The failure of debris dams impacted by the massive stones in a debris flow represents a difficult design problem. Reasonable materials selection and structural design can effectively improve the resistance impact performance of debris dams. Based on the cushioning properties of expanded polystyrene (EPS) concrete, EPS concrete as a buffer layer poured on the surface of a rigid debris dam was proposed. A three-dimensional numerical calculation model of an EPS concrete buffer layer/rigid debris dam was established. The single-factor theory revealed change rules for the thickness of the buffer layer concerning the maximal impact force of the rigid debris dam surface through numerical simulation. Moreover, the impact force-time/history curves under different calculation conditions for the rigid debris dam surface were compared. Simulation results showed that the EPS concrete buffer layer can not only effectively extend the impact time of massive stones affecting the debris dam but also reduce the impact force of the rigid debris dam caused by massive stones in the debris flow. The research results provide theoretical guidance for transferring the energy of the massive stone impact, creating a structural design and optimizing debris dams.
Because of their detrimental consequences—for example, injuries and economic losses related to damage to buildings, industrial facilities, and infrastructure—debris flows are among the most dangerous natural phenomena. There are many types of debris flow-control engineering, such as debris dams (check dams), grille dams, drainage canals, and stop-and-deposit fields. The debris dam is one of the most effective methods to control debris flow. A debris dam can effectively intercept solid particles in the debris flow and reduce its destructive power in downstream areas. Existing debris dams are mainly built of concrete or grouted rubble, which can not only block coarse particles but also drain away fine particles and slurry; however, a rigid debris dam is vulnerable to being washed away by the force of a debris flow’s impact, especially when that force is caused by massive stones in the debris flow. Large-scale debris flow in the mountainous part of Sichuan and southern Gansu is very common because of the area’s extreme weather and the May 12 Wenchuan earthquake. Large-scale debris flow usually includes massive stones. In the Wenjiagou “8.13” catastrophic debris flow [
Many scholars have researched new materials and structures to resolve the abovementioned issues. Wang and Zheng have designed a new support with a spring, which has been used in a new debris-flow dam. Their results show the impact-resisting effect of the new support [
That notwithstanding, new debris-flow dams with spring support and debris-flow elastic-steel-cable obstructions have disadvantages: they consume a large amount of steel, require complex structures, and have poor practicability. Although flexible gabion-arch dams have the advantage of comprising simple structures, they cannot be used to control and prevent large-scale debris flow; moreover, they have a short working life. It is practical to use the elasticity and toughness of waste tires to relieve the impact force of rolling stones, but forming a complete whole between waste tires and the structure surface remains a difficult problem. Because of the use of low-intensity EPS material, the buffering effect is poor when using separate EPS interlayers. To further improve the impact resistance of the structures, some academics have not only performed numerical simulation and experimental research on foam concrete as a protective energy-absorption cushion but also provided empirical formulas [
Massive stones in a debris flow have a high impact force. The failure of debris dams impacted by massive stones in a debris flow poses a difficult design problem. Reasonable materials selection and structural design can effectively improve the resistance-impact performance of debris dams. EPS concrete has an obvious yield platform when impacting. The strain increases, whereas stress remains unchanged, thus indicating both that EPS concrete has good impacting-compression ability and that EPS particles have high energy-absorption characteristics [
Stress-strain curve of concrete and EPS concrete [
Diagrammatic cross section of an EPS concrete buffer layer/rigid debris dam.
In Figure
Massive stones impact the debris dam with kinetic energy, which comprises all of the impact energy. The impact energies of the massive stones are obtained using the theorem of kinetic energy. The mathematical expression is
A debris dam is primarily constructed from C15 concrete, and the numerical calculation does not consider hierarchical placement, so the effect of reinforcement on concrete strength is ignored. The upper part of the debris dam section is 2.5 m, the underside is 8.5 m, the effective height of the debris dam is 10 m, and the length of the dam is 20 m. The front of the debris dam slope is 1 : 0.5, and the back-side slope is vertical. The length of the top edge of the overflow mouth is 10 m, whereas the length of the bottom edge is 9 m, and the height of the overflow mouth is 2 m. The massive stone is simplified as a sphere, and the diameter is 2 m. A buffer layer of EPS concrete is poured to a particular thickness on the upstream face of the rigid debris dam. The three-dimensional geometry model of the EPS concrete buffer layer/rigid debris dam and the stones are shown in Figure
A sketch of the three-dimensional geometry model of the debris dam and boundary condition.
Grid quality directly affects the results of the finite element analysis. The primary analysis involves the changed regulation of the impact stress and impact force of the debris-dam contact surface, thus refining the grid in the vicinity of the contact surface and increasing the grid far from the contact surface to meet the requirements of numerical-simulation accuracy and speed [
Meshing the debris dam and massive stones.
The massive stones act as a concentrated force on the debris dam; moreover, the massive stone itself has a very irregular shape. For the sake of convenience, each massive stone is simplified as a sphere, according to the principle of keeping the stone volume unchanged [
Without considering the plastic deformation of massive stones, the elastic model is used to describe the stone’s constitutive relation. Consider the plastic deformation of the EPS concrete buffer layer and concrete. The crushable foam model and concrete elastoplastic damage model are used to express the constitutive relation of the EPS concrete buffer layer and the concrete, respectively. Using concrete with 40% EPS and referring to the literature [
Mathematical and mechanical parameters of the material [
Materials | Density |
Elastic modulus |
Poisson ratio |
Dilatancy (°) | Eccentricity | Biaxial limit compressive strength/uniaxial limit compressive strength |
Constant stress ratio |
Viscosity parameter |
---|---|---|---|---|---|---|---|---|
Massive stone | 2,650 | 40 | 0.25 | — | — | — | — | — |
Concrete | 2,400 | 26.48 | 0.2 | 30 | 0.1 | 1.16 | 0.6667 | 0.0005 |
EPS concrete | 890 |
|
0.17 | — | — | — | — | — |
The elastic model includes the following three groups of equations [
The concrete damage model is used as the concrete strength criterion. The isotropic elastic damage and the isotropic tensile and compressive plasticity theories are used to characterize the inelastic behavior of concrete, and the nonassociated multiple sclerosis plasticity and isotropic elastic damage theories are introduced to describe the irreversible damage-generating material-fracture process [
Plastic flow depends on the flow potential function
The crushable foam model with isotropic hardening uses a yield surface that is an ellipse centered at the origin of the
The yield surface represents the Mises circle in the deviatoric stress plane. The shape factor,
The plastic Poisson ratio, which is the ratio of the transverse to the longitudinal plastic strain under uniaxial compression, must be in the range of –1 and 0.5, and the upper limit (
Plastic flow is associated when the value of
Alternatively, if only the shape of the yield surface is known and you choose to use associated plastic flow, the plastic Poisson ratio can be obtained from
The front, the black, and the upper surfaces of the debris dam are free, the bottom of the debris dam is fixed, and the
For convenience, the massive-stone volume is taken as constant and the stone’s impact velocity is changed to obtain different impact energies. The analysis cases are shown in Table
Analysis cases.
Keep |
Keep |
Change the |
---|---|---|
|
|
|
The dynamic response of the rigid debris dam to either the same or different thickness EPS concrete buffer layers under the same or different impact velocities is analyzed according to the simulation results, and the recommended formula for the optimum thickness of the buffer layer is given.
To compare how different thicknesses of EPS concrete buffer layers affect the normal contact stress and normal contact force of the rigid debris-dam contact surface, the normal contact-stress nephogram and normal contact-force nephogram of the rigid debris-dam contact surface are given when the impact velocity is equal to 4 m/s and the thickness of the EPS concrete buffer layer is equal to 0 m, 0.4 m, or 0.8 m. In addition, this paper analyzes the normal contact-stress nephogram and normal contact-force nephogram of the rigid debris-dam contact surface when the thickness of the EPS concrete buffer layer is equal to 0.6 m and the impact velocity is equal to 4 m/s. The normal contact-stress nephogram and normal contact-force nephogram of the rigid debris-dam contact surface are shown in Figures
Normal contact-stress nephogram when the impact velocity is equal to 4 m/s and the thickness of the EPS concrete buffer layer is equal to 0, 0.4, or 0.8 m (unit: Pa).
Figures
Normal contact-stress nephogram when the thickness of the EPS concrete buffer layer is equal to 0.6 m and the impact velocity is equal to 4 m/s (unit: Pa).
Normal contact-force nephogram when the impact velocity is equal to 4 m/s and the thickness of the EPS concrete buffer layer is equal to 0 m, 0.4 m, or 0.8 m (unit: Pa).
Normal contact-force nephogram when the thickness of the EPS concrete buffer layer is equal to 0.6 m and the impact velocity is equal to 4 m/s (unit: Pa).
The time-history curve of the normal contact force on the debris-dam contact surface and contact stress on the node with the maximum contact stress are given in Figures
The time-history curve of the normal contact force when the impact velocity is equal to 4 m/s and the thickness of the EPS concrete buffer layer is equal to 0 m, 0.2 m, or 0.4 m.
The time-history curve of the contact stress on the node with the maximum contact stress when the impact velocity is equal to 4 m/s and the thickness of the EPS concrete buffer layer is equal to 0 m, 0.2 m, or 0.4 m.
Figures
The changes of the maximum normal contact force and stress on the rigid debris-dam node with different impact velocities under different thicknesses of buffer layers are shown in Figures
The changes of the maximum normal contact force on the rigid debris-dam node with different impact velocities under different thicknesses of buffer layers.
The changes of the maximum normal contact stress on the rigid debris-dam node with different impact velocities under different thicknesses of buffer layers.
Figures
To express the effect of the EPS concrete buffer layer thickness for the contact force to the rigid debris-dam node more clearly, the contact force for the rigid debris-dam node with no buffer layer is subtracted from the contact force for the rigid debris-dam node with different thicknesses of EPS concrete buffer layers.
The relation curves between
The relation curve between the reduction of the maximum contact force (
The relation curve between the reduction of the maximum contact stress (
Figures
To further evaluate the effect of buffer layer thickness on the cushioning properties of the rigid debris dam under different impact velocities of massive stones, the relation curve between the thickness of the EPS concrete buffer layer and the equivalent plastic deformation of the rigid debris dam is shown in Figure
The relation curve between the thickness of the EPS concrete buffer layer and the equivalent plastic deformation of the rigid debris dam.
From Figure
In the EPS concrete buffer layer’s allowable working range, the thickness of the buffer layer has little influence on the cushioning performance; however, beyond the allowable range, the buffer performance increases as the thickness of the buffer layer increases. In the debris-dam protection project, the thickness of the EPS concrete cannot be too great. To make the EPS concrete buffer layer act as a better cushion and to maximize its performance to meet the needs of the project and to maintain rigid debris dams with no equivalent plastic deformation, the recommended formula between the optimum thickness of the buffer layer and the impact velocity of a massive stone is given as follows:
The relation between the impact energy and impact velocity of the massive stone is given in formula (
Based on the cushioning properties of EPS concrete, EPS concrete as a buffer layer poured on the surface of a rigid debris dam is proposed. A three-dimensional numerical calculation model of an EPS concrete buffer layer/rigid debris dam is established. According to the theory of a single factor, numerical simulation reveals that, with respect to the maximum impact force of the surface of a rigid debris dam, the rules change with the thickness of the buffer layer. The simulation results show the following: The EPS concrete buffer layer can effectively extend the impact time of a massive stone and reduce the impact force of the debris flow on the rigid debris dam due to the stone. In the EPS concrete buffer layer allowable working range, the thickness of the buffer layer has little influence on the cushioning performance; however, beyond the allowable range, the buffer performance increases as the thickness of the buffer layer increases. According to the results of the numerical simulation, the recommended formula for the optimum thickness of the buffer layer is obtained.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This paper is financially supported by Focus Deploying Projects of Chinese Academy of Sciences (Grant no. KZZD-EW-05-01-04) and National Key Technology R&D Program of the Ministry of Science and Technology (2014BAL05B01).