**A SYSTEM FOR THE PREDICTIVE SAFETY CALCULATION**

CAPPARELLI, Giovanna (Via Catania snc, Montalto Uffugo, 87046, IT)

DE LUCA, Davide L. (Corso Marco Polo 7, Rende, 87036, IT)

LA SALA, Gabriella (Via Livorno 11, Policoro, 75025, IT)

ZAFFINO, Thomas (Via Volterra 29, San Giovanni in Fiore, 87055, IT)

VENA, Mirko (Via Salerni snc, Montalto Uffugo, 87046, IT)

DONATO, Antonio (Via Palmiro Togliatti 13, Pianopoli, 88040, IT)

TRONCONE, Antonello (Via Mosca 21/A, Rende, 87036, IT)

**E02D1/02**WO2012160429A1 | 2012-11-29 |

US20140129198A1 | 2014-05-08 |

CLAIMS 1. A system (1 ) for the predictive calculation of a safety factor (FS) associated with a predetermined spatial portion of land, which system (1 ) comprises: - at least a first database (3) of rainfall data related to estimated values of rainfalls on the portion of land in a future time interval; - one or more remote sensors (2) apt to detect input data relating to hydrological, hydraulic, geological, geometric, location and time parameters associated with the portion of land and/or one or more databases (2') of such data; - a central unit (4) for processing said input data and rainfall data, said central unit (4) being in communication with at least one of said one or more sensors (2) and/or one or more databases (2') and said at least a first database (3), and further comprising: • a pre-processor (A) programmed for: o acquiring data from said sensor/s (2) and interfacing, possibly, with said one or more databases (2'); o processing the precipitation data from said first database (3); o generating the input files in the format required by a solver (B) to solve the analysis problem; • a solver (B) apt to simulate a response of the portion of land as a function of a given hydraulic load, programmed for: o building a hydrological model relating to the circulation of water within the portion of land as a function of said input data; o calculating the water content in the subsoil by returning the trend of pore pressures due to the effect of a pluviometric forcer, under conditions of total and partial saturation; o estimating the water content in the subsoil under the action of future trends of rainfall patterns; o building a geotechnical model of the portion of land related to tensions, deformations and displacements of points of the portion of land parameterized with respect to the hydraulic load acting on each one of said points; o calculating future tensions of the points of the portion of land under the application of a future hydraulic load; o calculating the threshold tensions of the points of the portion of land corresponding to a displacement/limit strain of said portion of land; • a post-processor (C) apt to process and plot the results obtained from simulations carried out with the above models, programmed for: - a safety factor (FS) of the portion of land associated with said future time interval as a function of a combination between said threshold tensions and said future tensions under the application of said future hydraulic load. 2. The system (1 ) according to the preceding claim, wherein said combination is a ratio, and said safety factor (FS) increases with the increase in said ratio. 3. The system (1 ) according to one of the preceding claims, comprising an interface element (5) in communication with said central unit (4), configured to allow the display of a graphical representation of said hydrological and geotechnical models and of the results of said simulations. 4. The system (1 ) according to the preceding claim, wherein said interface element (5) is configured to allow an operator to modify and/or select said input and rainfall data. 5. The system (1 ) according to claim 3 or 4, wherein said interface element (5) is remote with respect to said central unit (4). 6. A method apt to be implemented by a program to process the calculation of a safety factor (FS) associated with a predetermined spatial portion of land and which comprises the steps of: - providing one or more databases (2') of input data relating to hydrological, hydraulic, geological, geometric, location and time parameters associated with points of the portion of land and/or acquiring said data from one or more sensors (2) apt to the their detection; - providing at least one database (3) of rainfall data related to estimated values of rainfalls on the portion of land in a future time interval; - building a hydrological model relating to the circulation of water within the portion of land as a function of said input data; - calculating the water content in the subsoil by returning the trend of pore pressures due to the effect of a pluviometric forcer, under conditions of total and partial saturation; - estimating the water content in the soil under the action of future trends of rainfall patterns; - building a geotechnical model of the portion of land related to tensions, deformations and displacements of points of the portion of land parameterized with respect to the hydraulic load acting on each one of said points; - calculating future tensions of the points of the portion of land under the application of a future hydraulic load; - calculating the threshold tensions of the points of the portion of land corresponding to a displacement/limit strain of said portion of land; - estimating the factor of safety (FS) associated with the interval of prediction as a ratio between the threshold tensions and the relative tensions under the application of said future hydraulic load. 7. The method according to the preceding claim, comprising the phases of validation of said hydrological and geotechnical models. |

DESCRIPTION

Technical field of the invention

The present invention relates to a system and method for the analysis and evaluation, even in predictive way, of the conditions triggering landslides of a monitored area.

Background

The problem of hydrogeological instability is more and more frequent and it causes dangerous phenomena such as landslides or landslips even in areas historically not affected by the problem. This because deforestation and urbanisation with no control made the slopes vulnerable to the action of the atmospheric agents. When it rains, for example, if the side of a relief has not an adequate wooded cover, it runs the risk of being subjected to water infiltrations which in the long run can cause a detachment or sliding at least of the most superficial layers of the land. If the infiltrations go deep and the type of land of the considered area is particularly suitable to the occurrence of such problems, the phenomenon of the detachment of land from the slope can assume important proportions, by determining a serious problem from the environmental point of view.

Moreover, as it often happens, if building constructions have been erected on such slope the hydrogeological instability is amplified since the land is burdened even by the load of the constructions, and in this case there is the possibility of danger for human lives.

Then there is the need for monitoring constantly, in real time, the hydrogeological status of the territories potentially at risk.

Summary of the invention

The technical problem placed and solved by the present invention is then to provide a system and a method for calculating the instability of a slope, allowing to obviate the drawbacks mentioned above with reference to the known art.

Such problem is solved by a system according to claim 1 and by a method according to claim 6.

Preferred features of the present invention are set forth in the depending claims.

The proposed invention provides a system and a method which can be implemented by means of such system for analysing, simulating and predicting instability phenomena of the sides, in particular depending upon the variations in the pressure regime in the subsoil. The aim is to monitor the stability of the same in order to predict possible phenomena of hydrogeological instability.

The new aspect consists in implementing a tool capable not only to solve numerically the complex relationships underlying the physical phenomena under analysis, but at the same time arranged to integrate and interface with monitoring accessory tools, preferably in real time, or to connect to preferably constantly updated databases.

Such accessory tools can include a complete in situ monitoring system (meteorological stations, pluviometers, etc.). According to such embodiment, the system allows to process continuously the overall status of the slope under analysis, preferably in real time, by acquiring predicted rainfall data, by further providing the possibility of predicting a potential event scenario through estimated data.

Then, according to a first aspect, the invention provides a system and method for the hydrogeological monitoring of an area, such as a sloping land, subjected to circulation of water, for example due to rains. According to an additional aspect, the invention provides a system and method for the automatic calculation of a safety factor (FS), based upon data related to the area to be monitored.

Advantageously, as said before, the data can be detected in real time by using accessory instrumentation.

Moreover, according to a particularly advantageous aspect of the invention, the safety factor can be calculated in predictive way, based upon the probable values of rainfalls estimated in a future time interval.

Other advantages, features and use modes of the present invention will result to be evident from the following detailed description of some embodiments, shown by way of example and not for limitative purposes.

Brief description of the figures The figures of the enclosed drawings will be referred to, wherein:

- figure 1 shows a preferred embodiment of the invention system;

- figure 2 shows an example of discretization of the domain (studied portion of land) by generating mesh;

- figure 3 shows an example of graphical representation of an initial condition of hydraulic load acting on the domain;

- figure 4 shows a preferred operating scheme of a pre-processor A according to the present invention;

- figure 5 shows a preferred analytical mode for solving the equation controlling the water filtering motion in the domain land; - figure 6 shows schematically preferred equations constituting the mathematical algorithm for solving a geotechnical module (MG) according to the present invention;

- figure 7 shows a flow chart of a preferred operating mode of a post- processor C according to the present invention;

- figure 8 shows an exemplifying graphical representation of the trend of a related hydraulic load in the domain;

- figure 9 shows an exemplifying graphical representation of the trend of an absolute hydraulic load and of pressure surface contours in the domain;

- figure 10 shows an exemplifying graphical representation of the trend of the relative hydraulic load upon varying the domain depth;

- figure 1 1 shows an exemplifying graphical representation of the trend of the relative hydraulic load by abscissa, at a predetermined domain depth;

- figure 12 shows an exemplifying graphical representation of a hydraulic situation and of the overall safety factor of the domain in real time, together with related predictions after 3, 6 and 12 hours; - figure 13 shows an exemplifying graphical representation of all future trends of the precipitations generated by the invention system.

Detailed description of preferred embodiments

A first preferred embodiment of the invention system is represented schematically in figure 1 , wherein it is designated as a whole with 1 .

The system 1 is configured to perform a predictive calculation of a safety factor associated with the risk of triggering landslides in a predefined spatial portion of land. Under "triggering of landslides" the detachment of at least a part of said portion from the surrounding land is meant. By going more in details, the system of the invention is apt to perform an analysis of the instability of a portion of land upon occurring landslide phenomena due to a variation in the regime of pressures in the subsoil, in particular due to meteoric effects.

Apart from predicting possible landslide triggering phenomena, an additional object of the system 1 is to monitor the stability of portions of land potentially at risk, such as for example slopes and sides.

To this purpose, the system 1 comprises one or more sensors 2 (pluviometers, piezometers, TDR, tensiometers, clinometers, etc.) apt to detect information related to hydraulic, geometrical, geotechnical, etc., quantities associated with the portion of land to be monitored and/or to be analysed. Alternatively or in combination with at least a sensor 2, the system 1 can comprise one or more databases 2' of such data.

Furthermore, the system 1 comprises at least a first database 3 of rainfall data, that is data related to estimated/predicted values of the rainfalls on the portion of land in a future time interval.

The system core is constituted by a central unit 4 for processing said input data and rainfall data, which is in communication with at least one of the above- mentioned remote sensors 2 and/or database 2' and first database 3.

In particular, the central unit 4 is configured to receive data from the sensors/database. According to additional embodiments of the invention, the central unit 4 can be further configured to send signals related to control instructions to said sensors, in particular turning-on signals, turning-off signals, start and end time of detecting the parameters therefor said sensor is devised.

The central unit 4 comprises sub-units or processors such as pre-processor A, a solver B and a post-processor C. It is possible to divide the procedure for processing data of the central unit 4 in three main phases, each one followed by one of the so-called sub-units - shown by way of example in the block diagram of figure 1 - each one thereof implemented by one of the just mentioned components. Each phase is performed autonomously and consequentially by the different sub-units of the central unit 4, even without requiring the intervention of a user or outer operator.

In general terms, the pre-processor A is programmed for:

- acquiring data from the sensor 2 and interfacing, possibly, with the database 2'; - processing the precipitation data from the first database 3; - generating the input files in the format required by the solver processor B to solve the analysis problem.

The solver B is apt to simulate a response of the portion of land as a function of a given hydraulic load, in particular it is programmed for:

- building a hydrological model relating to the circulation of water within the portion of land as a function of the input data;

- calculating the water content in the subsoil by returning the trend of pore pressures due to the effect of a pluviometric forcer, under conditions of total and partial saturation;

- estimating the water content in the subsoil under the action of future trends of rainfall patterns;

- building a geotechnical model of the portion of land related to tensions, deformations and displacements of points of the portion of land parameterized with respect to a hydraulic load acting on each one of the points;

- calculating future tensions of the points of the portion of land under the application of the future hydraulic load;

- calculating the threshold tensions of the points of the portion of land corresponding to a displacement/limit strain of the portion of land.

The post-processor C is apt to process and plot the results obtained from simulations carried out with the above models, programmed for:

- displaying a safety factor FS of the portion of land associated with the future time interval as a function of a combination, in particular of a ratio, between the threshold tensions and the future tensions under the application of the future hydraulic load.

Moreover, the system 1 , the present invention relates to, can comprise an interface element 5 in communication with the central unit 4, configured to allow the display of a graphical representation of the hydrological and geotechnical models of the spatial portion of land of interest and of said results obtained from the simulations of the response of the portion of land at a predetermined hydraulic load applied thereto.

The interface element 5 preferably is configured to allow an operator to modify and/or to select the input data and the precipitation data which will be processed by the sub-units A, B, C.

Moreover, the interface element 5 can be remote with respect to the central unit 4, connected thereto by means of Internet connection or connections of other type, even wired, to allow the operator to manage the system even remotely.

The phases for processing data, implemented by the sub-units A, B and C will be described in details hereinafter, and mathematical examples of a preferred implementation thereof will be illustrated.

The pre-processor A is programmed in particular to perform an activity for preparing and implementing data entering the central unit 4 (Pre-processing). This activity consists in acquiring input data (data related to the system geometry, hydrological and mechanical parameters, boundary and initial conditions) and in coding such data for writing files requested to solve the problem under analysis by means of a calculation code. The so manipulated data will be used to build a model of the portion of land under analysis.

As anticipated, these data can derive from databases of various origin, from sensors or in situ instrumentation, then is it necessary to process such data to make the format thereof coherent with the data requested by the model.

Operatively, as far as the pre-processing phase implemented by the preprocessor A is concerned, the device allows an immediate management of the analysis domain by defining the geometry and the hydrological-hydraulic and geotechnical parameters necessary to define the problem completely. As far as the geometry is concerned, it is preferable to know:

• the section of the analysis domain, defined through the coordinates of the vertexes delimiting the contour thereof;

• the sequence of the several layers of land and the extension thereof, through the coordinates of the vertexes delimiting the single contours. As far as the hydraulic-geotechnical parameters are concerned, for each layer it is possible to know, for example:

• the specific weight of the land [γ];

• the coefficient of permeability to saturation [Ksat]; · the content of water to saturation [ds] and residue [&r];

• the coefficient of specific storing [Ss];

• the expression of the characteristic curve and the related parameters;

• the friction angle [φ'] and the cohesion [C] of the land;

• the module of longitudinal elasticity or Young module [E] and Poisson coefficient or coefficient of side contraction [v] of the land.

A numeric example of such parameters is shown hereinafter in Table 1 , wherein in particular even the values of m, n, a of the characteristic curve are shown, in this case of Van Genuchten.

The central unit 4 allows the user different modes for inserting the input data (ex.: manual by means of the specific element or device of user interface 5, from graphic files in ".dxf format, from suitably formatted text or XML files, etc.). In order to allow to manage significant amounts of information and to work for persistent time, the device is devised so as to separate logically and physically the application procedure from the data management, but providing indeed two distinct sub-units apt to the implementation thereof.

The subsequent phases are implemented by means of the solver B and the post-processor C. Such phases provide the building of a model of the monitored portion of land and a simulation (processing) of the response of such model of the portion of land under the action of the loads applied thereto. During this phase, the process for validating (calibrating and checking) the implemented model is also preferably performed. In fact, preferably in this phase the numeric solution of the complex mathematical relationships, underlying the physical phenomena connected to the filtration motions and the consequent problems of stability of the portion of land, is carried out. Generally, it is provided that the solver B comprises two models for processing the data for implementing the analytical process, preferably a first hydrological module Ml capable of modelling the circulation of water in the subsoil under conditions of total and partial saturation, and a second geotechnical module MG capable of defining the response in terms of slope stability and deformations. In particular, the hydraulic and geotechnical models work with the uncoupled approach pore pressures-deformations and tensions in the solid skeleton. The second module then allows to distinguish the scenarios which could determine the conditions for triggering a landslide. Moreover, if requested, the analysis can be provided with a study of the future development of the phenomenon based upon probabilistic scenarios of rains, through a module of stochastic generation.

The post-processor C manages the displaying of the results (Post-processing): it consists in processing, displaying and showing the results of the modelling implemented by means of the solver B.

The post-processor C can support different application programs for managing and displaying the results. The graphic interface is customizable and it allows the user to display the information of interest and to isolate the quantities related to the most significant domain areas. In particular, the post-processor C is programmed for:

- displaying the generated mesh, with detailed information related to the nodes and elements, both under starting condition and deformed condition;

- obtaining punctual information related to the measured quantities (hydraulic load, pore pressure, tensional and deforming status, shiftings);

- consulting the graph of the time trends of the same with respect to predefined control points managed by the user;

- diagramming the trend in time of an overall safety factor of the slope in order to know exactly the level of stability of the same; - displaying the future criticalities, in terms of distribution of the pore pressures, of the overall safety factor, of shiftings and of the stress-strain states, thanks to the module for generating future rains.

Each one of the single components of the device will be now described with greater detail in order to define the adopted implementation mode thereof. By way of example, in figure 4 the operating scheme of the pre-processor A is synthetized.

The acquisition of the geometry related to the domain under analysis (A1 ) preferably takes place by reading a file in ". DXF" format (compatible with AutoCad) or in ".TXT" format (compatible with GiD exporting format), wherein the vertexes are suitably shown characterizing the limit of the portion of land which coincides with the analysis section (domain), apart from those which detect the various layers thereof the section is constituted.

The geotechnical and hydrological parameters (A2) of each layer can be acquired by means of suitably formatted text file or XML file, and they can be introduced through the interface element 5 too. In particular, apart from the total number of the layers constituting the domain, even other parameters can be acquired (or defined).

Table 1 shows, with wholly exemplifying values, the list of the considered parameters. Table 1 .

ID 1 2 3

Ksat [m/min] 0.0019200 0.0600000 0.0019200

ΘΓ [-] 0.140 0.230 0.140

6s [-] 0.550 0.820 0.550 a [1 /m] -0.606 -5.000 -0.606 n [-] 1 .600 1 .710 1 .600 m [-] 0.380 0.420 0.380 Ss [1/m] 0.00000 0.00000 0.00000 φ' [°] 27.0 18.0 27.0 c' [kPa] 0.0 0.0 20.0

Y [kN/m ^{3 }] 19.0 20.0 20.0

E [MPa] 7000.0 7000.0 20000.0 u [-] 0.30 0.30 0.3

Once acquired the geometry and the hydrogeological features of the analysis domain, the software allows to obtain a discretization of the domain area (A3), in order to be able to solve thereon the mathematical equations in discrete form. An example of the domain discretization by means of mesh generation is shown by way of example in figure 2.

Before the data processing, it is possible to establish a series of control points (A4), therefor graphs are to be obtained, describing the trends of the considered quantities both in time and in space. The controls can be punctual (series of precise points thereof one wants to know the time trend of a quantity, for example of the hydraulic load) or to provide the definition of vertical profiles therefor it is possible to obtain the trend of one quantity (for example the hydraulic load) in a determined instant, depending upon the distance from a reference or depth point.

The last prerequisite to the processing phase is the generation (through suitable algorithm) or the acquisition from file (resulting from a previous processing) of the initial condition of the hydraulic load (A5). A graphical representation of the initial condition of hydraulic load acting on the portion of land or considered domain is shown by way of example in figure 3.

Figure 5 shows schematically a preferred analytical mode for solving the equation controlling the filtration motion, the analysis thereof is at the basis of the operation of the hydraulic module Ml.

The method implemented by the hydraulic module Ml, and preferably managed autonomously by the system 1 , is responsible for simulating the circulation of water in the slopes, controlled by Richards equation, by identifying the distribution of the pore pressures due to the effect of a pluviometric forcer.

By referring to figure 5, a description of each one of the preferred steps implemented by the hydraulic module Ml of the solver B is illustrated hereinafter:

- B1 ) Richards equation, in the preferred formulation used by the code, is obtained by the combination of the mass conservation equation with Darcy- Buckingham motion equation. Its solution allows to analyse the phenomena occurring under not stationary conditions and it returns the water content in the subsoil and the trend of pore pressures due to the effect of a pluviometric forcer, in wholly or partially saturated lands. The above-mentioned was applied even to very complex situations by stratigraphy and hydraulic features.

The infiltration analysis is mathematically described by means of an equation at the partial derivatives with highly not linear character, the numerical solution thereof becomes even more complex in case of particularly heterogeneous lands, variable boundary conditions and irregular domains.

- B2) Richards equation is solved by preferably applying the Finite Element Method. Inside each element the solution is represented by means of a small number of punctual values (nodal unknown quantities) and a low-degree polynomial used for interpolation. This allows to transform the continuous differential equation describing the problem in a discrete system of equations. The first step in solving the problem to the finite elements consists then in defining the shape of the element and in settling the shape functions Nj characterizing it. In the case under examination, relatively to a bidimensional domain, one chose to work with 4-node quadrangular finite elements and an interpolation function of the unknown quantity of bilinear type was used.

- B3) The discrete matrix formulation of Richards's equation is obtained by applying FEM formulated by means of Galerkin method. The latter represents a particular case of the Method of Weighted Residuals and it

L(f(x,y, z,t)) establishes that the residual error with: produced by the function and weighed by means of the same shape functions defining ψ, is minimized for each node so as to form an algebraic system (matrix form) equivalent to the starting differential function.

B4) The proper boundary conditions have to be imposed on the whole domain boundary and they can be numerically represented according to what defined in B4 respectively by means of assigning the value assumed by the unknown variable in the border points of the domain itself or by assigning the flow value so as to be able to contemplate the different possible cases and to make the model versatile.

B5) From applying Galerkin method for the formulation of Richards equation in discrete form, the expressions of the matrixes [P ^{e }] and [G ^{e }] of the element:

[G ^{e }] = {C _{su } (ξ, ιύ ΝϊΝ] ζξ, η) \} άΩ.

νεΐξη are obtained.

The outer forcer is represented by the rain event or by the different rain scenarios which one wants to simulate. Inside the analysis, such phenomenon is perceived by imposing a boundary condition imposed along the line for separating between the calculation domain and the atmosphere. In mathematical terms such flow appears in the equation with the following contribution: wherein q represents the flow rate entering through a determined surface and n the normal to the surface itself. The equation development in this case allows to determine the forcer vector {f ^{e }}.

The definition of the local matrixes of the elements is followed by an assembly phase which allows to build the global matrixes of the whole domain, so as to obtain Richards equation in the matrix form designated in B5.

- B6) The decoupling of the variable quantities performed by imposing B2 allowed to discretize spatially the domain by applying FEM at the same time allowing to monitor the trend of the phenomenon in time by means of time discretization at finite differences. The values of the unknown quantities and the time derivative thereof are replaced according to what specified in B6 wherein Θ represents a factor which defines the mode for defining ψ as weighed average of the values at two time instants and as a function thereof different integration schemes are obtained.

- B7) The solving scheme ends up by applying an iterative procedure according to Newton-Raphson scheme for each time step wherein the time domain has been discretized until determining an approximate solution evaluated with imposition of a predefined discard with respect to the previous solution.

Figure 6 shows schematically the equations constituting the mathematical algorithm for solving the geotechnical module MG; a description of the preferred steps for solving the same is shown hereinafter.

- C1 ) Let's consider a space area representing a storage subjected to the action of its own weight. Each land element has to be in equilibrium under the action of its own weight and of the forces transmitted by the adjacent elements. Then, indefinite equations of equilibrium shown above have to be fulfilled, by incorporating the effective effort definition. In the family of equations, 5 _{iz } is equal to 1 if xi coincides with the vertical axis and it is otherwise equal to zero, since γ is the weight of the land volume unit;

- C2) By applying Galerkin method the family of differential equations at point C1 ) can be written in the discrete form shown above, by dividing the continuum into finite elements. [k _{e }i] is the already known matrix of elastic stiffness of the element and [w] is a rectangular matrix formed by terms calculated as: wherein N are the shape functions depending upon the adopted type of finite element, {f} represents the vector of the node loads and it includes even the contribution due to the volume forces. The product [w] {u _{w }} represents in this approach a known vector as the node pore pressures u _{w } are provided by the hydraulic module;

- C3) The system of linear equations represents the global assembly of the equations of each finite element at point C2) so as to recreate the problem unitarity, wherein {U} is a vector of unknown quantities which provides the shiftings in all nodes wherein they are not prescribed by the boundary conditions (constraints or assigned shiftings). Since the model involves not linearity of material type, the search for the system solution takes place iteratively, by updating for each -th iteration (the subscript i appears in the system) the incremental vector of the forces {F} and by keeping constant the matrix of global stiffness [K _{G }];

- C4) The increases in shifting at level of the finite element u(i) extracted by the global vector {U},, are correlated to the increase in deformation by the matrix of the derivatives of the shape functions;

- C5) By assuming that the material has reached the yield value, the deformation "splits" into an elastic component (apex e) and a viscoplastics (apex "vp"); - C6) By considering the increase in the elastic deformation at point C5), it is possible to determine the increase in tension to the i-th iteration {Δδ}, as shown in the above corresponding equation, wherein D is the matrix of elastic stiffness for plane strain state. Such increase is additioned to the previous existing effort state.

The tensional state inside the plasticization criterion (the used criterion is that of Mohr-Coulomb) is then updated;

- C7) In order to generate the volume forces, the visco-plastic approach was adopted. In this method the material can support tensional states outside the plasticization surface for a certain finite "period". This means that the function of plasticization to Mohr-Coulomb, FMC, can be more than zero. The plastic deformations, in this algorithm, will be visco-plastic. The speed of visco- plastic deformation ί ^{1 }έ ^{' ρ }) ^{J } is linked to the function of plasticization FMC and it is expressed by the equation shown above at point C7);

- C8) By multiplying the speed of visco-plastic deformation ^{1 } , (determined at point C7), for the time interval At the increase in viscoplastic deformation to the -th iteration ί ^δε ^{ρ }Ι "· will be obtained;

- C9) The strain state is updated by adding the increase in viscoplastic

ίδε ^{νρ } 1- deformation to the -th iteration ^{J i } with the deformation of the preceding iteration;

- C10) the forces required so that the tensional redistribution could be used are calculated once the increase in viscoplastic deformation to the i-th iteration ί ^{1 } δ ^{~ } ε ^{'νρ }) ^{J i }· at point C9) is known. The iterative process is repeated until the used tensional redistribution generates tensional states in each point of Gauss which do not violate the plasticization criterion or which, in numerical terms, violates it within a certain tolerance defined in advance.

The geotechnical module MG preferably is constituted of two different calculation procedures: - analysis of the global stability in terms of safety factor (FS) of the slope;

- analysis of the slope response in terms of shiftings, deformations and tensions, upon varying the regime of the pore pressures.

Both procedures were implemented by solving the respective problems described by the same set of differential equations by reducing the latter to a system of algebraic equations through the finite element method.

The first procedure provides a quantity incorporating the slope stability information (the safety factor), the second one detects the shiftings and the variation in the strain tensional status upon varying the pore pressures, solved in the hydraulic module.

The two procedures differentiate in the strategy to be applied for searching for the solution.

In the case, the first approach (Shear Strength Reduction Method) is based upon a progressive decrease in the shear strength of the materials (Mohr- Coulomb criterion) τ = c + (σ - u) ^{■ } tan(^ ) by means of a certain factor (SRF), and on the consequent application of the analysis to the finite elements until a collapse mechanism is established.

The reducer parameter will be exactly the safety factor, defined as follows: wherein c'= effective cohesion; C'RI _{D }= reduced effective cohesion, corresponding to a rupture mechanism; φ -angle of resistance to cutting; of resistance to reduced cutting, corresponding to a rupture mechanism. As noted by Mohr-Coulomb principle, the tensions involving the solid continuum are the effective tensions, defined by the difference between the total tensions and the interstitial pressures, the latter obtained by the hydraulic analysis. This process is repeated for different values of the strength reduction factor (SRF), until the model becomes unstable (under such circumstance the analyses' results do not converge).

This determines the critical strength reduction factor (critical SRF), or safety factor, of the slope.

The stress-strain approach instead requires an analysis in incremental terms for calculating the deformations and the shiftings based upon the tensional variation correlated to that of the interstitial pressures.

Figure 7 shows by way of example a flow chart of the operation of the post- processor C.

As results from the processing module arrive, the software interface allows an instantaneous display of the involved hydraulic quantities, by allowing to obtain an estimation of the relative hydraulic load (D1 ), in a given moment, through a colouring obtained with both absolute (fixed scale) and relative (variable scale) chromatic scale, as it can be seen in figure 8.

Analogously, it is possible to display the colouring on fixed or variable scale of the absolute hydraulic load (D2). In this case, the interface is further capable of producing pressure surfaces therewith the trend of the flow can be detected easily, as it can be seen in the two stages of figure 9. The hydraulic situation related to a give time instant can be transmitted (D3) to an operation centre, in case of real time processing, for a subsequent evaluation by the operating staff.

For the control points established in the preprocessor phase (A), it is possible to display the trends of the hydraulic load (D4) over time, for each single point. The obtained graph can be compared with that of the trend of rains for the considered time period (example of figure 10, wherein the trend of the relative hydraulic load is shown upon varying the depth of the portion of land, for an assigned abscissa).

Analogously, the graphs of the trends of the hydraulic load in relation to the depth, for a certain abscissa (D5), for a determined time instant, can be obtained, as well as the graphs of the trends of the hydraulic load in relation to the abscissa, at a certain depth (D6) (example in figure 1 1 , wherein the trend of the relative hydraulic load by abscissa, at a given depth) can be displayed.

During processing, preferably the interface always displays the value of the overall safety factor of the slope (D7) related to the last processed instant, in case of ex post analysis.

In case of real time processing, preferably the values of the safety factor for the subsequent 3, 6 and 12 hours are estimated, which are added to the hydraulic situations determined based upon the rainfall predictions generated by the stochastic model implemented in the device. In this case both the situations of the hydraulic load (D3) and the values of the safety factors (D8) related to the predictions processed for the considered time instant are transmitted. An example is shown in figure 12, wherein a hydraulic situation and the overall safety factor of the slope in real time is represented, together with the related predictions after 3, 6 and 12 hours.

The used stochastic model is finalized to the time prediction of the precipitation heights on punctual spatial scale, of side, or suitable for hydrographic basins with reduced sizes.

The mathematical background is constituted by a distribution of joint probability between two random variables, designated H and Z:

- H is the precipitation height, with assigned time resolution At, (5-10-20 min, 1 h, etc.), to be predicted in the future time horizon;

- Z is a linear function of the rain heights immediately preceding the precipitation H to be predicted. In particular, Z considers v preceding rain heights, wherein v is the process memory, which is estimated by means of usual statistic techniques, and which represents the maximum time distance between two precipitation heights depending therebetween.

Depending upon the values assumed by the variable Z, the model allows the synthetic generation of a number (selected by the user and sufficiently high: for ex. 1000-10,000) of time trends of precipitation heights H in the prediction time horizon, the extension thereof is maximum equal to the process memory v; once exceeded such limit, the generated rains result to be independent from the quantity Z.

The representation of all generated future precipitation patterns constitute a model output, in technical terms designated as "spaghetti plot", of the type shown in figure 13.

From the set of all performed generations the rain time trend corresponding to a not exceeding probability (comprised between 50% and 99%) established in advance by the user, is selected. The trend of the so-obtained rain heights constitutes the model input to perform the prediction of the safety factor in the future time window.

The system of the invention according to what described above is intended in particular way to applications in the field of warning systems for mitigating the hydrogeological risk. The system is equipped with all components and necessary aids to be considered an independent tool, but equally susceptible to be integrated in a wider monitoring system of the circulation of water in the slopes.

The present invention has been sofar described with reference to preferred embodiments. It is to be meant that other embodiments belonging to the same inventive core may exist, as defined by the protective scope of the here below reported claims.

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