CN112924305B - Method for acquiring dynamic response data of passive pile plate stone blocking wall in collapse and rockfall geological disasters - Google Patents

Method for acquiring dynamic response data of passive pile plate stone blocking wall in collapse and rockfall geological disasters Download PDF

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CN112924305B
CN112924305B CN202110113831.XA CN202110113831A CN112924305B CN 112924305 B CN112924305 B CN 112924305B CN 202110113831 A CN202110113831 A CN 202110113831A CN 112924305 B CN112924305 B CN 112924305B
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刘红岩
薛雷
秦四清
祝凤金
赵雨霞
葛紫微
刘康琦
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China University of Geosciences Beijing
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    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
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    • G01N3/303—Investigating strength properties of solid materials by application of mechanical stress by applying a single impulsive force, e.g. by falling weight generated only by free-falling weight
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    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
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Abstract

The invention discloses a method for acquiring dynamic response data of a passive pile plate stone blocking wall in a collapse and rockfall geological disaster, which divides an impact force-deformation relation curve of a reinforced concrete pile plate wall under rockfall impact into 3 stages: stage I: in the elastic loading stage at the initial stage of collision, the contact force between the falling rocks and the reinforced concrete pile plate wall is determined as elastic contact; and stage II: in the plastic damage loading stage of the concrete pile plate wall, when the contact impact force exceeds the yield strength of the wall body, the concrete pile plate wall is subjected to plastic deformation and damaged; stage III: and in the unloading stage, when the reinforced concrete pile plate wall reaches the maximum compression deformation, the falling rock impact speed is reduced to 0, and the elastic deformation accumulated by the wall body can be rebounded and released. Geological practice examples show that the dynamic mechanical behavior of the reinforced concrete pile plate wall under rockfall impact can be well described, high-value reference can be provided for engineering design, and the method has a very good application prospect.

Description

Method for acquiring dynamic response data of passive pile plate stone blocking wall in collapse and rockfall geological disasters
Technical Field
The invention relates to the technical field of geological engineering, in particular to a method for acquiring dynamic response data of a passive pile plate stone blocking wall in a collapse and rockfall geological disaster.
Background
In recent years, geological disasters in western China and mountainous areas worldwide are frequent, wherein the percentage of collapse and rockfall disasters in all the geological disasters is up to 17%, and the disaster becomes the second largest slope geological disaster after landslide. The system has the characteristics of sudden occurrence, poor predictability, high speed, high energy, wide damage range, complex movement route, difficult monitoring and early warning and the like, thereby causing serious threat to infrastructure such as roads, railways and the like and arousing high attention of people. Aiming at the phenomena of collapse and rock fall of high-level dangerous rocks induced by strong earthquakes in recent years, a novel passive stone blocking scheme, namely a pile plate stone blocking wall, is a compound structure formed by adding a buffer layer on the basis of an anti-slide pile plate structure, has the advantages of small occupied area, good blocking performance, easiness in construction and the like, has outstanding advantages for protecting the rock fall with high impact energy, and achieves a primary good effect in practical application.
However, the stone blocking structure has relatively short appearance time, so that research on the stone blocking structure is relatively less, but other similar wall protection structures have some related research, and therefore, the current situation of the similar related research is reviewed here to inspire the research. In summary, the current research mainly focuses on 3 aspects of experimental research, theoretical research, numerical simulation, and the like. Firstly, in the aspect of experimental research, a rockfall impact test of the reinforced protective retaining wall is firstly carried out by Hearn and the like, and the result shows that the reinforced protective retaining wall can effectively intercept rockfall, but the impact kinetic energy of rockfall during the test reaches 1410kJ, so that the front surface of the retaining wall has the convex deformation of about 0.3-0.8 m. The field test research on the impact resistance of a large-proportion reinforced earth stone blocking wall structure model is also carried out by Peila and the like, the adopted falling rocks are concrete blocks with the weight of 9000kg, the wall body is impacted at the speed of 30m/s, and the test result shows that the falling rocks impact to cause certain deformation of the wall body, but the falling rocks impact to a protective structure is still an effective falling rocks impact protective structure. Arnold et al first proposed a deflection analytic solution model of the cantilever-type reinforced concrete retaining wall under falling rock impact based on a displacement model, and then tested the dynamic response of the reinforced concrete retaining wall by adopting a large-scale pebble impact model test, thereby verifying the rationality of the model. Secondly, in the aspect of theoretical research, the calculation of the impact force of the falling rocks on the reinforced concrete structure is mainly based on the Hertz contact theory, but the theory is based on elastic mechanics, the reinforced concrete structure usually has plastic characteristics under the impact of the falling rocks, and therefore the Hertz contact theory is subjected to elastic-plastic correction according to the fact that the structure is an ideal elastic-plastic body, and a formula for calculating the impact force of the debris flow boulder considering the elastic-plastic deformation of the material is further provided. The Chengqi and the like are based on a Hertz elastic collision theory and a Thornton elastic-plastic hypothesis, an impact force correction equation of the falling rocks to the structure is established by considering the material characteristics of the structure, the relative size of an impact object, the structural deflection and other factors, and the impact force correction equation is applied to the impact calculation of the anchor cable slide-resistant pile. Because the impact of the falling rocks on the reinforced concrete structure is not only related to the falling rocks characteristic, but also related to the mechanical property of the reinforced concrete structure, many researchers comprehensively consider the Hertz contact theory and the mechanical property of the reinforced concrete structure, and provide a dynamic response calculation method for the reinforced concrete structure under the impact of the falling rocks, for example, an Olsson establishes a dynamic response calculation model for the anisotropic composite board under the impact of small mass based on the Hertz contact theory and the impact indentation theory of the anisotropic composite board. Considering the plastic deformation and the damage effect of the layered composite plate under the impact action, the Zheng et al establishes a corresponding impact force calculation formula based on the Hertz contact theory and the permanent indentation theory of the plate under the impact action. On the basis of the characteristics, the elastic-plastic dynamic response of the reinforced concrete slab under the impact of falling rocks is researched. Finally, in the aspect of numerical simulation, dynamic response of the pile plate stone blocking wall under falling stone impact is simulated by moustache and the like by adopting ABAQUS software, and the whole dynamic process in the falling stone impact process is obtained through simulation, namely, an elastic pressing-in stage, a plastic pressing-in stage and an unloading rebounding stage after the pressing-in reaches the maximum value are carried out, and the whole dynamic process is completely consistent with the analysis result of an elastic-plastic theory. Yan et al simulated and studied the dynamic response of the reinforced concrete slab under the impact of the oval falling rocks by using ANSYS/LS-DYNA software, and it is considered that the falling rocks shape and the impact angle influence the impact force and the dynamic response of the reinforced concrete slab. The dane source and the like simulate and research the energy consumption performance of the waste tire under the impact of falling rocks by adopting ANSYS/LS-DYNA software, and the waste tire is considered to have obvious energy absorption effect, so that the impact effect of the falling rocks on the rigid stone blocking wall can be effectively relieved, and the protection capability of the rigid stone blocking wall is further improved.
However, although many scholars have conducted intensive studies on this problem, there are two major problems: (1) because the dynamic response of the reinforced concrete pile plate wall under the rockfall impact is an obvious dynamic process, the dynamic response of the reinforced concrete pile plate wall can be divided into 3 stages: the elastic compression stage at the initial stage of collision, the plastic deformation stage after the wall stress reaches the ultimate yield strength, and the elastic rebound stage after the wall reaches the maximum compression deformation.Although the studies of Zheng, wang dongpo and the like were also conducted according to the above 3 stages, they all considered that the modulus of elasticity of the reinforced concrete sheet wall was constant in the second stage, i.e., the plastic deformation stage, which is obviously not practical. Because the elastic modulus of the reinforced concrete pile wall is continuously reduced along with the increase of the plastic deformation in the plastic deformation stage, the elastic constant of the material is necessarily gradually reduced along with the increase of the plastic deformation because the plastic deformation process of the material, namely the damage process, is carried out. (2) The previous researches mostly provide the change curve of the impact force on the reinforced concrete pile plate wall along with the time[5，10-13]And a relation curve of impact force along with the deformation of the wall body is not given, so that the permanent deformation of the wall body under the impact of falling rocks cannot be obtained, and the later evaluation on the safety of the pile-plate wall is not facilitated.
Disclosure of Invention
The invention aims to provide a method for acquiring dynamic response data of a passive pile plate stone blocking wall in a collapse rockfall geological disaster.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows.
The method for acquiring dynamic response data of the passive pile plate stone blocking wall in the collapse rockfall geological disaster comprises the following steps:
A. obtaining the relationship between the contact pressure, the maximum contact pressure stress and the contact deformation:
first, the contact compressive stress distribution was confirmed to be:
Figure BDA0002919869980000021
in the formula: p (r) is contact compressive stress, P is contact pressure, a is contact radius; maximum contact compressive stress pmaxAt r-0:
Figure BDA0002919869980000022
the contact deformation consists of two parts:
δ＝δ1+δ2 (3)
in the formula: delta1、δ2The deformation amounts of 2 contact bodies are respectively;
the contact deformation and the contact area have the following relationship:
a2＝Rδ (4)
in the formula: r is the equivalent radius of the glass fiber,
Figure BDA0002919869980000031
R1、R2is the radius of 2 spheres;
contact pressure P, maximum contact pressure stress PmaxThe relationship to contact deformation δ is:
Figure BDA0002919869980000032
in the formula: e is the equivalent modulus of elasticity,
Figure BDA0002919869980000033
E1、μ1、E2、μ2the elastic modulus and poisson ratio of the two contact bodies are shown;
further, constructing a corresponding impact damage theoretical model according to the load-deformation response characteristic of the spherical particles under the impact load:
Figure BDA0002919869980000034
in the formula: d is the diameter of the spherical particles,
Figure BDA0002919869980000035
in order to be of an effective rigidity,
Figure BDA0002919869980000036
in the formula: d is the impact damage of the spherical particles, and K is the initial stiffness;
the impact damage variable D is defined as:
Figure BDA0002919869980000037
in the formula: deltacThe amount of compression deformation of spherical particles at the time of impact failure is set to δ ═ δcThe damage D ═ 1; gamma is the impact damage index;
further, the damage variable D of the particles is defined as:
Figure BDA0002919869980000038
wherein:
Figure BDA0002919869980000039
e is the effective and initial elastic modulus of the particles, respectively; deltay、δm、δcThe contact deformation amount corresponding to the initial yield of the particles, the maximum contact deformation amount in the particle collision process and the deformation amount corresponding to the complete breakage of the particles, namely D is 1, and delta is satisfied among the threey<δm≦δc(ii) a The relationship between contact pressure, maximum contact compressive stress and contact deformation taking into account material damage can thus be found to be:
Figure BDA00029198699800000310
B. acquiring the impact force of falling rocks on the reinforced concrete pile plate wall:
rockfall is determined as velocity v0The mass point of motion, reinforced concrete sheet pile wall are static plane, decompose impact velocity along level and vertical direction:
vx＝v0 sinθ，vy＝v0cosθ (11)
in the formula: v. of0、vx、vyRespectively is falling rockInstantaneous total impact speed, horizontal impact speed and vertical impact speed when contacting the reinforced concrete pile plate wall; theta is an impact angle;
what causes the impact damage to reinforced concrete sheet pile wall is horizontal impact, only considers the horizontal impact effect of falling stone, has:
Figure BDA0002919869980000041
in the formula: m is1、m2The quality of the reinforced concrete pile plate wall and the falling rock are respectively measured; v. of1The moving speed of the reinforced concrete pile plate wall is obtained; p is the impact force of falling rocks to the reinforced concrete pile plate wall; the following can be obtained:
Figure BDA0002919869980000042
Figure BDA0002919869980000043
in the formula: m is the equivalent mass of the compound,
Figure BDA0002919869980000044
integrating δ:
Figure BDA0002919869980000045
at the time of the maximum amount of compression,
Figure BDA0002919869980000046
the maximum compression obtained is:
Figure BDA0002919869980000047
further find the maximum impact force that the falling rocks produce:
Figure BDA0002919869980000048
further obtaining the corresponding maximum rockfall impact compressive stress as follows:
Figure BDA0002919869980000049
considering the material damage due to impact collision, the maximum impact force of falling rocks considering the damage is obtained as follows:
Figure BDA0002919869980000051
C. confirming the dynamic response of the reinforced concrete pile plate wall:
dividing an impact force-deformation relation curve of the reinforced concrete pile plate wall under falling rock impact into 3 stages:
the method comprises the following steps: and at the elastic loading stage of the initial collision stage, determining the contact force between the falling rocks and the reinforced concrete pile plate wall as elastic contact, and obtaining:
Figure BDA0002919869980000052
in the formula: deltayGenerating a deformation value when the initial yield is generated for the reinforced concrete pile plate wall;
II: in the plastic damage loading stage of the concrete pile plate wall, when the contact impact force exceeds the yield strength of the wall body, the concrete pile plate wall is subjected to plastic deformation and damaged, and the concrete pile plate wall is obtained by considering the damage:
Figure BDA0002919869980000053
in the formula: deltamThe maximum deformation value of the reinforced concrete pile plate wall is obtained;
③ stage III: in the unloading stage, when the reinforced concrete pile plate wall reaches the maximum compression deformation, the falling rock impact speed is reduced to 0, and the elastic deformation accumulated by the wall body can be rebounded and released; the relationship between the contact impact force and the deformation was confirmed as follows:
Figure BDA0002919869980000054
in the formula: dmIs the maximum deformation value delta before the unloading of the reinforced concrete pile plate wallmThe corresponding damage.
In a preferred embodiment of the present invention, in step a, the contact surface is set to a circle having a radius a.
As a preferable aspect of the present invention, in the step a, the relationship among the contact pressure, the maximum contact pressure stress, and the contact deformation is set in consideration of the relationship among the three components after the material is damaged by the falling rock impact.
As a preferred technical scheme of the invention, in the step C, a undetermined constant deltayThe determination method comprises the following steps: deformation value delta of reinforced concrete pile plate wall during initial yieldyThe stress corresponding to it is its initial yield strength σpyMeasured by a material mechanics test; contact force P of rockfall on reinforced concrete pile wallyAnd its yield strength sigmapySatisfies the following conditions:
Figure BDA0002919869980000055
in the formula: E. mu is the elastic modulus and Poisson's ratio of the material respectively; a. theyIs a material constant related to Poisson's ratio μ, when μ is 0.3 and 0.4, Ay1.61 and 1.74; the initial yield point of the material is the junction point of the elastic segment and the plastic damage segment, which belong to the elastic segment and the plastic damage segment at the same time, and the yield strength sigma of the material is knownpyThen the corresponding deformation delta at this time can be obtainedy。
As a preferred technical scheme of the invention, in the step C, the undetermined constant deltamThe determination method comprises the following steps: the maximum impact force and the maximum impact deformation of the reinforced concrete pile plate wall occur simultaneously, and the method comprises the following steps: pmax＝P(δ)|δ＝δm(24) (ii) a Obtaining an equation about δ m, wherein δ c is the impact deformation of the material when complete failure occurs, and is measured through experiments; by iteratively solving the equation, delta can be obtainedm。
As a preferred technical scheme of the invention, in the step C, in the third stage, after unloading is finished, the contact stress P (delta) is zero, and the corresponding residual deformation delta of the wall body is obtained0Namely the plastic deformation of the reinforced concrete pile-slab wall caused by the falling rock impact.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: aiming at the defects and problems of the prior art in multiple aspects, the damage to the reinforced concrete pile plate wall caused by rockfall impact is considered on the basis of the classical contact theory, and the damage contact theory is considered and used for geological disaster engineering practice; meanwhile, according to the dynamic response process of the reinforced concrete pile plate wall under the rockfall impact, a dynamic damage model of the reinforced concrete pile plate wall under the rockfall impact is provided, and the model parameter determination method is extended; finally, the invention carries out geological practice example-oriented research, and shows that the impact speed and the radius of falling rocks have larger influence on the dynamic mechanical response of the reinforced concrete pile plate wall, and the damage parameter delta of the reinforced concrete pile plate wallcAnd γ has a smaller influence on the calculation result, but when γ is smaller, the influence is more significant; the dynamic mechanical behavior of the reinforced concrete pile plate wall under rockfall impact can be well described, high-value reference can be provided for engineering design, and the method has a very good application prospect.
Drawings
FIG. 1 is a schematic view of mechanical interface contact.
Fig. 2 is a calculation model of a rockfall impact reinforced concrete pile wall.
Fig. 3 is a curve of the impact force-deformation relationship of the reinforced concrete sheet pile wall under the rockfall impact.
Fig. 4 is an impact force-deformation curve of the reinforced concrete sheet pile wall at different rockfall speeds.
Fig. 5 is an impact force-deformation curve of the reinforced concrete sheet pile wall under different rockfall radii.
Fig. 6 is an impact force-deformation curve of the reinforced concrete sheet pile wall under different damage parameters.
Detailed Description
The following examples illustrate the invention in detail. The raw materials and various devices used in the invention are conventional commercially available products, and can be directly obtained by market purchase.
In the following description of embodiments, for purposes of explanation and not limitation, specific details are set forth, such as particular system structures, techniques, etc. in order to provide a thorough understanding of the embodiments of the present application. It will be apparent, however, to one skilled in the art that the present application may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present application with unnecessary detail.
It will be understood that the terms "comprises" and/or "comprising," when used in this specification and the appended claims, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It should also be understood that the term "and/or" as used in this specification and the appended claims refers to any and all possible combinations of one or more of the associated listed items and includes such combinations.
As used in this specification and the appended claims, the term "if" may be interpreted contextually as "when", "upon" or "in response to" determining "or" in response to detecting ". Similarly, the phrase "if it is determined" or "if a [ described condition or event ] is detected" may be interpreted contextually to mean "upon determining" or "in response to determining" or "upon detecting [ described condition or event ]" or "in response to detecting [ described condition or event ]".
Furthermore, in the description of the present application and the appended claims, the terms "first," "second," "third," and the like are used for distinguishing between descriptions and not necessarily for describing or implying relative importance.
Reference throughout this specification to "one embodiment" or "some embodiments," or the like, means that a particular feature, structure, or characteristic described in connection with the embodiment is included in one or more embodiments of the present application. Thus, appearances of the phrases "in one embodiment," "in some embodiments," "in other embodiments," or the like, in various places throughout this specification are not necessarily all referring to the same embodiment, but rather "one or more but not all embodiments" unless specifically stated otherwise. The terms "comprising," "including," "having," and variations thereof mean "including, but not limited to," unless expressly specified otherwise.
Example 1 theory of elastic contact and improvements thereof
Referring to fig. 1, assuming that the contact surface is a circle with radius a, Hertz thus gives a complete solution for the elastic contact of 2 spheres at contact pressure P:
the contact compressive stress distribution is as follows:
Figure BDA0002919869980000071
in the formula: p (r) is contact compressive stress, P is contact pressure, and a is contact radius. Maximum contact compressive stress pmaxAt r-0:
Figure BDA0002919869980000072
the contact deformation consists of two parts:
δ＝δ1+δ2 (3)
in the formula: delta1、δ2The deformation amounts of the 2 contact bodies, respectively.
The contact deformation and the contact area have the following relationship:
a2＝Rδ (4)
in the formula: r is the equivalent radius of the glass fiber,
Figure BDA0002919869980000073
R1、R2is the radius of 2 spheres.
Contact pressure P, maximum contact pressure stress PmaxThe relationship to contact deformation δ is:
Figure BDA0002919869980000081
in the formula: e is the equivalent modulus of elasticity,
Figure BDA0002919869980000082
E1、μ1、E2、μ2the elastic modulus and poisson's ratio of the two contact bodies.
The above-mentioned Hertz 'contact theory only applies to materials in the elastic deformation phase, while in practical engineering the contact force calculated from them tends to be large, because when the contact compressive stress reaches the yield strength of the material, the material will deform plastically, at which point the classical Hertz' contact theory no longer applies. Therefore, many scholars improve the method, and at present, two types of improved models mainly exist: hertz plastic contact theory and damage contact theory. The former considers that when the contact stress reaches the yield strength of the material, the material is subjected to plastic deformation, how thought, Thornton and the like put forward a Hertz plastic contact theory based on an ideal elastic-plastic model, and the impact force obtained by calculation is obviously smaller than that obtained by calculation of a corresponding classical Hertz contact theory and better accords with the actual situation. However, with the development of damage mechanics, many researchers also introduce the theory of Hertz contact, for example, Travares and others construct a corresponding impact damage theoretical model according to the load-deformation response characteristic of spherical particles under impact load based on the theory of Hertz contact and the theory of continuous medium damage:
Figure BDA0002919869980000083
in the formula: d is the diameter of the spherical particles,
Figure BDA0002919869980000084
in order to be of an effective rigidity,
Figure BDA0002919869980000085
in the formula: d is the impact damage of the spherical particles and K is the initial stiffness.
And defining the impact damage variable D as:
Figure BDA0002919869980000086
in the formula: deltacThe amount of compression deformation of spherical particles at the time of impact failure is set to δ ═ δcThe damage D ═ 1; gamma is the impact damage index.
Then, as can be seen from equation (8), any impact contact deformation of spherical particles will cause damage, however, according to Hertz's contact theory and indoor indentation test: when the contact deformation delta of the spherical particles is less than the initial yield deformation deltayWhen D is 0, the particulate matter is in a completely elastic contact state and no damage occurs. It is clear that equation (8) does not describe the situation when the particles are in full elastic contact, which is a drawback of this model.
Because rocks and concrete in the nature are natural damaged materials and have a large number of micro cracks, micro holes and other microscopic defects, the collision among particles inevitably causes the initiation, expansion and convergence of the micro cracks, and further causes the degradation of the macroscopic physical and mechanical properties of the particles, specifically the reduction of the elastic modulus of the particles until the final damage. The reduction in elastic modulus can therefore be used to define the damage variable. A typical particle collision load-contact deformation curve can be divided into 4 stages: the initial impact phase, elastic impact phase, plastic damage impact phase and unload rebound phase of the particles are generally ignored due to the short first phase. In the elastic contact stage, the load-contact deformation among the particles accords with the Hertz elastic contact theory, and the particle contact deformation belongs to elastic deformation, so that no damage is generated; when the contact pressure exceeds the initial yield pressure of the particles, the pressure-contact deformation curve begins to deviate from the Hertz elastic contact theoretical curve, and the particle materials begin to be damaged, namely, the particle materials enter a plastic damage collision stage; when the collision pressure peak value, namely the maximum compression deformation amount is reached, the elastic unloading and rebounding stage is started, the deformation is elastic in the elastic unloading and rebounding stage, and the damage is kept unchanged. The damage variable D of the particles can thus be defined as:
Figure BDA0002919869980000091
wherein:
Figure BDA0002919869980000092
e is the effective and initial elastic modulus of the particles, respectively; deltay、δm、δcThe contact deformation amount corresponding to the initial yield of the particles, the maximum contact deformation amount in the particle collision process and the deformation amount corresponding to the complete breakage of the particles, namely D is 1, and delta is satisfied among the threey<δm≦δc。
The relationship between contact pressure, maximum contact compressive stress and contact deformation taking into account material damage can thus be found to be:
Figure BDA0002919869980000093
example 2 impact force of falling rocks on reinforced concrete pile wall
Assuming that the falling rocks are mass points moving at a velocity v0 and the reinforced concrete sheet wall is a stationary plane, a calculation model is established as shown in fig. 2.
The impact velocity can be resolved first in the horizontal and vertical directions:
vx＝v0 sinθ，vy＝v0 cosθ (11)
in the formula: v. of0、vx、vyRespectively representing the instantaneous total impact speed, the horizontal impact speed and the vertical impact speed when the falling rocks contact the reinforced concrete pile plate wall; θ is the impact angle.
Since the main cause of impact damage to the reinforced concrete sheet pile wall is horizontal impact, only the horizontal impact effect of falling rocks is considered here. According to Newton's second law, there are:
Figure BDA0002919869980000094
in the formula: m is1、m2The quality of the reinforced concrete pile plate wall and the falling rocks are respectively measured; v. of1The moving speed of the reinforced concrete pile plate wall is obtained; and P is the impact force of falling rocks to the reinforced concrete pile plate wall.
Then, from equation (12):
Figure BDA0002919869980000095
then, from equations (5) and (13):
Figure BDA0002919869980000096
in the formula: m is the equivalent mass of the compound,
Figure BDA0002919869980000101
integrating δ, one can obtain:
Figure BDA0002919869980000102
at the time of the maximum amount of compression,
Figure BDA0002919869980000103
the maximum compression that can be achieved thereby is:
Figure BDA0002919869980000104
the maximum impact force generated by falling rocks can be obtained by substituting formula (16) for formula (5):
Figure BDA0002919869980000105
then the corresponding maximum falling rock impact compressive stress is obtained from equations (2), (5), (16) and (17):
Figure BDA0002919869980000106
as can be seen from section 2, when material damage due to impact collision is considered, formula (9) is substituted for formula (17), and the maximum impact force of falling rocks considering damage is obtained as:
Figure BDA0002919869980000107
EXAMPLE 3 dynamic response of reinforced concrete sheet pile wall
Engineering practice shows that the rock falling impact force can cause certain damage and damage to the reinforced concrete pile plate wall, and therefore, the Hertz contact theory considering damage is more consistent with the actual situation.
The impact force-deformation relation curve of the reinforced concrete pile plate wall under falling rock impact can be divided into 3 stages:
the method comprises the following steps: spring loading phase at early stage of collision
At the initial stage of collision, because the impact force of falling rocks to reinforced concrete pile board wall is less, and correspondingly the deformation of wall body is also less, consequently the wall body still is in the elastic deformation state, and the contact force between the two satisfies elasticity Hertz contact theory, promptly:
Figure BDA0002919869980000108
in the formula: deltayThe deformation value at initial yield is generated for the reinforced concrete pile plate wall.
II: the plastic damage loading stage of concrete sheet wall, along with the continuation of impact process, contact impact force and wall body deformation constantly increase promptly, when the contact impact force surpassed the yield strength of wall body, will lead to it to produce plastic deformation, appear damaging, the contact impact force should satisfy the Hertz contact theory of considering the damage this moment, promptly:
Figure BDA0002919869980000111
in the formula: deltamThe maximum deformation value of the reinforced concrete pile plate wall.
③ stage III: and in the unloading stage, namely when the reinforced concrete pile plate wall reaches the maximum compression deformation, the falling rock impact speed is reduced to 0, and the elastic deformation accumulated by the wall body can be rebounded and released. At this stage, the wall will not generate new damage, and the existing damage will not recover, so the elastic modulus of the wall at this stage is the elastic modulus when the peak deformation occurs, and the relationship between the contact impact force and the deformation is:
Figure BDA0002919869980000112
in the formula: dmIs the maximum deformation value delta before the unloading of the reinforced concrete pile plate wallmThe corresponding damage.
When unloading is finished, the contact stress P (delta) should be zero, and the corresponding wall residual deformation delta can be obtained0Namely the plastic deformation of the reinforced concrete pile-slab wall caused by the falling rock impact.
As can be seen from the expressions (20) to (22), when the reinforced concrete pile panel wall is subjected to rockfall impactWhen analyzing dynamic response, the undetermined constant delta must be determinedyAnd deltamThe determination method thereof is discussed below.
(1)δyDetermination method
Deformation value delta of reinforced concrete pile plate wall during initial yieldyThe stress corresponding to it is its initial yield strength σpyThis can be measured by a material mechanics test. Vu-Quoc et al are based on the Hertz contact theory, and believe that the contact force P of rockfall on the reinforced concrete pile wall when the material meets the Von Mises yield criterionyAnd its yield strength sigmapySatisfies the following conditions:
Figure BDA0002919869980000113
in the formula: E. mu is the elastic modulus and Poisson's ratio of the material respectively; a. theyIs a material constant related to Poisson's ratio μ, when μ is 0.3 and 0.4, Ay1.61 and 1.74.
Since the initial yield point of the material is the boundary point of the elastic segment and the plastic damage segment, and thus belongs to both the elastic segment and the plastic damage segment, it should satisfy both the second formula (23) and the second formula (5), if the yield strength σ of the material is knownpyThe corresponding deformation delta at that time can be obtainedy。
(2)δmDetermination method
As can be seen from the foregoing, the maximum impact force and the maximum impact deformation of the reinforced concrete sheet wall occur simultaneously, and thus, the following equations (19) and (21) can be obtained:
Figure BDA0002919869980000121
from this, one can derive a reference to δmEquation (where δcThe impact deformation amount when the material is completely damaged can be measured through tests), and delta can be obtained by solving the equation iterativelym。
Example 4, example study
The calculation model is as shown in fig. 2, assuming that the impact velocity is v0 and the impact angle is θ at the moment when the falling rocks contact the reinforced concrete pile plate wall, taking the falling rocks calculation parameters as: the shape is spherical, the radius is 1.0m, and the density is 2500kg/m3Mass 10467kg, elastic modulus 20GPa, Poisson's ratio 0.2, v 05m/s, θ 30 °; taking a reinforced concrete pile board wall between two adjacent pile bodies as an independent research object, wherein the calculation parameters are as follows: the shape of the rectangular parallelepiped, the dimension of the rectangular parallelepiped is 3.0m × 3.0m × 0.3m, the elastic modulus is 10GPa, the Poisson ratio is 0.3, and the density is 2600kg/m3Yield strength sigmapy150MPa, damage factor deltac＝30mm、γ＝4。
The calculation process and the result are as follows:
the method comprises the following steps: spring loading phase at early stage of collision
First, δ can be obtained from the above calculation parameters and the equations (5) and (23)yWhen the maximum elastic impact force is 1.15MN, namely the deformation of the reinforced concrete pile panel wall under the rockfall impact is increased from 0 to 2.43mm, the corresponding contact impact force is correspondingly linearly increased from 0 to 1.15 MN.
II: plastic damage loading stage in middle collision
Firstly, the maximum value delta of the impact deformation of the reinforced concrete pile plate wall is obtained according to the formulas (19), (21) and (24)m7.91 mm. Then at deltay～δmAnd taking a plurality of delta values, obtaining the contact impact force P (delta) in the formula (21), and drawing a plastic damage loading curve of the concrete pile plate wall by using the points.
③ stage III: elastic unloading stage at later stage of collision
Firstly, the maximum value delta of the impact deformation of the reinforced concrete pile wallmThe corresponding maximum damage value D was determined at 7.91mmm0.00156. The corresponding permanent deformation amount delta can be obtained by substituting formula (22) and setting the contact impact force P (delta) to 003.15 mm. At deltam～δ0Taking a plurality of values, obtaining the corresponding contact impact force P (delta) by using a formula (22), and drawing by using the points to obtain the reinforced concrete pile plateElastic unloading curve of wall.
The relationship curve of impact force, damage and deformation between rockfall and the reinforced concrete pile plate wall is shown in fig. 3, and it can be found that: the impact force-deformation curve can be divided into 3 sections: an elastic loading phase, a plastic damage loading phase and an elastic unloading phase. In the elastic loading stage, the reinforced concrete pile plate wall is elastically deformed, and the impact force of falling rocks on the reinforced concrete pile plate wall and the deformation of the reinforced concrete pile plate wall meet a linear relation; when the impact force is increased to the yield strength of the reinforced concrete sheet pile wall, the reinforced concrete sheet pile wall begins to enter a plastic damage deformation stage. From the slope of the curve, the slope of the plastic damage loading stage is larger than that of the elastic loading stage, because after the reinforced concrete enters the plastic state, a plastic strengthening stage occurs, namely if the reinforced concrete generates a small displacement, a large force must be applied, so that the slope of the curve of the plastic section is steep, which is consistent with the rule obtained by thinking and the like. After the peak impact force is reached, the rockfall impact speed is reduced to zero, then the reinforced concrete pile plate wall starts to perform unloading rebound, the elastic deformation part of the reinforced concrete pile plate wall starts to recover, and the rockfall impact force and the total deformation are gradually reduced. When the falling rock impact force is reduced to zero, the corresponding deformation is the permanent deformation of the reinforced concrete pile plate wall, namely the residual plastic deformation. Secondly, as can be seen from the damage-deformation curve, in the example, only the damage is generated in the stage II, and the maximum damage value is only 0.0015, namely the damage is small, so that the curve of the stage II is similar to the linear relation. In addition, the damage variable definition shown in the formula (9) shows that the magnitude and δ of the damage valuecAnd gamma, so that the accurate description of the damage evolution law of the reinforced concrete pile plate wall depends on the accurate determination of the two damage constants to a great extent, as shown in figure 3.
Example 5 analysis of parameter sensitivity
From the computational model presented herein, it can be seen that the dynamic response of a reinforced concrete pile-slab wall under rockfall impact is not only related to its own physico-mechanical properties, but is also largely influenced by rockfall parameters. Therefore, the influence of rockfall and reinforced concrete calculation parameters on results is researched by adopting parameter sensitivity analysis.
(1) Falling speed of stone
The falling rock speeds are taken to be 2.5, 5, 7.5 and 10m/s respectively, and the rest parameters are not changed, so that the calculation result shown in FIG. 4 shows that: firstly, with the increase of the rockfall impact speed, the maximum impact deformation generated by the reinforced concrete pile board wall is gradually increased from 3.17mm to 4.66 mm, 6.24 mm and 7.91mm, and correspondingly, the maximum impact force is gradually increased from 1.67MN to 2.73 mm, 3.84 mm and 5.03MN, which shows that the larger the rockfall impact speed is, the larger the impact force on the reinforced concrete pile board wall is, and the larger the maximum impact deformation is correspondingly generated; secondly, with the increase of the rockfall impact speed, the residual deformation of the reinforced concrete pile plate wall is gradually increased from 0.25mm to 1.0, 2.0 and 3.15mm, namely the residual deformation is increased, which indicates that the greater the rockfall impact speed is, the more remarkable the plastic deformation of the reinforced concrete pile plate wall is, namely the more serious the overall damage to the reinforced concrete pile plate wall is. ③ the falling rock impact velocity does not change the linear section of the curve, because the linear section of the curve is determined by the yield strength of the material and the Hertz elastic contact theory, and is not influenced by the falling rock impact velocity.
(2) Radius of falling rocks
Taking the radius of the falling rocks to be 0.25, 0.5, 0.75 and 1m respectively, the corresponding mass of the falling rocks to be 163.5, 1308.3, 4415.6 and 10466.7kg respectively, and the rest of the parameters are unchanged, it can be seen from the calculation results shown in fig. 5 that: firstly, as the rockfall radius is increased, the mass of the rockfall is correspondingly increased, so that the maximum impact deformation of the rockfall on the reinforced concrete pile board wall is gradually increased from 3.22mm to 4.73 mm, 7.45 mm and 7.91mm, and correspondingly, the maximum impact force is gradually increased from 0.54MN to 1.53 MN, 3.64 MN and 5.03MN, which indicates that the impact force on the reinforced concrete pile board wall caused by the increase of the rockfall radius is larger, and the maximum impact deformation is correspondingly larger; ② with the increase of the rockfall radius, the residual deformation of the reinforced concrete pile board wall is gradually increased from 1.71mm to 2.10 mm, 3.45 mm and 3.15mm, namely the residual deformation is generally increased, but when the rockfall radius is increased to a certain extentThen, an abnormal condition occurs, for example, the residual deformation amount when the rockfall radius is 0.75m is larger than the residual deformation amount when the rockfall radius is 1m, which indicates that the impact damage of the rockfall to the reinforced concrete sheet pile wall will be more and more serious with the increase of the rockfall quality, and it is assumed here that the damage evolution law of the reinforced concrete sheet pile wall is certain, namely δ in equation (9)cAnd gamma are invariant, so this inevitably introduces some error.
(3) Damage parameter of reinforced concrete pile wall
In the injury model herein, there is primarily δcAnd γ, the influence of which on the calculation results is shown in fig. 6, and it can be seen that: is along with deltacThe impact force-deformation curve of the reinforced concrete pile plate wall has certain change, but the change range is small, namely when delta iscThe maximum impact deformation of the reinforced concrete pile panel wall gradually decreases from 8.06mm to 7.92, 7.90 and 7.89mm when the thickness is gradually increased from 15mm to 20, 25 and 30mm, and correspondingly the maximum impact force is gradually increased from 4.947MN to 5.005, 5.022 and 5.024 MN; meanwhile, the residual deformation of the reinforced concrete pile plate wall is reduced to 3.15mm, 3.1mm and 3.1mm from 3.24mm, which shows that deltacThe impact response of the increase in the amount of the concrete pile wall is relatively small and almost negligible, and as can be seen from fig. 6(a), the 4 curves are also substantially coincident, which indicates δcThe influence on the calculation result is not great. The variation range of the impact force-deformation curve of the reinforced concrete sheet wall is rapidly reduced along with the increase of gamma, namely when the gamma is gradually increased from 1 to 2, 3 and 4, the maximum impact deformation generated by the reinforced concrete sheet wall is gradually reduced from 9.18mm to 8.07, 7.92 and 7.89mm, and correspondingly, the maximum impact force is gradually increased from 4.4946MN to 4.945, 5.014 and 5.024 MN; meanwhile, the residual deformation of the reinforced concrete pile plate wall is reduced from 4.05mm to 3.25 mm, 3.15mm and 3.1mm respectively, which shows that the impact response influence of the increase of gamma on the reinforced concrete pile plate wall is increased rapidly firstly, and then the increase amplitude is reduced rapidly. Meanwhile, as can also be seen from fig. 6(b), when γ is increased from 1 to 2, the change amplitude is most significant, and then the change amplitude is changedIt is rapidly reduced. This is because γ is a damage index, and it is understood from the formula (9) that the base number of damage is less than 1, and since the base number of damage is small in the present example, when γ is 1, the damage is relatively large, and therefore the corresponding reinforced concrete damage is also large, the slope of the curve plasticity section is significantly reduced, and the residual deformation is also maximum. As γ increases, the change of the lesion is relatively small, and thus, as shown in fig. 6(b), when γ is 2, 3, and 4, the corresponding 3 curves are not very different and substantially coincide with each other. ③ by contrast of deltacThe influence of the two damage parameters of gamma and gamma on the calculated result can be found, and the influence of gamma on the calculated result is more obvious relatively, especially when gamma is used<2, therefore, the sample value of γ should be obtained more accurately in the reinforced concrete damage test.
In conclusion, the embodiment of the invention can be seen that aiming at the defects and problems of the prior art in multiple aspects, on the basis of the classical contact theory, the damage of rockfall impact on the reinforced concrete pile plate wall is considered, and the damage contact theory is considered and used for geological disaster engineering practice; meanwhile, according to the dynamic response process of the reinforced concrete pile plate wall under the rockfall impact, a dynamic damage model of the reinforced concrete pile plate wall under the rockfall impact is provided, and the model parameter determination method is extended; finally, the invention carries out geological practice example-oriented research, and shows that the impact speed and the radius of falling rocks have larger influence on the dynamic mechanical response of the reinforced concrete pile plate wall, and the damage parameter delta of the reinforced concrete pile plate wallcAnd γ has a smaller influence on the calculation result, but when γ is smaller, the influence is more significant; the dynamic mechanical behavior of the reinforced concrete pile plate wall under rockfall impact can be well described, high-value reference can be provided for engineering design, and the method has a very good application prospect.
The above-mentioned embodiments are only used for illustrating the technical solutions of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; such modifications and substitutions do not substantially depart from the spirit and scope of the embodiments of the present invention, and are intended to be included within the scope of the present invention.

Claims (5)

1. The method for acquiring the dynamic response data of the passive pile plate stone blocking wall in the collapse rockfall geological disaster is characterized by comprising the following steps of: the method comprises the following steps:
A. obtaining the relation among the contact pressure, the maximum contact pressure stress and the contact deformation between the collapse falling stones and the passive pile plate stone blocking wall:
first, the contact compressive stress distribution was confirmed to be:
Figure FDA0003641113150000011
in the formula: p (r) is contact compressive stress, P is contact pressure, a is contact radius; maximum contact compressive stress pmaxAt r-0:
Figure FDA0003641113150000012
the contact deformation consists of two parts:
δ*＝δ1+δ2 (3)
in the formula: delta1、δ2Respectively 2 contact body deflection, delta*Deformation by contact;
the contact deformation and the contact area have the following relationship:
a2＝Rδ* (4)
in the formula: r is the equivalent radius of the glass fiber,
Figure FDA0003641113150000013
R1、R2radius of 2 contact bodies;
contact pressure P between two contact bodies, maximum contact pressure stress PmaxAnd is connected withDeformation by touch delta*The relationship between them is:
Figure FDA0003641113150000014
in the formula: e*In order to be equivalent to the modulus of elasticity,
Figure FDA0003641113150000015
E1、E2、μ1、μ2the elastic modulus and poisson ratio of the two contact bodies are shown;
constructing a corresponding impact damage theoretical model according to the load-deformation response characteristic of the spherical particles under the impact load:
Figure FDA0003641113150000016
in the formula: p0The contact impact force between the two particles; d is the diameter of the spherical particles,
Figure FDA0003641113150000017
in order to be of an effective rigidity,
Figure FDA0003641113150000018
in the formula: dsImpact damage of spherical particles, K is initial stiffness;
will impact damage variable DsIs defined as:
Figure FDA0003641113150000019
in the formula: deltacThe amount of compression deformation at the time of impact failure of spherical particles, when delta*＝δcDamage Ds1 is ═ 1; gamma is the impact damage index;
change of damage D of the particlessIs defined as:
Figure FDA0003641113150000021
wherein:
Figure FDA0003641113150000022
e is the effective and initial elastic modulus of the particles, respectively; delta. for the preparation of a coatingy、δmRespectively the contact deformation corresponding to the initial yield of the particles, the maximum contact deformation in the particle collision process, deltay、δm、δcDelta is satisfied between the threey<δm≤δc(ii) a The equation (5) is a relationship among the contact pressure, the maximum contact compressive stress and the contact deformation in the completely elastic state, and when the contact pressure exceeds the yield strength of the material, damage will occur in the material, and the elastic modulus of the material after damage can be obtained from the equation (9), whereby the contact pressure P in consideration of the damage of the material can be obtained by considering the equations (5) and (9) in combinationDMaximum contact compressive stress pDmaxThe relationship to contact deformation is:
Figure FDA0003641113150000023
B. acquiring the impact force of falling rocks on the reinforced concrete pile-slab wall:
rockfall is determined as velocity v0The mass point of motion, reinforced concrete sheet pile wall are static plane, decompose impact velocity along level and vertical direction:
vx＝v0 sinθ，vy＝v0 cosθ (11)
in the formula: v. of0、vx、vyRespectively representing the instantaneous total impact speed, the horizontal impact speed and the vertical impact speed when the falling rocks contact the reinforced concrete pile plate wall; theta is an impact angle;
what causes the impact damage to reinforced concrete sheet pile wall is horizontal impact, only considers the horizontal impact effect of falling stone, has:
Figure FDA0003641113150000024
in the formula: m is1、m2The quality of the reinforced concrete pile plate wall and the falling rocks are respectively measured; v. of1The moving speed of the reinforced concrete pile plate wall is obtained; prThe impact force of falling rocks on the reinforced concrete pile plate wall is obtained; by modifying formula (12):
Figure FDA0003641113150000025
in the formula: m is the equivalent mass of the compound,
Figure FDA0003641113150000026
delta is the deformation of the reinforced concrete pile plate wall;
Figure FDA0003641113150000027
integrating over δ:
Figure FDA0003641113150000031
at the time of the maximum amount of compression,
Figure FDA0003641113150000032
the maximum compression obtained was:
Figure FDA0003641113150000033
by substituting equation (16) for equation (5), the maximum impact force generated by falling rocks can be determined:
Figure FDA0003641113150000034
the corresponding maximum rockfall impact compressive stress is obtained as follows:
Figure FDA0003641113150000035
considering material damage caused by impact collision, obtaining maximum impact force P of falling rocks considering damageDrmaxComprises the following steps:
Figure FDA0003641113150000036
wherein: d is damage to the reinforced concrete pile plate wall caused by rockfall impact;
C. confirming the dynamic response of the reinforced concrete pile plate wall:
dividing an impact force-deformation relation curve of the reinforced concrete pile plate wall under falling rock impact into 3 stages:
the method comprises the following steps: in the elastic loading stage of the initial collision stage, the contact force between the rockfall and the reinforced concrete pile plate wall is determined as elastic contact, and the impact force P is obtaineder(δ) the relationship to the deformation δ of the reinforced concrete sheet wall is:
Figure FDA0003641113150000037
in the formula: deltaryGenerating a deformation value when the initial yield is generated for the reinforced concrete pile plate wall;
II: in the plastic damage loading stage of the concrete pile plate wall, when the contact impact force exceeds the yield strength of the wall body, the concrete pile plate wall is subjected to plastic deformation and damaged, and the impact force P is obtained by considering the damageDr(δ) the relationship to the deformation δ of the reinforced concrete sheet wall is:
Figure FDA0003641113150000038
in the formula: deltarmThe maximum deformation value of the reinforced concrete pile plate wall is obtained;
③ stage III: in the unloading stage, when the reinforced concrete pile plate wall reaches the maximum compression deformation, the falling rock impact speed is reduced to 0, and the elastic deformation accumulated by the wall body can be rebounded and released; obtaining the impact force Pur(δ) the relationship to the deformation δ of the reinforced concrete sheet wall is:
Figure FDA0003641113150000041
in the formula: dmIs the maximum deformation value delta before the unloading of the reinforced concrete pile plate wallrmThe corresponding damage.
2. The method for acquiring the dynamic response data of the passive pile plate stone blocking wall in the collapse rockfall geological disaster according to the claim 1, wherein: in step a, the contact surface is set to a circle with a radius a.
3. The method for acquiring the dynamic response data of the passive pile plate stone blocking wall in the collapse rockfall geological disaster according to the claim 1, wherein: in the step A, the relationship among the contact pressure, the maximum contact pressure stress and the contact deformation is set to be the relationship among the three after the material is damaged under the falling rock impact.
4. The method for acquiring the dynamic response data of the passive pile plate stone blocking wall in the collapse rockfall geological disaster according to the claim 1, wherein: in step C, the undetermined constant deltaryThe determination method comprises the following steps: deformation value delta of reinforced concrete pile plate wall during initial yieldryThe stress corresponding to it is its initial yield strength σpyMeasured by a material mechanics test; contact force P of rockfall on reinforced concrete pile wallryAnd its flexionClothing strength sigmapySatisfies the following conditions:
Figure FDA0003641113150000042
in the formula: e0、μ0Respectively the elastic modulus and the poisson ratio of the material; a. theyIs the Poisson ratio mu0Relative material constant, when0When not equal to 0.3 and 0.4, Ay1.61 and 1.74; the initial yield point of the material is the junction point of the elastic segment and the plastic damage segment, which belong to the elastic segment and the plastic damage segment at the same time, and the yield strength sigma of the material is knownpyThe corresponding deformation delta at the moment can be obtainedry。
5. The method for acquiring the dynamic response data of the passive pile plate stone blocking wall in the collapse rockfall geological disaster according to the claim 1, wherein: in step C, the undetermined constant deltarmThe determination method comprises the following steps: the maximum impact force and the maximum impact deformation of the reinforced concrete pile plate wall occur simultaneously, and the method comprises the following steps:
Figure FDA0003641113150000043
to obtain a value related to deltarmBy solving the equation iteratively, delta can be obtainedrm。
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