Numerical Analysis and Experimental Study of the Mechanical Response of Pavement Slab Supported on an Inhomogeneous Settlement

Abstract

The inhomogeneous settlement of subgrade seriously affects the safety of aircraft operation. To investigate the mechanical response of pavement slabs supported on an inhomogeneous settlement, a three-dimensional model of aircraft load–pavement structure–heterogeneous pavement was established; then, the inhomogeneous settlement conditions were simulated by setting a different reaction modulus between adjacent subgrades. Finally, both numerical simulation and experimental study methods were used to analyze the flexural tensile stress and vertical displacement of the pavement slab in inhomogeneous settlement conditions under the loading effects of typical aircrafts (A320 and B737-800). The results indicate that the strain of pavement slabs increases as the change rate of an inhomogeneous subgrade support increases. Increasing the thickness of the pavement slab and reducing the inhomogeneous subgrade support can effectively improve the mechanical performance of the pavement structure. For B737-800, with the change rate of the inhomogeneous subgrade support increasing from 0% to 85.71%, the amplitude of the flexural tensile stress of the pavement slab increased by 34%. The pavement slab with a thickness of 0.36 m experienced flexural–tensile failure. For pavement slabs with thicknesses of 0.38 m and 0.40 m, the maximum inhomogeneity of the subgrade roof support should not exceed 33% or 62%, respectively. Therefore, the effect of the horizontal inhomogeneous subgrade support caused by long-term environmental action should be considered when designing pavement slabs.

1. Introduction

Airport construction has developed rapidly in China in recent years, and rigid pavements are widely used in airfield pavements for their advantages regarding strength, stability, and durability. Airfield pavements of several kilometers in length frequently pass across different geological units, leading to complex features of airport subgrades. Due to the existence of different features between new and old subgrades, local subgrade instability caused by water seepage and inadequate compaction occur, which lead the runways to usually experience inhomogeneous settlement conditions during service periods. In this condition, aircraft loading generates a stress concentration phenomenon on the lower stiffness side of the pavement. Furthermore, frequent aircraft loading aggravates the fatigue damage of rigid pavements, which seriously affects the airworthiness of runways. Thus, studying the mechanical response of rigid pavements under inhomogeneous settlement conditions is necessary to ensure the safety of aircraft operation.

The inhomogeneous settlement of subgrade is widely studied in the field of highways. Research indicates that the force deformation characteristics of highway construction and expansion are different, and these differences are mainly manifested in the different consolidation degrees of the foundation under the new and old subgrade of highway reconstruction and expansion projects. This has caused the differential settlement of foundations, which is reflected in the top surface of the subgrade, and eventually causes the longitudinal cracking of the road surface [1,2,3,4]. Xiao used a centrifuge model test combined with a finite element method (FEM) to investigate the development law of transverse differential settlement between the modern tram pile-plank-supported subgrade and the surrounding pavement subgrade and suggested a critical transverse differential settlement rate according to the requirements of allowable tensile stress [5]. Yao studied the influence of stress on pavements based on granite residual soil subgrade, investigating the effects of stress-dependent water retention on settlements during rainfall and evaporation [6]. Zhao discussed ground settlement and pavement tensile stress under different tunnel depths and proposed displacement and stress control limitations to meet the structural stability requirements of the pavement [7]. Existing research on the settlement of transport infrastructure has tended to focus on railway, highway, pipeline, and tunnel engineering, while few studies have analyzed the inhomogeneous settlement of subgrade in runway engineering. In fact, runways have a larger aircraft load and cause greater disturbance to rigid pavements. Thus, the runways are different from railway, highway, pipeline, and tunnel engineering.

Due to the difficulty in obtaining an analytic solution for dynamic problems, standard and modified finite elements are widely used in this field [8,9,10]. Ning simulated the settlement of a soft soil foundation and the construction process using elastic–plastic finite element analysis software [11]. Zhao used the finite element method (FEM) to determine the surface settlement and deformation laws under different construction conditions, including the change law of longitudinal and lateral pavement settlement following the progress of excavation [12]. Dong studied the dynamic response of airport pavement with various temperature and aircraft loading conditions [13]. Compared with the numerical analysis method, the test study could obtain the stress performance of airport pavements under a complex environmental load action, which was an important method to study the performance of airport pavements. Fu and Liu investigated the influence of temperature, humidity, frost heave, and snow melting on the dynamic response of airport pavements and showed that the total frost-heaving quantity in the pavement shoulder area was greater than that of the pavement area [14,15]. Park studied the effects of temperature on the deflection and load transfer capacity of airport pavement; the analysis showed that variations in daily expansion and contraction strain cycles were more evident near the top surface of the pavement slab, where the ambient temperature affects it directly [16]. Wei used field tests to study differential settlements and pavement cracking along the joint between the new subgrade and the old embankment and proposed three indexes for new and old subgrades, which should be viewed as the basis for the design and construction of new subgrades and old embankments [17].

Due to the inhomogeneous compaction of subgrade filling and long-term environmental loading action, runways are usually under inhomogeneous settlement conditions during service periods. However, few studies focus on the inhomogeneous distributed subgrade effects on runways. To ensure the safety of aircraft operation, it is necessary to study the time-varying effect of inhomogeneous subgrade on the flexural tensile stress and thickness of concrete pavement slabs to provide a basis for airport long-life pavement structure design methods.

In this paper, a three-dimensional finite element analysis model of an aircraft load pavement with an inhomogeneous, horizontal subgrade structure is established. Considering factors such as aircraft wheel load type and rigid pavement thickness, the time-varying effect of an inhomogeneous subgrade support on the mechanical response of pavements under aircraft loads is analyzed. A scale model test of an airport pavement structure supported on an inhomogeneous subgrade is developed.

2. Numerical and Analysis Methods

2.1. Flexural Tensile Stress Calculation of Pavement Slab

The flexural tensile stress of the pavement slab is generated by the combined actions of the temperature and aircraft loads. When the flexural tensile stress of the pavement slab is less than the ultimate flexural tensile stress of the material, the pavement slab is safe. The formula for the flexural tensile strength of the pavement slab is shown in Equation (1):

$${\gamma }_r({\sigma }_{pr}+{\sigma }_{tqr})\le f_r$$

(1)

where ${\gamma }_r$ represents the reliability coefficient, which is taken as 1.20; ${\sigma }_{pr}$ represents the load fatigue stress; ${\sigma }_{tqr}$ represents the temperature fatigue stress; and $f_r$ represents the ultimate flexural tensile stress, which is taken as 5.0 MPa.

The inhomogeneous temperature distribution on the cross-section of the rigid pavement will lead to curling deformation of the pavement. To calculate the temperature fatigue stress of the rigid pavement, it is necessary to determine the natural division of the airport area and correct the temperature gradient for different plate thicknesses. In this paper, the temperature gradients are corrected based on the natural division II of highways, shown as

Table 1. Temperature gradients corresponding to different plate thicknesses.

Slab Thickness/m	Maximum Temperature Gradient/(°C/m)
0.36	58.96
0.38	55.44
0.40	51.92

.

2.2. Model Parameters of the Pavement and Foundation

Figure 1 demonstrates the three-dimensional model of an aircraft load pavement structure paved on inhomogeneous subgrade support, and the Winkler pavement base model is used for subgrade simulation. Each node has the same degree of freedom along the X and Y directions (X represents the direction of travel, Y represents the direction of width, and Z represents the direction of depth). In addition, only the horizontal direction was set with constraints in this paper.

The plane size of the concrete pavement slab is set as 5 m × 5 m, and the plane size of the subgrade, cushion and pavement base are set as 10 m × 10 m. The pavement structure is considered an elastic material. To simulate the time-varying effect of the inhomogeneous horizontal distribution of the subgrade, the reaction moduli of the subgrade are set as 10 MPa, 20 MPa, 40 MPa, 60 MPa and 70 MPa, respectively, and corresponding parameters are listed in

Table 2. Material properties of pavement structures.

Pavement Layer	Elasticity Modulus (MPa)	Poisson Ratio	Density (kg∙m−3)	Thickness (m)	Resilience Modulus (MPa)	Reaction Modulus (107 MPa)
cement concrete pavement layer	36,000	0.15	2400	0.36, 0.38, 0.40	/	/
cement stabilized macadam base	/	0.25	/	0.2	1500	/
natural sand cushion	/	0.3	/	0.3	200
subgrade	/	/	/	/	/	10, 20, 40, 60, 70

.

2.3. Type and Position of Aircraft Wheel Load

Table 3. Wheel load parameters of different aircraft types.

Aircraft Model	B737-800		A320
Weight (kN)	792.60		774.00
Partition coefficient of landing gear	0.95		0.95
Distance of landing gear (m)	5.72		7.60
Number of landing gear wheel	2		4
Number of landing gear	2		2
Spacing of landing gear wheel (m)	St	0.86	0.78
	SL1	/	1.01
	SL2	/	/
Tire pressure (MPa)	1.47		1.14

presents the parameters of wheel load for A320 and B737-800. The size and value of the aircraft’s wheel loads are also listed in

Table 4. Load size and value of aircraft wheels.

Aircraft Model	Tire Pressure (MPa)	Wheel Print Area (m2)	Wheel Print Length (m)
A320	1.14	0.16	0.4
B737-800	1.47	0.13	0.36

. According to the Specifications for Airport Cement Concrete Pavement Design (MH/T5004-2010), the most disadvantageous position for a B737-800 airplane is the middle edge of the slab joint, and thus this position is taken into account for analyzing the mechanical response of the rigid pavements.

2.4. Inhomogeneous Distribution of Horizontal Subgrade

To simulate the spatial effects of the horizontal distribution of the inhomogeneous subgrade, the factors of the distribution range and reaction modulus of the inhomogeneous subgrade are considered in this paper. The pavement structure model is divided into 2 × 2 areas, as shown in Figure 2, A, B, C and D, which represent the different subgrades with various reaction moduli. In this model, Y1 and Y2 represent the sizes of different subgrades along the vertical direction, and X1 and X2 represent the sizes of different subgrades along the horizontal direction.

Table 5. Horizontal distribution of the pavement subgrade.

Condition		Y1:Y2	X1:X2	Reaction Modulus of Subgrade (MPa)
1	I	1:4	1:4	A = D = 70, B = C = 10~70
	II	1:4	1:4	A = D = 10~70, B = C = 70
2	I	2:3	2:3	A = D = 70, B = C = 10~70
	II	2:3	2:3	A = D = 10~70, B = C = 70
3	I	2:3	1:4	A = D = 70, B = C = 10~70
	II	2:3	1:4	A = D = 10~70, B = C = 70

presents the reaction modulus of the inhomogeneous subgrade based on various conditions.

The change rate of inhomogeneous subgrade support β is introduced to represent the level of the horizontal inhomogeneous distribution in the pavement subgrade:

$$\beta =\frac{{\mathrm{E}}_{max}-{\mathrm{E}}_{min}}{{\mathrm{E}}_{max}}$$

(2)

where β represents the change rate of inhomogeneous subgrade support, β = 0 represents the uniform subgrade, E_max represents the maximum value of the reaction modulus in the inhomogeneous subgrade, and E_min represents the minimum value of the reaction modulus in the inhomogeneous subgrade. The thicknesses of the pavement slab are considered as 0.36 m, 0.38 m and 0.40 m, respectively.

3. Effect of Inhomogeneous Subgrade Support

3.1. Flexural Tensile Stress of Pavement Slab

The relationship between the maximum flexural tensile stress of the pavement slab and the change rate of inhomogeneous subgrade support for different aircraft type are presented in Figure 3 and Figure 4, respectively. The highest flexural tensile stress is taken as the flexural tensile stress of each condition in Group I and Group II.

Figure 3 shows that the flexural tensile stress of the pavement slab increases with the change rate of inhomogeneous subgrade support. For instance, when the thickness of the pavement slab is 0.36 m and β is 85.7%, the flexural tensile stress of the pavement slab reaches 6.93 MPa, which has increased 34.9% for the condition of β, which is 14.29% (1.51 MPa).

Although increasing the thickness of the pavement could alleviate the effects of inhomogeneous settlement, the thicker pavement also requires more financial investment, and it may also cause some other problems. Thus, quantifying the influence of thickness change on the mechanical response benefit to design the airport rigid pavements. To satisfy the flexural stress of the pavement slab for the ultimate flexural stress condition, β should not exceed 38% (0.36 m) and 70% (0.40 m), respectively. On the basis of these findings, we conclude that the inhomogeneous settlement affects the flexural tensile stress of rigid pavements significantly. Therefore, for the A320, the value of β should not exceed 38% (0.36 m), 57.5% (0.38 m) and 70% (0.40 m), respectively.

On the other hand, the wheel load type also affects the mechanical response of the pavement structure. For example, to ensure the safety under the ultimate flexural tensile stress condition, the value of β should be less than 57.5% (A320) and 33% (B737-800) when the thickness of the pavement slab is 0.38 m. In Figure 4c, when the thickness of the pavement slab is 0.38 m and 0.40 m, the values of β should not exceed 33% and 62%, indicating that the allowable change rate of the inhomogeneous subgrade support increases with the thickness of the pavement slab. The findings lead us to conclude that the effect of inhomogeneous subgrade support on the mechanical response of pavement structures should not be ignored in the design process of pavement structures.

3.2. Vertical Displacement of Pavement Slab

The interaction between the vertical displacement of the pavement slab and the inhomogeneous subgrade support under loads of different aircrafts are presented in Figure 5 and Figure 6, respectively.

Figure 5 and Figure 6 show that the vertical displacement of the pavement slab increases with inhomogeneous subgrade support. As seen in Figure 5a, when the thickness of the pavement slab is 0.36 m, the vertical displacement of the rigid pavement slab reaches 0.752 mm (β = 14.29%) and 1.26 mm (β = 71.43%), respectively. Increasing the thickness of the pavement slab can efficiently reduce the vertical displacement of the pavement slab. For A320 aircraft with the constant value (β = 14.29%), the vertical displacement of the rigid pavement slab increases from 0.752 mm to 0.706 mm with the thicker of the pavement slabs (from 0.36 m to 0.40 m).

3.3. Stiffness Degradation of Pavement Slab

The damage plastic constitutive model is used to simulate the nonlinear behavior of pavement concrete, further analyzing the effect of inhomogeneous subgrade support on the stiffness degradation of rigid pavement slabs.

The characteristics of the damage factor under the wheel load of the A320 aircraft are shown in Figure 7. It can be seen that the stiffness degradation of the pavement slab becomes more severe with the increasing extent of the inhomogeneous subgrade support. Under the condition of uniform subgrade support (β = 0%), the tensile and compressive damage factors of rigid pavement (with the thickness is 0.36 m) are 3.796 × 10⁻² and 8.729 × 10⁻⁴. With the increase in the inhomogeneous support degree (β = 71.43%), the tensile and compressive damage factors reach 5.197 × 10⁻² and 1.326 × 10⁻³, which have improved 36.90% and 51.91%, respectively.

Figure 8 illustrates the tensile and compressive damage distributions of various aircraft loads with a constant condition (thickness of 0.36m and condition 1). It can be seen that the stiffness degradation of the pavement slab is located at the bottom of the rigid pavement slab under the load of the A320 aircraft. While for the B737-800 aircraft, the stiffness degradation caused by the tension of the pavement is mainly located on the bottom of the slab, and the stiffness degradation caused by the compression mainly locate on the top of the slab. In addition, the degradation of pavement stiffness caused by tension is significantly larger than that caused by compression.

4. Pavement Scale Model Test

4.1. Stiffness Degradation of Pavement Slab

A laboratory scaled model test is carried out to investigate the effect of inhomogeneous horizontal subgrade support on the mechanical response of the pavement structure. According to the similarity principle, a reduced scale of 1:5 was selected. The plane size of the test panel is set as 1 m × 1 m, and the thicknesses of the panel are 0.07 m and 0.08 m, respectively.

Rubber plates and silica gel plates are used to simulate the inhomogeneous subgrade support of the pavement, see Figure 9. The reaction modulus is measured by a bearing plate method under four common conditions, including: four silica gel plates (10 cm thick); one rubber plate (5 cm thick) and three silica gel plates (5 cm thick); two rubber plates (5 cm thick) and two silica gel plates (5 cm thick); and three rubber plates (5 cm thick) and one silica gel plate (5 cm thick). The positions of the strain gauges are shown in Figure 10. The reaction moduli of the four conditions are 42.08 MPa, 50.29 MPa, 60.16 MPa and 70.13 MPa (more details in

Table 6. Horizontal distribution of the pavement subgrade.

Condition of Test	Reaction Modulus of Subgrade	Distribution Range of Subgrade
1	I: A/D zone: 70.13 Mpa, B/C zone: 42.08 MPa	X1:X2 = 2:3, Y1:Y2 = 2:3; X1:X2 = 2:3 Y1:Y2 = 1:4;
	II: A/D zone: 42.08 MPa, B/C zone: 70.13 MPa
2	I: A/D zone: 70.13 MPa, B/C zone: 50.29 MPa
	II: A/D zone: 50.29 MPa, B/C zone: 70.13 MPa
3	I: A/D zone: 70.13 MPa, B/C zone: 60.16 MPa
	II: A/D zone: 60.16 MPa, B/C zone: 70.13 MPa
4	A/B/C/D zone: 70.13 MPa	Uniform subgrade

), respectively, and the measurement test of the reaction modulus of the pavement’s foundation is shown in Figure 11. A loading platform is assigned to simulate the effect of aircraft load on the rigid pavement, which weigh 120 kg, see Figure 12.

4.2. Analysis Results of the Model Test

To analyze the time-varying effect of inhomogeneous subgrade support, the strain of the pavement slab is studied with different pavement slab thicknesses (0.07 m and 0.08 m).

(1)

Effect of β on the pavement slab strain

Figure 13 and Figure 14 show that the variation of strain is inhomogeneous with various support conditions. As shown in Figure 13a, the strain at point 1 reaches 47 με and 57 με when β is 0% and 39%, indicating that reducing the inhomogeneous subgrade support can effectively control the strain of the pavement slab. It can also be found that the strain values of No. 1, No. 3, No. 2 and No. 4 gradually decrease, which indicates that the strain of the pavement slab approaches the maximum value at the load position.

(2)

Effect of slab thickness on strain

Figure 15 and Figure 16 show the relationship between the strain gauge number and strain. In Figure 15c, the strain of the pavement slab reaches 53.81 με and 49.34 με with different slab thicknesses (0.07 m and 0.08 m), and the amplitude of the strain is reduced by 8.31%. The results suggest that increasing the thickness of the rigid pavement can significantly reduce the strain of the pavement slab.

5. Conclusions

To investigate the mechanical response of pavement slabs supported on an inhomogeneous settlement, this work sets four different foundation reaction moduli to simulate this circumstance. The conclusion quantifies the influence of reaction modulus variation along the horizontal direction of the pavement panel, and the control standard of the reaction modulus under various pavement slab types is also proposed, drawn as follows:

(1)

When inhomogeneous subgrade support is used instead of uniform subgrade support, the flexural tensile stress and vertical displacement of the pavement structure increase. For B737-800 aircraft, when the slab thickness is 0.38 m and the change rate of inhomogeneous subgrade support increases from 0% to 85.71%, the flexural tensile stress of the pavement slab increases by 1.60 MPa, and the flexural tensile stress can increase as much as 34%.

(2)

The flexural tensile stress of the pavement slab increases with inhomogeneous subgrade support. For A320 aircraft, when the thickness of the pavement is 0.36 m and the change rate of inhomogeneous subgrade support increases from 14.29% to 85.7%, the flexural tensile stress of the pavement increases from 4.51 MPa to 6.93 MPa, and the flexural tensile stress of the pavement is increased by 34.9%.

(3)

By increasing the thickness of the pavement slab, the range of the change rate of inhomogeneous subgrade support can be effectively improved. For A320 aircraft, as the thickness of the pavement slab increases from 0.36 m to 0.4 m, the inhomogeneous degree limit of the top support can be increased from 38% to 70%.

(4)

To ensure the safety of the pavement slab structure, when the thickness of the pavement slab under the action of the A320 aircraft is 0.36 m, 0.38 m, or 0.40 m, inhomogeneous subgrade support should not exceed 38%, 57.5%, or 70%, respectively. When the thickness of the pavement slab is 0.36 m under the action of the B737-800 aircraft, the flexural tensile stress of the pavement exceeds the ultimate flexural tensile stress of the material; when the thickness of the pavement is 0.38 m or 0.40 m, the inhomogeneous subgrade support should not exceed 33% or 62%, respectively.

(5)

The strain generated by the pavement slab increases when inhomogeneous subgrade support is considered by the model test. Increasing the thickness of the rigid pavement slab and reducing the inhomogeneous subgrade support can effectively reduce the strain generated by the stress of the rigid pavement.