grinding coagulation soil, also needs to calculate mixed The load fatigue stress of box-like basic unit, needs to use the thickness of composite base in calculating.Because the elastic modelling quantity of rigid base is half Rigidity underlayment or tens times of flexible underlayment, after composite base is processed by composite plate, thickness is as straight by basic unit and underlayment Connect addition, the most overly conservative and inadequate science；Conversion, lotus after conversion is entered by nominal stress again as directly taken the thickness of rigid base Carry stress bigger than normal；Calculate surface layer plate load stress time equally exist Similar Problems, as composite base by composite plate at Reason, the bending stiffness of composite base is directly added by the bending stiffness of rigid base and the bending stiffness of semi-rigid underlayment, with Sample due to tens times that the bending stiffness of rigid base is semi-rigid underlayment, this simple the most directly addition, make composite base Bending stiffness substantially dominated by rigid base, result of calculation is the most too conservative.Thus, it is necessary to a kind of composite base of research and development The Laminate construction thickness method for designing of cement concrete pavement, effectively solve in current specifications without rigid base and semi-rigid underlayment or With the problem of the composite base cement concrete pavement structure layer thickness method for designing of flexible underlayment composition, and with reference to it His method is the most scientific and reasonable and overly conservative and that cause unnecessary waste problem when being designed.

Summary of the invention

The technical problem to be solved is that the Laminate construction thickness researching and developing a kind of composite base cement concrete pavement sets Meter method, it is possible to resolve in current specifications without rigid base and semi-rigid underlayment or with the composite base water of flexible underlayment composition The problem of cement concrete road surface structare layer Thickness Design Method, and effectively solve the inadequate section when being designed with reference to additive method Learn reasonable and overly conservative problem.

In order to solve above-mentioned technical problem, the structure sheaf of a kind of composite base cement concrete pavement provided by the present invention Thickness Design Method, it is as follows that its technical scheme implements step:

(1) the comprehensive Composite resilient modulus of ground at the bottom of computing board E_t

The modulus of resilience and the distance of roadbed apex distance level of ground water according to subgrade soils determine comprehensive modulus of resilience E in roadbed top₀, then Elastic modulus E according to pellet layer_aAnd thickness h_aDetermine the comprehensive Composite resilient modulus E of ground at the bottom of plate_b, at the bottom of computing board, ground is comprehensive Composite resilient modulus E_t:

$E_t={\left(\frac{E_b}{E_0}\right)}^a{E}_0$

α=0.86+0.26ln (h_a)

(2) equivalent bending stiffness and the equivalent thickness of composite base are calculated

Elastic modulus E according to rigid base₁And thickness h₁, semi-rigid underlayment or the elastic modulus E of flexible underlayment₂And Thickness h₂, the Composite resilient modulus E of composite base is calculated by the method for weighted sum of squares_x:

$E_x=\frac{h_1^2{E}_1+h_2^2{E}_2}{h_1^2+h_2^2}$

When composite base is made up of rigid base and semi-rigid underlayment, the moment of flexure that composite base cross section undertakes is by upper The moment of flexure of layer rigid base plate, the moment of flexure of lower floor's semi-rigid base laminate, and upper strata rigid base plate, the semi-rigid base of lower floor The moment of flexure three part composition that laminate axial force produces, bending stiffness corresponding to three parts is respectively D₁、D₂、D₃, based on thin plate It is assumed that the equivalent bending stiffness D of composite base_xFor:

D_x=D₁+D₂+D₃

Wherein:

In formula: e is plate cross section relative compressive rigidity, v₁For the Poisson's ratio of upper strata rigid base plate, v₂For the lower floor semi-rigid end The Poisson's ratio of basal plate,K is Coating combination coefficient, and general interlayer is bonding state, and k takes 1。

By above expression formula it follows that

$D_x=\frac{E_1{h}_1^3}{12(1-{v_1}^2)}+\frac{E_2{h}_2^3}{12(1-{v_2}^2)}+\frac{{(h_1+h_2)}^2}{4}{(\frac{1-{v_1}^2}{E_1{h}_1}+\frac{1-{v_2}^2}{E_2{h}_2})}^{-1}$

Again by:

In formula: h_xFor the equivalent thickness of composite base, v_xFor the Poisson's ratio of composite base, can approximate and be taken as rigid base Poisson's ratio v of plate₁, the equivalent thickness h of composite base_xFor:

$h_x={\left[\frac{12(1-{v_1}^2)D_x}{E_x}\right]}^{1/3}$

When composite base is made up of rigid base and flexible underlayment, owing to flexible underlayment no longer possesses thin plate spy Levy, by composite, composite base is considered as entirety, the equivalent bending stiffness D of composite base_xFor:

D_x=D₁+D₂

Wherein: D₁、D₂It is respectively rigid base and the bending stiffness of flexible underlayment,

$D_x=\frac{E_1{h}_1^3}{12(1-{v_1}^2)}+\frac{E_2{h}_2^3}{12(1-{v_2}^2)}$

Again by:Poisson's ratio v of composite base_x, approximation is taken as the Poisson's ratio of rigid base's plate v₁, h_xFor the equivalent thickness of composite base, can obtain:

$D_x=\frac{E_x{h}_x^3}{12(1-{v_1}^2)}$

The equivalent thickness h of composite base_xFor:

$h_x=\left\{\frac{1}{E_x}\right[E_1{h_1}^3+\frac{E_2{h_2}^3(1-{v_1}^2)}{1-{v_2}^2}]{\}}^{1/3}$

(3) load stress is calculated

Elastic modulus E according to Portland Cement Concrete Surface Course plate_c, thickness h_c, Poisson's ratio v_c, calculate the bending stiffness of surface layer plate D_c:

$D_c=\frac{E_c\×{h_c}^3}{12\×(1-{v_c}^2)}$

Calculate pavement structure total radius of relative stiffness r_g:

$r_g=1.21{\left(\frac{D_c+D_x}{E_t}\right)}^{1/3}$

Calculate standard axle load 100kN, solid axle by elastic foundation doubling plate model and carry P_m(drawing according to investigation) is at critical load position The load stress σ at place_ps、σ_pm:

${\mathrm{\σ}}_{\mathrm{ps}}=\left(\frac{1.45\×{10}^{-3}}{1+\frac{D_x}{D_c}}\right)\×r_g^{0.65}\×h_c^{-2}\×{100}^{0.94}$

${\mathrm{\σ}}_{\mathrm{pm}}=\left(\frac{1.45\×{10}^{-3}}{1+\frac{D_x}{D_c}}\right)\×r_g^{0.65}\×h_c^{-2}\×P_m^{0.94}$

Calculate composite base load stress σ at critical load position_bps:

${\mathrm{\σ}}_{\mathrm{bps}}=\left(\frac{1.45\×{10}^{-3}}{1+\frac{D_c}{D_x}}\right)\×r_g^{0.68}\×h_x^{-2}\×{100}^{0.94}$

(4) other calculate and design content

By elastic foundation doubling plate model, calculate the load fatigue stress of surface layer plate, solid axle and carry P_mThe peak load produced Stress, basic unit's load fatigue stress, and the maximum temperature stress of surface layer plate and temperature fatigue stress, during calculating, interlayer connects Touch condition parameter r_βIt is calculated as follows:

$r_{\mathrm{\β}}={\left[\frac{D_c\×D_x}{(D_c+D_x)\×k_n}\right]}^{1/4}$

In formula: k_nFor vertical contact stiffness, when having bituminous concrete interlayer, value is 3000MPa/m, without bituminous concrete During interlayer:

$k_n=\frac{1}{2}{(\frac{h_c}{E_c}+\frac{h_x}{E_x})}^{-1}$

Load fatigue stress according to surface layer plate, temperature fatigue stress, peak load stress, the calculating of maximum temperature stress As a result, and the load fatigue stress of composite base, carry out structural limits state check, not produce limit fracture as testing Calculation standard, determines whether the Laminate construction thickness of the composite base cement concrete pavement drafted meets requirement, as being unsatisfactory for requirement Then repeat said process, pass through until structural limits state is checked.

Beneficial effects of the present invention is as follows:

The present invention provides the Laminate construction thickness method for designing of a kind of composite base cement concrete pavement, it is possible to resolve without just in current specifications Property basic unit and semi-rigid underlayment or the composite base cement concrete pavement structure layer thickness design side with flexible underlayment composition The problem of method, is the useful supplement to current specifications, and the inadequate science when being designed with reference to additive method that effectively solves is closed Reason and overly conservative problem.In the method for designing of current specifications, the process for composite base can only have multiple for reference Plywood model, but composite plate model is primarily directed to basic unit and subbase course material character feelings that are close and that all can process by thin plate Condition, as basic unit and underlayment are rigid material or are stabilized with inorganic binder class material.For rigid base and the semi-rigid end Basic unit or the composite base with flexible underlayment composition, rigid base typically uses lean concrete or grinding coagulation soil, also needs meter Calculate the load fatigue stress of composite base, calculating needs to use the thickness of composite base.Elastic modelling quantity because of rigid base It is semi-rigid underlayment or tens times of flexible underlayment, and after composite base is processed by composite plate, thickness is as by basic unit and the end Basic unit is directly added, the most overly conservative and inadequate science；Enter conversion by nominal stress again as directly taken the thickness of rigid base, change After calculation, load stress is bigger than normal；Similar Problems is equally existed, if composite base is by compound when calculating surface layer plate load stress Plate processes, the bending stiffness of the composite base bending stiffness by rigid base and the direct phase of bending stiffness of semi-rigid underlayment Add, also due to the bending stiffness of rigid base is tens times of semi-rigid underlayment, this simple directly addition, make mixing The bending stiffness of formula basic unit is dominated by rigid base substantially, and result of calculation is the most too conservative.The present invention divides rigid base with semi-rigid Underlayment and rigid base and flexible two kinds of situations of underlayment, it is determined that composite base equivalent bending stiffness and the meter of equivalent thickness Calculation method, solves problem present in the design of composite base cement concrete pavement structure layer thickness, can be prevented effectively from mixing Formula basic unit cement concrete pavement produces unnecessary waste because Laminate construction thickness design is unreasonable and occurs that earlier period damage is serious Problem, has good social and economic effects.

Proposing in the Report on the Work of the Government of 2016, China will strengthen infrastructure in " 13 " period, " 13 " period is newly-built and reconstructs highway mileage open to traffic about 30,000 kilometers, and the pavement structure layer thickness that the present invention relates to sets Having a extensive future of meter method, potential social and economic effects is notable.

Detailed description of the invention

In order to be more fully understood that the present invention, below with reference to specific embodiment, the present invention is described in further details, is retouched The embodiment stated is only in order to illustrate technical scheme, not in order to limit the present invention.

Embodiment 1

It is 95% that certain cement concrete pavement in freeway builds the target reliability degree that base period is 30 years, and safe class is One-level.Drafting pavement structure form is: normal concrete surface layer (elastic modulus E_c, thickness h_c, Poisson's ratio v_c, flexural tensile strength Standard value is f_r)+4cm bituminous concrete interlayer+grinding coagulation soil matrix layer (elastic modulus E₁, thickness h₁, Poisson's ratio v₁, curved draw Strength standard value is f_r1)+cement stabilized macadam underlayment (elastic modulus E₂, thickness h₂, Poisson's ratio v₂)+graded broken stone pellet layer (elastic modulus E_a, thickness h_a)。

The modulus of resilience and the distance of roadbed apex distance level of ground water according to subgrade soils determine comprehensive modulus of resilience E in roadbed top₀, then Elastic modulus E according to pellet layer_aAnd thickness h_aDetermine the comprehensive Composite resilient modulus E of ground at the bottom of plate_b, at the bottom of computing board, ground is comprehensive Composite resilient modulus E_t:

$E_t={\left(\frac{E_b}{E_0}\right)}^{\mathrm{\α}}{E}_0$

α=0.86+0.26ln (h_a)

Elastic modulus E according to grinding coagulation soil matrix layer₁And thickness h₁, the elastic modulus E of cement stabilized macadam underlayment₂And Thickness h₂, the Composite resilient modulus E of composite base is calculated by the method for weighted sum of squares_x:

$E_x=\frac{h_1^2{E}_1+h_2^2{E}_2}{h_1^2+h_2^2}$

The moment of flexure that composite base cross section undertakes is at the bottom of by the moment of flexure of upper strata grinding coagulation soil matrix laminate, lower layer of water cement-stabilizing broken stone The moment of flexure of basal plate, and the moment of flexure that upper strata grinding coagulation soil matrix laminate, lower layer of water cement-stabilizing broken stone underlayment plate axial force produce Three parts compositions, bending stiffness corresponding to three parts is respectively D₁、D₂、D₃, based on thin plate it is assumed that composite base etc. Effect bending stiffness D_xFor:

D_x=D₁+D₂+D₃

Wherein:

In formula: e is plate cross section relative compressive rigidity,K takes 1.

By above expression formula it follows that

$D_x=\frac{E_1{h}_1^3}{12(1-{v_1}^2)}+\frac{E_2{h}_2^3}{12(1-{v_2}^2)}+\frac{{(h_1+h_2)}^2}{4}{(\frac{1-{v_1}^2}{E_1{h}_1}+\frac{1-{v_2}^2}{E_2{h}_2})}^{-1}$

Again by:

In formula: h_xFor the equivalent thickness of composite base, v_xFor the Poisson's ratio of composite base, can approximate and be taken as grinding coagulation Poisson's ratio v of soil matrix laminate₁, can obtain:

$h_x={\left[\frac{12(1-{v_1}^2)D_x}{E_x}\right]}^{1/3}$

Elastic modulus E according to Portland Cement Concrete Surface Course plate_c, thickness h_c, Poisson's ratio v_c, calculate the bending stiffness of surface layer plate D_c:

$D_c=\frac{E_c\×{h_c}^3}{12\×(1-{v_c}^2)}$

Calculate pavement structure total radius of relative stiffness r_g:

$r_g=1.21{\left(\frac{D_c+D_x}{E_t}\right)}^{1/3}$

Calculate standard axle load 100kN, solid axle by elastic foundation doubling plate model and carry P_m(drawing according to investigation) is at critical load position The load stress σ at place_ps、σ_pm:

${\mathrm{\σ}}_{\mathrm{ps}}=\left(\frac{1.45\×{10}^{-3}}{1+\frac{D_x}{D_c}}\right)\×r_g^{0.65}\×h_c^{-2}\×{100}^{0.94}$

${\mathrm{\σ}}_{\mathrm{pm}}=\left(\frac{1.45\×{10}^{-3}}{1+\frac{D_x}{D_c}}\right)\×r_g^{0.65}\×h_c^{-2}\×P_m^{0.94}$

Calculate composite base load stress σ at critical load position_bps:

${\mathrm{\σ}}_{\mathrm{bps}}=\left(\frac{1.45\×{10}^{-3}}{1+\frac{D_c}{D_x}}\right)\×r_g^{0.68}\×h_x^{-2}\×{100}^{0.94}$

By elastic foundation doubling plate mechanical model, calculate load fatigue stress σ of surface layer plate_pr, solid axle carry P_mProduce Peak load stress σ_p,max, composite base load fatigue stress σ_bpr, the maximum temperature stress σ of surface layer plate_t,maxTired with temperature Labor stress σ_tr, interface conditions parameter r during calculating_βIt is calculated as follows:

$r_{\mathrm{\β}}={\left[\frac{D_c\×D_x}{(D_c+D_x)\×k_n}\right]}^{1/4}$

In formula: k_nFor vertical contact stiffness, take 3000MPa/m.

Load fatigue stress σ according to surface layer plate_pr, temperature fatigue stress σ_tr, peak load stress σ_p,max, maximum temperature Stress σ_t,maxResult of calculation, and composite base load fatigue stress σ_bprResult of calculation and safety index γ_r, enter Row structural limits state is checked, not produce limit fracture as checking computations standard: γ_γ(σ_pr+σ_tr)≤f_r、γ_γ(σ_p,max+σ_t,max) ≤f_r、γ_γ×σ_bpr≤f_r1。

Determine whether the Laminate construction thickness of the composite base cement concrete pavement drafted meets requirement, as being unsatisfactory for requirement Then repeat said process, pass through until structural limits state is checked.

Embodiment 2

It is 95% that certain cement concrete pavement in freeway builds the target reliability degree that base period is 30 years, and safe class is One-level.Drafting pavement structure form is: normal concrete surface layer (elastic modulus E_c, thickness h_c, Poisson's ratio v_c, flexural tensile strength Standard value is f_r)+4cm bituminous concrete interlayer+grinding coagulation soil matrix layer (elastic modulus E₁, thickness h₁, Poisson's ratio v₁, curved draw Strength standard value is f_r1)+dense bitumen stabilization gravel underlayment (elastic modulus E₂, thickness h₂, Poisson's ratio v₂)+graded broken stone Pellet layer (elastic modulus E_a, thickness h_a)。

The modulus of resilience and the distance of roadbed apex distance level of ground water according to subgrade soils determine comprehensive modulus of resilience E in roadbed top₀, then Elastic modulus E according to pellet layer_aAnd thickness h_aDetermine the comprehensive Composite resilient modulus E of ground at the bottom of plate_b, at the bottom of computing board, ground is comprehensive Composite resilient modulus E_t:

$E_t={\left(\frac{E_b}{E_0}\right)}^{\mathrm{\α}}{E}_0$

α=0.86+0.26ln (h_a)

Elastic modulus E according to grinding coagulation soil matrix layer₁And thickness h₁, the springform of dense bitumen stabilization gravel underlayment Amount E₂And thickness h₂, the Composite resilient modulus E of composite base is calculated by the method for weighted sum of squares_x:

$E_x=\frac{h_1^2{E}_1+h_2^2{E}_2}{h_1^2+h_2^2}$

The equivalent bending stiffness D of composite base_xFor:

D_x=D₁+D₂

Wherein: D₁、D₂It is respectively grinding coagulation soil matrix layer and the bending stiffness of dense bitumen stabilization gravel underlayment,

Again by:Poisson's ratio v of composite base_x, approximation is taken as the Poisson's ratio of grinding coagulation soil matrix layer v₁, can obtain:

$D_x=\frac{E_x{h}_x^3}{12(1-{v_1}^2)}$

$h_x=\left\{\frac{1}{E_x}\right[E_1{h_1}^3+\frac{E_2{h_2}^3(1-{v_1}^2)}{1-{v_2}^2}]{\}}^{1/3}$

Elastic modulus E according to Portland Cement Concrete Surface Course plate_c, thickness h_c, Poisson's ratio v_c, calculate the bending stiffness of surface layer plate D_c:

$D_c=\frac{E_c\×{h_c}^3}{12\×(1-{v_c}^2)}$

Calculate pavement structure total radius of relative stiffness r_g:

$r_g=1.21{\left(\frac{D_c+D_x}{E_t}\right)}^{1/3}$

Calculate standard axle load 100kN, solid axle by elastic foundation doubling plate model and carry P_m(drawing according to investigation) is at critical load position The load stress σ at place_ps、σ_pm:

${\mathrm{\σ}}_{\mathrm{ps}}=\left(\frac{1.45\×{10}^{-3}}{1+\frac{D_x}{D_c}}\right)\×r_g^{0.65}\×h_c^{-2}\×{100}^{0.94}$

${\mathrm{\σ}}_{\mathrm{pm}}=\left(\frac{1.45\×{10}^{-3}}{1+\frac{D_x}{D_c}}\right)\×r_g^{0.65}\×h_c^{-2}\×P_m^{0.94}$

Calculate composite base load stress σ at critical load position_bps:

${\mathrm{\σ}}_{\mathrm{bps}}=\left(\frac{1.45\×{10}^{-3}}{1+\frac{D_c}{D_x}}\right)\×r_g^{0.68}\×h_x^{-2}\×{100}^{0.94}$

By elastic foundation doubling plate mechanical model, calculate load fatigue stress σ of surface layer plate_pr, solid axle carry P_mProduce Peak load stress σ_p,max, composite base load fatigue stress σ_bpr, the maximum temperature stress σ of surface layer plate_t,maxTired with temperature Labor stress σ_tr, interface conditions parameter r during calculating_βIt is calculated as follows:

$r_{\mathrm{\β}}={\left[\frac{D_c\×D_x}{(D_c+D_x)\×k_n}\right]}^{1/4}$

In formula: k_nFor vertical contact stiffness, take 3000MPa/m.

Load fatigue stress σ according to surface layer plate_pr, temperature fatigue stress σ_tr, peak load stress σ_p,max, maximum temperature Stress σ_t,maxResult of calculation, and composite base load fatigue stress σ_bprResult of calculation and safety index γ_r, enter Row structural limits state is checked, not produce limit fracture as checking computations standard: γ_γ(σ_pr+σ_tr)≤f_r、γ_γ(σ_p,max+σ_t,max) ≤f_r、γ_γ×σ_bpr≤f_r1。

Determine whether the Laminate construction thickness of the composite base cement concrete pavement drafted meets requirement, as being unsatisfactory for requirement Then repeat said process, pass through until structural limits state is checked.

Claims (1)

1. the Laminate construction thickness method for designing of a composite base cement concrete pavement, it is characterised in that include following step Rapid:

(1) the comprehensive Composite resilient modulus of ground at the bottom of computing board E_t

(2) equivalent bending stiffness and the equivalent thickness of composite base are calculated

Elastic modulus E according to rigid base₁And thickness h₁, semi-rigid underlayment or the elastic modulus E of flexible underlayment₂And it is thick Degree h₂, the Composite resilient modulus E of composite base is calculated by the method for weighted sum of squares_x:

$E_x=\frac{h_1^2{E}_1+h_2^2{E}_2}{h_1^2+h_2^2}$

When composite base is made up of rigid base and semi-rigid underlayment, the equivalent bending stiffness D of composite base_xFor:

$D_x=\frac{E_1{h}_1^3}{12(1-{v_1}^2)}+\frac{E_2{h}_2^3}{12(1-{v_2}^2)}+\frac{{(h_1+h_2)}^2}{4}{(\frac{1-{v_1}^2}{E_1{h}_1}+\frac{1-{v_2}^2}{E_2{h}_2})}^{-1}$

The equivalent thickness h of composite base_xFor:

$h_x={\[\frac{12(1-{v_1}^2)D_x}{E_x}\]}^{1/3}$

When composite base is made up of rigid base and flexible underlayment, the equivalent bending stiffness D of composite base_xFor:

$D_x=\frac{E_1{h}_1^3}{12(1-{v_1}^3)}+\frac{E_2{h}_2^3}{12(1-{v_2}^2)}$

The equivalent thickness h of composite base_xFor:

$h_x={\{\frac{1}{E_x}\[E_1{h_1}^3+\frac{E_2{h}_2^3(1-{v_1}^2)}{1-{v_2}^2}\]\}}^{1/3}$

(3) load stress is calculated

Elastic modulus E according to Portland Cement Concrete Surface Course plate_c, thickness h_c, Poisson's ratio v_c, calculate the bending stiffness of surface layer plate D_c:

$D_c=\frac{E_c\×{h_c}^3}{12\×(1-{v_c}^2)}$

Calculate pavement structure total radius of relative stiffness r_g:

$r_g=1.21{\left(\frac{D_c+D_x}{E_t}\right)}^{1/3}$

Calculate standard axle load 100kN, solid axle by elastic foundation doubling plate model and carry P_m(drawing according to investigation) is at critical load position Load stress σ_ps、σ_pm:

${\mathrm{\σ}}_{ps}=\left(\frac{1.45\×{10}^{-3}}{1+\frac{D_x}{D_c}}\right)\×r_g^{0.65}\×h_c^{-2}\×{100}^{0.94}$

${\mathrm{\σ}}_{pm}=\left(\frac{1.45\×{10}^{-3}}{1+\frac{D_x}{D_c}}\right)\×r_g^{0.65}\×h_c^{-2}\×P_m^{0.94}$

Calculate composite base load stress σ at critical load position_bps:

${\mathrm{\σ}}_{bps}=\left(\frac{1.41\×{10}^{-3}}{1+\frac{D_c}{D_x}}\right)\×r_g^{0.68}\×h_x^{-2}\×{100}^{0.94}$

(4) other calculate and design content

By elastic foundation doubling plate model, calculate the load fatigue stress of surface layer plate, solid axle and carry P_mThe peak load produced should Power, basic unit's load fatigue stress, and the maximum temperature stress of surface layer plate and temperature fatigue stress, interlayer contact during calculating Condition parameter r_βIt is calculated as follows:

$r_{\mathrm{\β}}={\[\frac{D_c\×D_x}{(D_c+D_x)\×k_n}\]}^{1/4}$

In formula: k_nFor vertical contact stiffness, when having bituminous concrete interlayer, value is 3000MPa/m, without bituminous concrete interlayer Time:

$k_n=\frac{1}{2}{(\frac{h_c}{E_c}+\frac{h_x}{E_x})}^{-1}$

Load fatigue stress according to surface layer plate, temperature fatigue stress, peak load stress, the calculating knot of maximum temperature stress Really, and the load fatigue stress of composite base, carry out structural limits state check, not produce limit fracture as checking computations Standard, determines whether the Laminate construction thickness of the composite base cement concrete pavement drafted meets requirement, as being unsatisfactory for requiring then Repeat said process, pass through until structural limits state is checked.