Monitoring data can be analysed using hydrostatic-season-time models.Olivier Crépon and Michel Lino* report on ISL’s use of this method of analysis
The analysis of monitoring data is an important factor when determining the behaviour of a dam. Over the last ten years, increased knowledge has led to the development of analytical methods which can exploit the mass of data obtained by monitoring, yielding excellent results.
Basic hydrostatic-season-time models (HST), and other recent developments, have further enhanced the analysis of dam behaviour. HST models are widely used in France and the French-speaking world, but are little known or used elsewhere, particularly in English-speaking countries.
ISL has contributed to the development of these models and has integrated them, in what is intended to be a user-friendly way, into the company’s Monitor program. The examples given below, which explain the principles behind Monitor, are taken from monitoring a 50m high multiple-arch dam.
Database approach
Dam monitoring produces a large quantity of data. This data has to be managed and, in the case of automatic dam monitoring, it has to be managed in real time. The data concern the geometry of the dam, the layout of measuring apparatus and the dam’s characteristics (which may be changing), and the measurements themselves.
The heart of the Monitor program is therefore a database. It was designed specifically for this application, with special functions for analysing monitoring data. These include:
•Description of the dam.
•Location and description of measuring instruments.
•Selection of measurement intervals.
•Calculation of physical measurements from the raw measurements provided by the instruments.
•Sorting.
•Application of Boolean criteria, calculated fields and local values, classical statistical operations, etc.
Graphic processing
The monitoring data essentially consists of taking a series of measurements from the dam over a period of time. Monitor gives a spatial representation of the quantities measured, in the form of cross-sections of the dam. Some types of display do not involve special mathematical processing. Examples would be: water pressures and levels in the foundation of the multiple-arch dam, with the reservoir at its full supply level; and the evolution of the reservoir level and the readings from the upstream piezometer against time. These displays can be used for a preliminary analysis of the dam’s behaviour. Monitor obtains these graphs and carries out dynamic updating as new measurements are entered into the database.
Modelling and surveillance
Monitor uses the multiple correlation method to draw up models for follow-up and surveillance of monitoring measurements. For dam monitoring, this method was developed by Electricité de France under the name méthode d’analyse saisonniére globale (global seasonal analysis method). It is also known as the HST model. This is a numerical model which takes account of the various factors affecting measurements. The model adopted by Electricité de France is written as the sum of three terms:
M(z,t,t) = H(z) + S(t) + T(t) where:
H(z) is the effect of hydrostatic thrust on the dam, represented by a fourth-degree polynomial.
S(t) is the seasonal effect, represented by the sum of four sine functions with one-year and six-month periods.
T(t) is irreversible effects, represented by a linear combination with negative (dwindling effects) and positive (amplifying effects) exponential functions.
Monitor generalises the method and optimises the shape of the function of explanatory variables: the physical nature of the problem to be modelled guides the choice of explanatory variables and the shape of the functions of these variables. The program gives a very flexible description of the explanatory variables and builds the shape of the explanatory functions best suited to the physical problem being dealt with.
The model is not immutable; it is very general and can adapt to all sorts of circumstances.
For modelling, the user can use a wide range of mathematical functions:
•Polynomial functions.
•Jump functions, to take account of any discontinuities.
•Trigonometric functions, for representing periodic effects.
•Exponential functions, to take account of asymptotic trends.
Explanatory variables include addition, multiplication, temporal derivation to take account of dependencies relative to the speed of phenomena, and temporal integration to take account of cumulative effects. The choice of explanatory variables is arbitrary. Although the hydrostatic (reservoir level), season, and time variables are the basic explanatory variables for a dam, they can be complemented by temperature, rainfall, piezometric levels, or any other relevant physical variable.
Once the modelling has been done, surveillance involves comparing the measurements taken with the forecasts of the model.
Detecting drift
When the analysis described was carried out at a 50m high dam, displacements at the top of the dam, revealing downstream drift, were discovered.
An HST model was run and the temporal drift was modelled by a succession of jumps separated by periods of reversible behaviour. Monitor automatically determined the date and amplitude of the jumps. The jump mechanism can be validated with respect to continuous drift by comparison with a linear-drift model. This result affected the diagnosis of the cause of drift, which was attributed to a concrete problem — an alkali-aggregate reaction. With Monitor’s surveillance function the latest measurements are compared to the forecasts of the model.
Separation of hydrostatic and seasonal effects
Changes in dam behaviour in response to thermal or seasonal effects and to variations in the reservoir level are mostly reversible. By separating hydrostatic and seasonal effects, some paradoxical behaviour can be better understood.
At the multiple-arch dam the reservoir level and dam displacement were measured by pendulum. It can be seen in the diagrams on the previous page that early in August 1992, although the reservoir level was dropping quickly, the dam was being displaced downstream at some speed. This phenomenon, which is worrying at face value, is understood if the seasonal and hydrostatic effects are separated: the lower reservoir level in summer means the seasonal effect (downstream displacement due to expansion of the arches) outweighs the hydrostatic effect. This behaviour does not occur under normal operating conditions when the reservoir level in the northern hemisphere’s summer (August) is generally higher and the hydrostatic effect is relatively greater. Comparison with the forecast model showed that the readings in August and September 1992 were perfectly normal, whereas at first sight it could be thought they were abnormal.
Statistical and deterministic models
The modern approach to dam surveillance is founded on the combined use of HST statistical models and finite-element geomechanics models.
Separation of the seasonal and hydrostatic components of measured displacements makes it possible to determine the mechanical characteristics of a finite-element model by adjusting the two effects calculated separately. For arch dams, where hydrostatic and seasonal effects have the same order of magnitude, this separation is indispensable.
Delayed and culminative effects
Some physical phenomena depend not only on the instantaneous value of a variable, but also on its speed of application. In mechanics, these are visco-elastic or visco-plastic effects. A typical case in dams is the effect the speed at which the reservoir level rises has on piezometric levels. By taking account of the speed at which the reservoir level changes, the contrasting piezometric response times (lag before attaining steady-state conditions) can be modelled. Monitor calculates the temporal derivative of a variable and can
take it into account as an explanatory variable.
Other phenomena are linked not to the instantaneous value but to the integral of the variable over a certain time. For instance, the filling of a reservoir does not depend directly on rainfall but on the rainfall during the filling season. Another example is the effect of rainfall on measurement of leakage or a piezometric reading. In both these cases, the relevant explanatory variable is a sum of rainfalls over a certain characteristic time during which the phenomenon occurs. Monitor includes an integration tool for calculating these variables.
Considering the accumulated rainfall over a ten-day period, with the speed at which the reservoir level changes, results in significant improvement to models for forecasting piezometric levels and leakage, particularly for semi-permeable embankment dams and foundations.