geomicnics — Wikipedia
The geomechanics is the geotechnical mathematical tool; It synthesizes soil mechanics, rock mechanics, underground hydraulics and part of the seismic [ first ] .
During geotechnical studies to develop and/or exploit the terrestrial subsurface: project, build and maintain a work; Ensure the stability of an embankment or cutting slope, underground excavation, support, estimate that of a natural side; Avoid rupture and limit the compaction of a work foundation; estimate the flow of a well, a drain, a excavation to exhaust … We must pose geomechanics problems and solve them by calculation; They concern the deformation or displacement of the geomaterial, soil, rock and/or water, under the action of gravity with which specific efforts can be associated, induced by a natural event or by the implementation of the basement a construction site; They are generally loads of embankment or foundations, discharges of galleries or cuttings, hydrostatic or current pressures …
The geomechanics that are generally confused with geotechnics is its mathematical tool, necessary but insufficient; Geology – structural geology, geomorphology, geodynamics – and geophysics – electric, seismic – must indeed provide it with the models of forms, states and behaviors of the massifs of real geomaterials studied, which it needs to fix the initial conditions – States – and at the limits – The forms – of its analytical or digital calculations of schematic and frozen behaviors of virtual environments, applications of theories based on linear, deterministic “laws” – Hooke, Coulomb, Terzaghi, Darcy.
In geotechnical practice, geomechanics, geology and geophysics are inseparable, interdependent and complementary. The means of geophysical prospecting allow a “visualization” of the subsoil which specify the geological cuts – morphology and structure: the models of form obtained by seismic surveys and tomographies are essential for geomechanics to validate its specific models of calculations.
For the geomechanic, a soil is a furniture geomaterial whose mechanical parameters have low values; It can be an alluvial grave as well as an arrencated granite … It gives the word rock, on the other hand, much closer to common sense by calling rock a compact and hard geomaterial, whose parameters have high values. The state and the mechanical behavior of a soil essentially depend on its water content; Those of a rock, sound of alteration, cracking and fracturing.
The virtual environments manipulated by geomechanics are continuous, immutable, homogeneous, isotropic, free, sometimes non -heavy (without constraint); These are the models of natural, tangible, discontinuous, variables, heterogeneous, anisotropic, constrained, heavy …, reduced to a few characteristic parameters used in calculations. We can remember:
- Sols: furniture geomaterials, more or less rubbing and/or plastic whose cohesion is low. It decreases until it disappears (liquefaction) by increasing the water content.
- Characteristic parameters: density, water content, friction angle, cohesion …
- Roches: compact and hard geomaterials whose resistance to simple compression is greater than a few MPa. It decreases and/or disappears by physical alteration (hydration), chemical (dissolution) and/or mechanical (fragmentation).
- Characteristic parameters: seismic speed, elastic module, compression, traction resistances, shear …
The study of the mechanical behavior of furniture coverage formations, the floors, stands out for soil mechanics, the oldest, the best known and the most practiced in these disciplines because most geotechnical problems arise for implementation of these training courses during the construction of most suburface works; The mechanics of rocks are the adaptation to the studies of the mechanical behavior of more or less deep hard formations. The distinction of soil mechanics and rock mechanics that handle the same theories according to similar approaches is historic and practical: since the XIX It is century: soil mechanics with earthworks and building; Since the middle of XX It is Century: mechanics of rocks to large works – dams, galleries….
The study of the flow of water in the permeable subsoil under the effect of gravity and/or by pumping comes out of underground hydraulics.
These three disciplines have practically the same means of collecting field data – surveys, tests on-site (penetrometer, pressiometer …) and laboratory (eedometer, triaxial …), the same models of geometric or digital forms, very schematic – two dimensions, straight, circles …, built on local data, few and little Precise – Values of a few parameters supposed to characterize the virtual environment representing the geomaterial (density, angle of friction, cohesion, permeability …) – the same calculation methods – integration of very complex field equations of which, at best, we do not know than surface equipotentials. This imposes initial conditions and simplistic limits on more or less complicated, reduced calculations in fine To biunivocal formulas – to a single cause (effort, pressure, constraint, etc.) always strictly corresponds to a single effect (displacement, deformation, flow, etc.) -, the results of which are only orders of magnitude. Since XVIII It is Century, these results were successively obtained by graphic, then trigonometric, analytical and finally digital calculation methods that now, we use more or less jointly.
In practice, depending on the nature and structure of the subsoil of the site studied and from data obtained in the field and/or in the laboratory by geology, seismic, polls and tests, the approach of geomechanics consists of Build a geometric or digital form model, to be imposed in the virtual environment of which the behavior model corresponding to the geotechnical problem posed, then to apply the appropriate calculation method to obtain the expected result.
The form model must be simple enough for its mathematical manipulation to be convenient and effective: space is two dimensions in the plane of the main constraints; The figures are the sections perpendicular according to the axis of the average stress; The limits are generally right segments and arcs of circle, more rarely ellipse arcs, logarithmic spiral, cycloid …; The extension of the unlimited parts of the figures is infinite. The virtual environment is continuous, homogeneous, isotropic, free of constraints, confined, immutable, reduced to resistance parameters, permeability, compressibility … measured by more or less standardized tests on-site or on samples. The geomaterial is made up of mineral and water, among other things,; If we neglect water in its behavior, the environment is single -shaped; If it is not overlooked, it is biphasic.
His behavior model is generally a deterministic cause-effect relationship: an external mechanical action-force, pressure-produces a reaction of the model-displacement, deformation-and/or the environment-constraint, rupture, flow … In most cases, We calculate the greatness of the effect according to the “intensity” of the cause by a biunivia formula resulting from a theoretical integration calculation: the final static state is obtained that the form model reaches instantly from its state initial static. Thus, a geomechanical event is the instant effect of a timeless isolated action; It is determined by a “law” which forces action; Theoretically, it can be reproduced identically anywhere and anytime; The virtual environment in which it manifests itself is instantly transformed; He does not evolve.
The environments, the models of form and behavior of the geomechanics must be compatible with those of geology, but they cannot obviously not be: lithology indicates that the rocks are much more diverse and varied than the environments of geomechanics , reduced to three standard “floors”, furniture – sand (rubbing) and clay (plastic), possibly mixed in variable quantities – and hard rocks – whatever nature (elastic?); Structural geology and geomorphology indicate that the natural forms of rock formations can never be reduced to simple geometric forms: no geomaterial is homogeneous and isotropic, indefinitely identical to itself towards depth and laterally; The surface of the ground, a stratum, a flaw is never flat and never makes a constant angle compared to a horizontal or vertical mark; No fold is cylindrical …; Geodynamics indicates that the alterable geomaterial is not immutable, that it does not react instantly and in an agreed way to the various actions to which it can be subjected …
Thus, the strictly deterministic geomechanical approach leads well to a precise mathematical result, but to obtain it, it was necessary to schematize geological reality so that it has only a practical value of an order of magnitude; It is therefore reduced by means of a safety coefficient so that the work projected and built on its basis is solid, specific to its destination and the rest without suffering damage; In order not to oversize the work, this coefficient must be as small as possible, but we do not know how to achieve it by calculation; So there is always what Verdeyen called a Perlimpim powder.
By means of graphic curves of time-effects, the qualitative analysis of this complex behavior is possible but insufficient to obtain a particular result; To do this mathematically, we must analyze each stage of behavior – elasticity, plasticity, rupture – by means of an overly specific theory of a standard problem to be generalized without having to use complicated and poorly founded developments; Thus, in the current state of our knowledge but undoubtedly in essence, a unitary theory of geomechanics cannot be formulated: this is what most practitioners think (Collin, Fellenius, Terzaghi …), but not always The theorists (Poncelet, Boussinesq, Caquot …) who endeavored to achieve it, vainly so far, except perhaps Ménard with the theory of the pressom which actually only applies to the use of this device and the corresponding calculation method.
However, the fundamental theories of geomechanics are circumstantial: they were formulated independently of each other by their respective authors who were practical engineers to solve very specific technical problems posed by the design and construction of objects and/or New works, based on observations of phenomena which they supposed influential and on simple experiences, short durations, that geomechanics calls tests. The linear formulation of these theories is a schematization which corresponds to short definition intervals, because the means of experimentation and calculation of which they had did not allow more, and the relative simplicity of the works they had to build n ‘ did not demand more; They then facilitated the developments of theories; They always facilitate our practical calculations.
The tests that we do to measure the parameters of the materials in the basement of a site, on-site During polls or in the laboratory on samples are in fact experiences to validate these theories … whose results are not always very convincing, because the alignment of the representative points of the measures on a Cartesian lair is only obtained by more or less extensive smoothing.
The theories of elasticity (hooke), plasticity and rupture (Coulomb) apply in continuity to the deformation of a waterproof monophasic environment subject to an increasing effort; Thus, in the elasto-plastic model of Hooke/Coulomb, it successively undergoes an elastic deformation, a plastic shift and rupture. The theory of consolidation (Terzaghi) applies to the deformation of a permeable biphasic environment subject to a constant effort. The theory of underground hydraulics (Darcy) applies to the flow of water in a permeable indeformable environment subjected to a pressure gradient.
Elasticity [ modifier | Modifier and code ]
The geomechanical theory of elasticity is based on the law of Hooke, proportionality of the effort ratio (c)/deformation (d) expressed by the module of young (e) of the environment, constant if the maximum increasing effort is quite low For the deformation to be strictly reversible when it decreases: E ≈ C/D.
It can be applied to certain mechanical behaviors of soils and rocks; In particular, for foundations and galleries, we always try to ensure that under the effect of the loads that are imposed on it, the deformations of the geomaterial do not come out of the elastic domain.
Without giving a clear definition, the geomechanics apply it to a pseudo-elastic environment and define as many “elastic” modules among themselves and the Young module, as test devices and calculation methods of which they have, which can lead to dangerous practical confusion. Several tests make it possible to measure such modules; the test on-site the pressiometer is the most common and the simplest of them; In the laboratory, you can use simple compression or triaxial.
It also applies to the propagation of seismic waves which impose low constraints on a massif of geomaterial, characterized by its speed (V).
Plasticity and rupture [ modifier | Modifier and code ]
The theory of plasticity and rupture is based on the law of Coulomb; It concerns more particularly of the mooding, single-mansic, materials.
Coulomb has established the linear formula allowing to predict the breaking by shear of a geomaterial furniture under the combined effect of a traction (t) and a compression (n): t = c + n*tg, in which C (Cohesion) and φ (angle of friction) are the constant parameters characteristic of the material and its compactness-in fact, C and φ depend on N and the curve representative of this function is half the so-called intrinsic curve of the material that ‘We convert to the right by smoothing. If the representative point (m) of the state of the material characterized by a couple C/φ is located under the curve, C and φ are virtual, the material is elastic; If it is on the curve, it is at its limit of adhesion beyond which at the same time arises the shift and occurs the rupture; If it is above the curve, C disappears and a part of φ persists, it slides plastically.
Theoretical calculations can only use purely rubbing environments whose cohesion is zero or purely coherent environments whose friction angle is zero; Obviously, there are not such real geomaterials. In practice, if it is small in front of n*tgφ, the material is said to be rubbed; If it is large, the material is said to be cohesive. If it is very large, Coulomb’s law is no longer relevant; We characterize the hard and brittle material – rocks and resistant floors – by its resistance to simple RC compression, practical parameter very easy to measure by means of a simple press; We admit that RC ≈ 2 tsp.
Several tests of field and laboratory make it possible to measure the cohesion and the friction angle of a geomaterial. In the laboratory, depending on whether or not compact the material of the test pieces, whether we load it more or less quickly and that we drain or not, we carry out more or less consolidated (C), drained (D) tests (D) , slow that give different C/φ couples respectively: CD (consolidated, drained or slow), Cu (consolidated, not drained or rapid), Uu (not consolidated, not drained or rapid), u; In practice, it is poorly controlled the testing of the test, a more or less drained and consolidated material, more or less slow effort. The shear test at the Casagrande box is the most common and the simplest; It gives generic C/φ couples -CD or UU -, largely sufficient for current applications; The triaxial test allows you to carry out all types of tests; The manipulations are very long, very complicated and the results obtained are rarely necessary in practice.
The consolidation [ modifier | Modifier and code ]
The theory of consolidation was proposed by Terzaghi; It concerns sablo-clay materials biphasic furniture.
Under the constant action of its own weight in the nature or that of an external load, such a material is more and more consolidated as time passes: its index of the voids and its water content decrease, its density and its mechanical resistance increases, its permeability decreases; The natural phenomenon is the mechanical part of the diagenesis which transforms the sediments furnished into sedimentary rocks on a geological time scale; The phenomenon induced by a vertical external load as the weight of a structure is a compassionate on a human scale. Conversely, if the action is a discharge, the index of the gaps and the water content of the material increases, its density and its mechanical resistance decrease; The natural phenomenon is the mechanical part of the alteration which transforms hard rocks into furniture alteritis; The induced phenomenon is swelling – cutting slope, excavation background, gallery walls…; Under certain conditions, the geomaterial can alternately tasting by drying out and swelling by hydrating.
The deformation is said to be pseudo-elastic: the stress/deformation ratio is not constant as the young module of linear elastic behavior; It depends on the interstitial pressure and its variations which depend on the permeability of the material; The duration of the settlement but not its value also depend on permeability. To be able to deal with the constraint/deformation of the primary settlement by means of a biunivia formula facilitating application calculations, Terzaghi has defined a curious constant, the CC compression index which binds the index of voids to the logarithm Decimal of the effective stress σ ‘: CC = -δe/δlogσ’ and to treat its deformation/time relationship, it defined another constant, barely less strange, the CV consolidation coefficient; They are measured by means of eedometer in which the leaflet, saturated and drained is subject to an increasing axial effort and then decreasing by levels whose durations are adapted to the responses of the material.
Underground hydraulics [ modifier | Modifier and code ]
The theory of underground hydraulics is based on Darcy’s law; It stipulates that in a permeable material, the flow speed V (q/s) and the hydraulic gradient I (ΔH/L) are linearly linked by an empirical and composite constant, permeability k – v = k*i – which would only depend on the aquifer material; In fact it is a parameter that synthesizes the specific influences of many characters of the material to which it is attributed – granulometry, nature and shape of grains, compactness, structure … – and fluid that circulates there – nature, viscosity, temperature , chemical composition… ; Among other things, it can vary by consolidation, clogging, breakage … of the material.
Permeability has dimensions [L.T −1 ] but not the nature of a speed; V is not the effective speed of flow of water in the material but a convenient abstraction to replace in tensorial calculations the ratio Q/S, quantity of water which passes through the surface unit of material perpendicular to lines current, in the unit of time.
You cannot take “intact” samples from inexpensive and permeable materials such as alluvial, or fragile sands and serious, like cracked rocks; Permeability can only be measured there by means of testing on-site , Lefranc tests and pumping trials in the first, sledge tests in the latter. The permeability of fairly consistent and not very permeable materials such as more or less sandy clays, is measured in the laboratory by means of variable load permeameters as a fitted eedometer, generally during a consolidation test. During a test, the stabilized flow rates corresponding to successively increased loads are measured; We then draw the flow/load diagram, a straightened line whose slope measures permeability.
These theories have been developed to facilitate the resolution of standard problems by means of graphic and/or analytical methods relatively simple to use; It could only be done by multiplying the simplifying hypotheses; The simplest methods require the most and must therefore be used with circumspection to solve practical problems.
Most geomechanical formulas have very complicated, often trigonometric expressions; In practice with paper and a pencil, it was impossible to use them without risk of error and check their results; This is the reason why many partial abacks and tables have been established and are always used, although now we can do these calculations automatically without risk of error – except data … by checking the result Using the corresponding abacus.
Geomechanics manipulates quantities which, under different names, have the same dimensions – strength, weight, effort, load, push, stop: [M.L. −2 ] – Pressure, stress, module, cohesion, unitary resistance: [M.L −1 .T −2 ] … To make homogeneous certain formulas that use them, it often introduces more or less mysterious “coefficients of shapes”.
The Hooke/Coulomb elasto-plastic model [ modifier | Modifier and code ]
The theories of elasticity (hooke), plasticity and rupture (Coulomb) apply in continuity to the deformation of a single-shaped medium subjected to an increasing effort which, in the elasto-plastic model of Hooke/Coulomb , successively undergoes elastic deformation, plastic deformation, rupture and shift.
In practice, we separate studies of deformation of rupture studies. Indeed, reaching the limit state of service of the geomaterial is unacceptable, because a plastic deformation of this material can lead to serious damage if not the ruin of works poorly suited to undergo it and which would thus be beyond their ultimate limit state ; It is the application of a safety coefficient to the result of the calculation which in principle allows that the geomaterial-operating set is in “elastic” condition.
Elastic balance [ modifier | Modifier and code ]
Boussinesq has calculated the stresses and displacements in an elastic, semi-infinite, without initial and therefore not weighing environment, limited by an infinite plane, subject to an external effort. For the effect of a punctual load, perpendicular to the surface of the medium, it has established a fairly complicated formula, but the geomechanics generally need to know that the maximum normal stress Δz to ensure that it is lower at the limits of elasticity and/or rupture of the geomaterial and to calculate the compaction according to the theory of consolidation; We simplify this formula by means of a dimensionless I influence coefficient that is found in the form of a table or abaque in the works of soil mechanics; More simply, we can admit that at increasing depths, the effect of the load is regularly distributed over surfaces which grow at a more or less arbitrary pyramid angle, without resulting in large practical differences.
Newmark’s graphic integration process establishes the influence of a rectangular load vertically from an angle of a rectangle: the value of the influence coefficient I to a given depth depends on this depth and dimensions of the rectangle ; It is obtained by tables and/or abacus; We calculate the influence of any load on any surface by summons of the influences of rectangles; This process is well suited to digital calculation.
Various authors including Fröhlich and Westergaard have proposed formulas supposed to improve that of Boussinesq; They are even more complicated without overall, their practical results being better, because they are based on the same general simplifying hypotheses and on additional specific assumptions.
Plastic balance [ modifier | Modifier and code ]
The study of the plastic balance of a furniture material is based on the application of Coulomb theory to define the adhesion limit of the material on the rupture surface. The determination of the position and the shape of the rupture surface, that of the distribution and the value of the constraints on this surface are the mathematically insoluble problems, or at least which can only receive particular solutions, based on hypotheses more or less realistic simplifying calculation; The massif is limited horizontally by a base and a free surface, vertically by a rigid screen or an embankment; It consists of a homogeneous, isotropic and invariant material; It is subject to the action of gravity and/or external force; The plastic deformation of the material before rupture is neglected; The rupture surface is a regulated surface whose position is not known in the massif; perpendicular to the plane, the width of the rupture surface is infinite; The massif in which the rupture occurs was originally in balance; The inertia does not intervene in the process: the rupture is general, instantaneous; The slipped materials disappear without participating in the new balance of the massif, now limited to the rupture surface, the trace of which in the plane of the figure is a right segment or a circle arc.
The flow of water in a permeable environment [ modifier | Modifier and code ]
In a permeable environment, the flow of water is supposed to be governed by Darcy’s law within the framework of the theory of general hydraulics; The analytical resolution of any permanent underground flow problem is in principle possible but rarely simple; It is barely better in digital calculation; We therefore prefer to solve the flow/fedding problems which often arise and which lend themselves to it, by means of methods like that of Dupuit, the simplest and the most convenient to calculate the permanent flow of elementary exhaustion works, trenched Draining, well … depending on loss of loads in areas and for simple limits. The devices of complex works are modeled as large simple works. Transitional flow problems are treated in Theis’s method.
The geomechanical problems that a geotechnician may have to resolve are countless: no site, no work, no situation is identical or even analogous to another; Here are those that are most often encountered and whose solutions in principle are the easiest to obtain.
Stability of slopes and defense walls [ modifier | Modifier and code ]
The stability of a natural slope, that of the walls of an excavation or a “earth” dam, poses the problem of the stability of an embankment, possible support and drainage. It can be resolved analytically by the method due to Rankine of the critical height of the embankment – height beyond which a given slope is potentially unstable – and/or the corner of Coulomb, or graphically and digitally by the method due to Fellenius improved by Bishop slices or safety coefficient on shift.
The analytical calculations which flow from these methods imposed many simplifying hypotheses but remained very complicated; Computers now makes it possible to take into account all the elements of the balance of forces acting on the model, including permanent water flows or not, existing or projected works, the most perfected defects … Digital software with distinct elements, often using the screen to improve the solution by subjecting to the form of successive deformations under the formation model according to the conditions imposed on it; There are many sources of data and/or calculation inaccurate; It is therefore prudent if not obliged to validate the software used in a given case and to criticize the results which it provides to which a safety coefficient is applied that is often minimized for reasons of site savings; It is with rigor acceptable for a preliminary draft or for the very short term, but not for the long term or if a possible shift is likely to jeopardize a neighboring work and/or A stronger , a human life.
Foundations [ modifier | Modifier and code ]
The choice of the type of foundations of a work – superficial (shooting soles, isolated soles, raft), semi -projection (well), deep or special (anchored piles, floating piles) – Pose of specific geotechnical problems of foundation rupture and of stability of work with clashes, both geological (nature of the geomaterials, structure of the site of the site …) Geomechanics (model of shape, parameters of environments …) and constructive (implantation, architecture, structure, etc.).
The movements likely to affect foundations are elastic or consolidation cups, swelling, plastic breaks, – switching, punching or shifts; We have to accommodate cuts; swelling can be avoided; It is essential to avoid breaks; These phenomena are obviously closely linked in practice, but geomechanics only knows how to treat them independently. In fact and contrary to what is generally believed, the stability of the works on the cuts takes precedence over the risk of rupture of their foundations, because if the first is assured, the second is almost surely – what it Obviously must be checked.
What is called the admissible constraint or pressure of a foundation is that which is deducted from the ultimate load calculable by the means of the geomechanics by reducing it by a safety coefficient (1/3 in general) – To do more seriously without more practical efficiency, we are now talking about a semi-probabilist method of justification of work according to Eurocode 7; This load depends on the mechanical characteristics of the seat geomaterial, the calculation method, the shape, the surface and the depth of the foundation …
The case of superficial foundations is the most common in practice:
From the laboratory tests, the rupture calculations are based on extensions of Coulomb theory and the parameters measured at the Casagrande Box or the Triaxial: the Rankine/Prandtl method allows the calculation of the ultimate load q of a superficial foundation by considering it as the sum of a term of depth and a term of surface; Terzaghi proposed a ” Approached method »Taking into account cohesion. Those of cuts are based on Terzaghi’s theory and the parameters measured with eedometer applied to elastic balance according to the Boussinesq method.
According to Ménard’s theory from the pressing test, the rupture parameter is the limit pressure; That of the compaction is the pressing module.
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We study the extraction of groundwater in a massif made up of permeable aquifer material to operate it by pumping in a well or drilling or to dry out a excavation whose bottom is under the level of the tablecloth.
In practice, there is a problem with the flow/demerits relationship in a given work and situation; The parameters used are the flow gradient which is easily measured from a network of piezometers established around the extraction point and the permeability coefficient of the massif aquifer which is measured correctly only on-site , by tests Lefranc. The Dupuit method is the simplest and most convenient to solve this problem. The result is an order of magnitude that must be specified by a pumping test in a test well.
We can remember from all that precedes that geomechanics is an essential collection of recipes whose mathematical rigor is purely formal.
Words stability and balance of static describe the state of sites and/or works, seats and/or objects of obviously dynamic travel: geomechanical calculation indicates that such a slope of height and slope data, made up of a furniture material density, water content, cohesion and angle of friction given, is stable; The geological observation of its site leads to doubt it; The embankment is apparently stable, sometimes for a long time: the calculation was right; A shift occurs, often following a thunderstorm: the observation was not misleading; The calculator had forgotten or ignored that between the time, the rock would alter: at the time of the shift, the values of the density, the water content, the cohesion and the friction angle of the material were no longer Those used for calculation, and the behavior model did not allow the natural variability of these mathematical constants by alteration of the material; with constant geometry, it can be estimated by iteration the values of the parameters corresponding to a possible shift; But we will not know how and when they may be reached. The geological criticism of the geomechanical result is therefore always necessary.
: document used as a source for writing this article.
- A. Caquot & J. Kerisel – Treaty of soil mechanics – 4 It is Edition (1966) – Gauthier -Villars, Paris.
- R. L’Herminier – Soil and road mechanics – (1967) – Dissemination of construction techniques, Paris.
- F. Homand, P. Duffaut et al. – Rock mechanics manual – T1, foundations (2000) – T2, applications (2005) – Press of the School of Mines, Paris.
- G. Schneebeli – Underground hydraulics – (1987) – Eyrolles, Paris.
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