Experimental and numeric survey of the modelling of a subsidence M. CAUDRON National Institute of Applied Science, Lyon, FRANCE
ABSTRACT: This PIRD is attached to the modelling of a fontis while using the analogical material of SCHNEEBELI. As we saw it in the preliminary report to this survey, certain problems are going to appear, like taking account of cohesion in the small rollers. In order to remedy there, we will use the following plan: In a first part, we will achieve a bibliographic survey of the phenomenon and of the works achieved in this domain. The material of SCHNEEBELI being merely rubbing, we will try in a second part to find a solution to introduce cohesion. The continuation of this part will be dedicated to the survey of this new material therefore, to the characterisation of its behaviour and to the validation of its use for the modelling of a fontis. The last part will be about the initial topic of the PIRD: the survey and the experimental modelling of a fontis. For that we will use the material above and will compare its behaviour to the one of the material of SCHNEEBELI. The goal of this part is to provide the bases for an ulterior survey to the validation of the software PFC2D about the modelling of fontis.
1. BIBLIOGRAPHY The bibliographic survey that we are going to achieve won't bring any major modifications to the different studies that have been done by people working lately on a topic close to the our. We especially think about the works of C. LIU: "Foisonnement and Stability of the Subterranean Cavities Little Deep " and of A. ABBASS FAYAD: "Survey of the soil-structure interaction due to the movements of the land generated by fontis ". These are not the only people who have worked on this topic or on projects in relation with the object of our work but their works are recent and allow to establish an interesting bibliographic basis for the continuation of the project. We will start therefore with presenting the notion of risk, linked to the existence of subterranean cavities, then we will see the notion of fontis to approach the historic of the various modellings finally done. 1.1.
The prediction of this risks pass by five stages: the role of the time, the propagation of the messes toward the surface, the quantification of the messes, the prevention and finally the detection of the cavities. 1.2.
The notion of fontis
A fontis designates the instability of the roof of an subterranean cavity that collapses, generating an bell-shaped ascent (denomination of bell of fontis). This ascent can emerge, to which case we attend to a crater-shaped downfall localised to a part of floor. It arrives however that this risk doesn't emerge in surface for two possible reasons. Either the bell of ascent arrived to a steady configuration, or the foisonnement of the collapsed materials is sufficiently important to permit the filling of the cavity by itself. These two possibilities are enough current for cavities situated to more of 50m of depth. 1.3.
Historic of the modelling of fontis
The risks of the subterranean cavities
All subterranean work, that it is a tunnel, a mine, a boring, a cavity of storage,…, generates in the basement of the distortions that ascends until the surface of soil. We can separate the life of each piece of work in three distinct phases: the phase of construction, the phase of exploitation, the phase of postexploitation (second life).
For a long time, people tempt to foresee and to build a model of the apparition of fontis. We have the empiric methods (as the one of VACHAT, 1982) come then the analytic methods and finally the numeric methods. The empiric methods are based on the observations made through experiences and the measures achieved on real cases. The analytic methods make an analogy between the phenomena met in Resistance of the Materials and the
mechanisms possible of creation of a fontis. The numeric methods are used when the problem is too much complicated for being solved by any other method. They use processes of numeric analysis as the finished differences, the finished elements. These methods possess each their advantages and their inconveniences: for example, the empiric and analytic methods are simple to apply and provide some results very quickly.
2. The Program of the survey The INERIS is elected by the Ministry of The environment for a survey of risks and solutions on the settlings of soil and the formation of fontis. The goal of this axis of research is to develop a reliable modelling that permits the warning upstream of the formation of fontis and these consequences. It must also tempt to explain the reason of the different accidents, this in order to find some solutions to avoid that they reproduce. Our work is going to consist in tempting to validate the approach made by PFC2D with comparisons to experimental modellings. These experiences use the bidimensional analogical material of SCHNEEBELI. He showed that the survey of the problems in mechanics of soils with a material without cohesion can amount to two measurements. One replaces the soil therefore by a stacking of bidimensional cylindrical rollers. On the other hand, the bidimensional nature and the properties (weak rubbing angle: between 20° and 25° and hopeless cohesion) don't permit to respect to the best the conditions of likeness. It presents nevertheless the following advantages: Easiness of setting the work. Possibility of obtaining of the complete displacement field with the help of a specific technique. The obtainment of the totality of the displacement field is achieved by numeric imagery and the use of the software of interrelationship of numeric pictures: the software SIFASOFT. We are going to tempt to represent the state of cohesion in this analogical material in order to be closer of the real conditions. The absence of cohesion in this material is one of the main problems met at the time of the representation of the phenomenon of fontis. In a first part, we will find a means to represent a sort of cohesion in this analogical material.
2.1.
Introduction of the cohesion
We considered different solutions to introduce the cohesion in the rollers of SCHNEEBELI, for example, the use a viscous product like glue, the grease or the paint. All these solutions present a problem of confinement of the addition and have been dropped therefore. We kept only one solution that is the use of paper strips between some layers of rollers. To validate this model, we will use two types of tests: the structure of Thrust-Abutment and the biaxial tests. 2.2.
The biaxial test
The biaxial test The biaxial tests permit to determine the intrinsic features of the material, φ and c for a soil. We have compared the tests without strips of paper and those with the papers. We get the following results: Without papers: ϕ = 24° and c = 0kPa With the papers: ϕ = 19° and c = 2.5kPa We have tempted to validate the results obtained by the biaxial tests then while achieving some experiences on the structure of Thrust-Abutment. We also compare the behaviour of the soil massif without strips to the one with strips. 2.3.
The test of Thrust-Abutment
This test consists in soliciting a massif of soil by Thrust, afterwards by abutment. To every stage of the experience, we measure the efforts applied on the mobile wall. This allows us to know the strengths of Thrust, next those of abutment, exercised by the moving corner of soil. While applying the theory of the Coulomb corner, next
the one of Boussinesq, we can recover the characteristic features of the analogical soil.
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The test of Thrust-Abutment To the final we keep the following features for the analogical soil: ϕ = 19° and c = 2.5kPa .
Evolution of the settling surface during the experience
3. Modelling of the fontis We now pass to the modelling of the phenomenon of fontis on a big structure permitting to put in place until two square meters of rollers. We chose to achieve two experiences, one without strips and the other with. However none of the two tests will use a building to measure the impacts on such a structure. We take some photos at every stage with the help of a photoscope to be able to know the displacements by using the software SIFASOFT developed by F. MORESTIN of the Laboratory of Mechanics of the Solid of the INSA of Lyons. This method permits to get a precision of the order of 5/100 of millimeter.
etp 1-3 etp 5-7 etp 9-11 etp 13-15 etp 17-19 etp 21-23
The results are very little different between the two tests, notably on the shape of the settling. However when one observes the horizontal displacements, we note a difference not to the level of the amplitude but to the level of the importance of the zone concerned. So in the test with strips, we mobilize a superior width of 35% to the one equivalent without strips. y (mm) 5
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The model of fontis After having skinned the results, we use the software SIFASOFT and get the following results: S max = 34mm in the two case
We can also compare the surfaces of the settling obtained to the one determined while using the empiric formula of Atkinson: H − D 2 S max = Sclé 1 − k D and the formula of the curve of Gauss:
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We get very near results, what seems normal because the cohesion only appears very rarely in the empiric formulas giving the maximum settling. That can let suppose the weak influence of this one therefore on the distribution of the settling. To conclude on this part, we can keep the weak difference existing between the two tests and the results provided by an empiric formula. The big likeness between the two experiences can be due to the too weak cohesion that we introduced: it would be interesting to redo the same manipulations with a very superior cohesion. We can also keep that in the case of one soil presenting a cohesion, the horizontal displacements are sensitive to a bigger distance of the fontis what can be damaging for the infrastructures then submitted to a shearing.
4. Conclusion and perspectives This project allowed us to familiarize us with the work of research. It was of more interesting to find a technological solution to build a model of the existence of cohesion within a merely powdery material. We try to manage the work of validation of a model through different experiences and the crosscheck of the results. The second part is centred on the topic first of the PIRD: "Experimental survey and modelling of a fontis ". We compared the differences between the behaviour of the rollers of SCHNEEBELI and the coherent analogical material in a global way. It results that the differences are minimal. It is too verified at the level in the shape of the surface of the settling and of the rupture lines. The strips are not sufficiently stiff to modify by fundamental manner the answer of the material to a phenomenon of fontis. Indeed the cohesion that we bring is of about 2.5 kPa whereas the one measured on the lithographic strata of the represented fontis is to the minimum of 200 kPa and can be going as far as reaching a value of 1 MPa. Besides, we introduced a sort of global cohesion in our analogical material: when one becomes attached to a more local level, one doesn't observe cohesion, what is a fundamental difference with one coherent soil, anymore. These two points are the reasons of the flagrant difference absence between the two experiences of modelling of fontis. Nevertheless it is not a failure for as much, because we have verified the adequacy of an empiric method of prediction in the shape of the settling, in this case the formula of Atkinson and al.
And the perspectives: As perspectives of research, we can first of all keep the introduction of a strong enough cohesion to the local level in the rollers of SCHNEEBELI. The second perspective is the use of these experiences, the Thrust-Abutment, the biaxial tests or the modelling of fontis to wedge a software using the distinct elements in his/her/its modelling. It is about PFC2D (PFC for Particle Flow Code). Indeed, this software doesn't use the usual parameters to represent a soil, by example j, c and the different modules "œdométrique", "pressiométrique" and other, nor even the parameters characterizing a continuous environment: E, n, s,… While using spherical distinct elements, it introduces the notion of contact strengths. So to characterize the aggregation of particles used, it is necessary to use some parameters linked with difficulty to the features frequently employed. The comparison with a similar environment: the analogical material of SCHNEEBELI, permits to calibrate the parameters of the software thus therefore to value its possibilities to represent of a faithful manner the reality.
