manual de usuario software Cadam-ENG- Software PDF

Preview

Summary

tutorial software cadam 2d para optimizacion de presas de concreto que mejora el tiempo y conceptos para el entendimiento del comportamiento de las presas de gravedad...

Description

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/222211284

Computer aided stability analysis of gravity dams—CADAM ArticleinAdvances in Engineering Software · July 2003 DOI: 10.1016/S0965-9978(03)00040-1

CITATIONS

READS

44

10,671

3 authors: Martin Leclerc

Pierre Léger

Polytechnique Montréal

Polytechnique Montréal

27 PUBLICATIONS641 CITATIONS

115 PUBLICATIONS1,968 CITATIONS

SEE PROFILE

René Tinawi Polytechnique Montréal 56 PUBLICATIONS1,268 CITATIONS SEE PROFILE

Some of the authors of this publication are also working on these related projects:

Hybrid simulations View project

Modeling damping in numerical nonlinear seismic time history analysis View project

All content following this page was uploaded by Pierre Léger on 10 November 2017. The user has requested enhancement of the downloaded file.

SEE PROFILE

Advances in Engineering Software 34 (2003) 403–420 www.elsevier.com/locate/advengsoft

Computer aided stability analysis of gravity dams—CADAM ´ ger*, Rene´ Tinawi Martin Leclerc, Pierre Le Department of Civil Engineering, ´Ecole Polytechnique de Montre ´ al, University of Montreal Campus, P.O. Box 6079, Station CV, Montreal, Que., Canada H3C 3A7 Received 6 March 2002; accepted 3 March 2003

Abstract This paper presents the main features and organisation of CADAM, a computer program, freely available, that has been developed for the static and seismic stability evaluations of concrete gravity dams. CADAM is based on the gravity method using rigid body equilibrium and beam theory to perform stress analyses, compute crack lengths, and safety factors. Seismic analyses could be done using either the pseudostatic or a simplified response spectrum method. CADAM is primarily designed to provide support for learning the principles of structural stability evaluation of gravity dams. It could also be used for research and development on stability of gravity dams. In adopting several different world-wide published dam safety guidelines, a large number of modelling options have been implemented. These include (i) crack initiation and propagation, (ii) effects of drainage and cracking under static, seismic, and post-seismic uplift pressure conditions, and (iii) safety evaluation procedures using deterministic, allowable stresses and limit states probabilistic analyses (Monte-Carlo simulations). Structural stability evaluation of a 30 m dam is presented to illustrate the use of CADAM. q 2003 Elsevier Science Ltd. All rights reserved. Keywords: Concrete gravity dams; Stability analysis; Computer aided design; Gravity method; Floods; Seismic response; Monte-carlo simulations

1. Introduction There are over 4800 large concrete gravity dams in existence throughout the world outside China. In North America, in particular, the average age of these dams is about fifty years. The static and seismic safety of existing concrete gravity dams is therefore a continuous concern to dam owners owing to the ageing processes altering their strength and stiffness, as well as revised predictions of the maximum loads associated to severe floods and earthquakes. It is thus required to perform periodic reassessment of their static and seismic structural stability under extreme loads for which these dams were not designed. In addition, owners with a large number of dams need to assess the safety of these structures and prioritise their investment when undertaking expensive rehabilitation works to accommodate a probable maximum flood or a maximum credible earthquake. It is obvious that if under these extreme conditions structural damage can be tolerated, * Corresponding author. Tel.: þ1-514-340-4711x3712; fax: þ 1-514340-5881. E-mail address: [email protected] (P. Le ´ger).

the reservoir must be contained to avoid a catastrophe downstream. A progressive methodology is normally adopted starting with the gravity method based on rigid body equilibrium and beam theory before considering linear or nonlinear finite element models, if necessary [1,2]. FERC [3,4], CDA [5], USACE [6], Ancold [7], and USBR [8] present guidelines for dam safety assessment based on the gravity method. Nevertheless, even the gravity method, which is relatively simple to understand and apply, can be lengthy when evaluating crack length, especially for inclined failure planes, or when using a pseudo-dynamic technique. On the other hand, finite elements in the linear or nonlinear range have their share of difficulties related to stress singularities or crack propagation particularly with discrete cracks. Therefore there was a need to develop an interactive userfriendly software, such as CADAM [9], to assess very quickly for a given dam the safety margins under extreme loads (Fig. 1). Alternatively, CADAM risk analysis capabilities are useful to classify which structures are the most vulnerable within a portfolio of dams. In addition to safety issues, there are several differences among adopted guidelines regarding:

0965-9978/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0965-9978(03)00040-1

404

M. Leclerc et al. / Advances in Engineering Software 34 (2003) 403–420

Fig. 1. CADAM loading conditions for static and seismic analyses: (a) basic static analysis conditions; (b) pseudo-static seismic analysis; (c) pseudo-dynamic seismic analysis.

(a) cracking initiation and propagation criteria, (b) static and seismic uplift pressures along joints and cracks, and (c) safety evaluation format (allowable stress, limit state method). Moreover, the response of spillways and gravity dams during the 1996 Saguenay flood in Quebec, Canada emphasised once more the need to consider overtopping and floating debris while performing flood safety assessment [10]. Seismic safety evaluations are very frequently conducted using the pseudo-dynamic (response spectrum) method as presented by Chopra [11] in complement to the pseudo-static seismic coefficient (rigid body) method. Although these calculations are well documented, they are complicated due to the iterative nature of crack length calculation and its consequence on the uplift pressures. As

noted above, there is also a growing interest in performing risk based safety evaluation where the probability of failure of a dam is evaluated considering explicitly uncertainties in strength and loading modelling parameters through suitable probability density functions [12]. In most engineering offices, in-house spreadsheets are developed and adapted on a case by case basis to perform dam stability analysis following particular safety guidelines. This is due to the very lengthy and tedious computations, particularly when pseudo-dynamic seismic analyses are considered. Moreover, there are no widely available computational tools: (a) for learning the principles of stability analysis in the academic or professional environment, and, (b) for performing research and development on the structural safety of gravity dams.

M. Leclerc et al. / Advances in Engineering Software 34 (2003) 403–420

We have thus identified needs to develop, and put in the public domain, a comprehensive computer program, CADAM, to perform stability evaluation of gravity dams based on the gravity method. This paper presents the organisation and computational features of CADAM to provide a fully integrated computing environment with output reports and graphic support to visualise input parameters and output performance indicators as required in practice (stresses, crack length, resultant position, safety factors). Several modelling options have been included allowing users: † to perform static, pseudo-static, pseudo-dynamic, and probabilistic safety assessment, † to corroborate hand calculations with computer calculations to develop the understanding of the computational procedures, † to conduct parametric analysis on the effects of geometry, strength of materials and load magnitudes on the structural response, † to compare uplift pressures, crack propagation, and shear strength (peak, residual) assumptions from different dam safety guidelines [3 – 8], and, † to study different strengthening scenarios including posttensioning. After presenting an overview of CADAM main features and analysis options, specific modelling techniques adopted for basic static analyses, flood, and seismic as well as probabilistic analyses are discussed. Applications related to the structural response of a 30 m high gravity dam are described for illustrative purposes. The paper ends with perspectives for future CADAM developments.

2. Basic principles of the gravity method The evaluation of the structural stability of a dam against sliding, overturning and uplifting along concrete lift joints is performed considering two distinct analyses: † A stress analysis to determine eventual crack length and compressive stresses (Fig. 2). † A stability analysis to determine: (a) the safety margins against sliding along the joint considered, and (b) the position of the resultant of all forces acting on the joint. The gravity method considers the dam as a cantilevered structure and is based (a) on rigid body equilibrium to determine the internal forces acting on the potential failure plane (joints and concrete-rock interface), and (b) on beam theory to compute stresses. The use of the gravity method requires several simplifying assumptions regarding the structural behaviour of the dam and the application of loads [4]:

405

† The dam body is divided into lift joints of homogeneous properties along their length; the mass concrete and lift joints are initially assumed uniformly elastic (uncracked state). † All applied loads are transferred to the foundation by the cantilever action of the dam without interactions with adjacent monoliths. † There is no interaction between the joints, that is, each joint is analysed independently from the others. † Normal stresses are linearly distributed along horizontal planes. † The uplift pressures intensity could be modified along a crack, depending upon the drainage condition and rate of crack opening (static vs. seismic conditions). 2.1. Stress analysis CADAM uses an iterative procedure summarised in Fig. 2b to compute the crack length, Lc : Once the crack initiation criterion indicates the formation of a crack, the iterative computation begins. The crack length is computed using a bi-section method and the uplift pressures are updated according to the selected drainage options until the crack propagation criterion indicates stress equilibrium and crack arrest. To consider stress concentration at the crack tip, the criterion for crack initiation may be different than that for crack propagation. Closed form formulations to compute crack length while updating uplift pressures as water penetrates the crack are only available for simple cases where the crack is considered horizontal, a no-tension criterion is used and without drainage. The iterative computation of crack length when concrete tensile strength is nonzero or for an inclined plane requires the computational power of a computer. In most guidelines, uplift pressures are considered as external load acting on the surface of the joint. The stress at the crack tip, sn; is computed while including uplift pressures in the force resultant (in the crack propagation iterative procedure) [3,6,8,13]. This calculation produces a linear effective normal stress distribution,s n ; even in the case where a nonlinear uplift pressure distribution is present along the base due to drainage or cracking:

sn ¼

P

V ^ A

P

My I

ð1Þ

where P

V ¼ sum of all vertical load including uplift pressures, A P ¼ area of uncracked ligament, M ¼ moment about the centre of gravity of the uncracked ligament of all loads including uplift pressures, I ¼ moment of inertia of the uncracked ligament, y ¼ distance from centre gravity of the uncracked ligament to the location where the stresses are computed.

406

M. Leclerc et al. / Advances in Engineering Software 34 (2003) 403–420

Fig. 2. (a) Existing dam vs. idealized structural models. (b) Iterative procedure for crack length computations.

Alternatively, uplift pressures could be considered as an internal load along the joint [4]. The stresses at the crack tip are computed from total stresses without uplift pressures. Uplift pressures are then subtracted from total stress to obtain effective stresses, sn to be used for crack initiation (propagation) criterion [4]. These effective stresses may not exhibit a linear distribution along a joint. For a stability analysis, the basic shear-friction sliding safety factor (SSF) formula along a horizontal plane is given as: P ð V 2 UÞtan f þ cAC P ð2Þ SSF ¼ H where P V ¼ Sum of vertical forces excluding uplift pressures, U ¼ uplift pressure force resultant, f ¼ friction angle (peak value or residual value), c ¼ Cohesion (apparent for rough unbonded joint or real for bonded joint); for apparent cohesion, the user may

specify a minimal value of compressive stress, spn ; to determine the compressed area upon which cohesion could be mobilised, AC ¼ area in compression (a function of the crack length) and P H ¼ sum of horizontal forces. Eqs. (1) and (2) have been enhanced in CADAM to consider inclined lift joints and all relevant seismic load components.

3. CADAM—overview of main features and analysis options 3.1. Programming and computing environment Developers tend to divide along language boundaries. Once they know a programming language, they identify themselves by it: ‘a Cþ þ programmer,’ ‘a Delphi

M. Leclerc et al. / Advances in Engineering Software 34 (2003) 403–420

developer’, etc. The key is applicability and each programming language is as a specialized tool. A hammer specialist does not make a good carpenter. The authors find Cþþ , Delphi, and Java to all be useful languages, and even a little Visual Basic applies when appropriate.

407

Delphi shares the compiler back end with Cþ þ Builder compiler, so the efficiency of the generated codes is comparable. In reliable benchmarks [14], Microsoft Visual Cþþ rated tops in speed and size efficiency in many cases. Although these small advantages are unnoticeable for

Fig. 3. CADAM overall organization.

408

M. Leclerc et al. / Advances in Engineering Software 34 (2003) 403–420

general applications. Visual Basic operates in an interpreted mode and is quite reactive. However, Visual Basic speed rates well behind Delphi and Cþþ tools. Java-based tools such as Borland JBuilder and Microsoft Visual Jþþ approach compile times of Delphi. However, Java speed efficiency leaves something to be desired, because Java is an interpreted language. CADAM has been developed using Borland Delphie 6 compiler [15]. Borland Delphi is an object-oriented, visual programming environment to develop 32-bit applications for deployment on Windows and Linux platforms. Using Delphi, the programmer can create highly efficient applications with a minimum of manual coding. Delphi provides all the tools needed to develop, test, debug, and deploy applications, including a large library of reusable components, a suite of design tools, applications and form template, and programming wizards. These tools simplify software coding and shorten development time. Delphi can be used to write Windows and Linux graphical user interface (GUI) applications, console applications, service applications, dynamic-link libraries (DLLs), and other programs. Delphi includes features to write easily

distributed applications, including client/server, multitiered, and Web-based systems. Delphi has been adopted at first for its object oriented programming environment. The other reason for this choice is that often the complete design methodology is only worked out in full detail at the programming stage. Therefore understanding of the design engineering problem is more important than knowledge and experience of programming [16]. Finally, the ease of programming, support, and suitability for engineering design software, are all additional reasons for adopting this programming language for this particularly complex engineering analysis and design problem. 3.2. Overall program organisation and analysis options Fig. 3 presents CADAM overall organisation. The dam geometry (Fig. 4a,b), material properties (Fig. 4c) the various load conditions, cracking options, and load combinations are first specified as input data for subsequent structural analyses, outlined in Fig. 1. The following analysis options are currently available: (1) static analyses,

Fig. 4. Definition of dam model: (a) dam-foundation-reservoir system and CADAM interface; (b) dam geometry; (c) material properties.

M. Leclerc et al. / Advances in Engineering Software 34 (2003) 403–420

(2) seismic analyses, (3) post-seismic analyses, (4) incremental load analysis, and (5) probabilistic safety analysis.

4. Static loading conditions The load conditions supported by CADAM are shown in Fig. 1. Some particular features are described in the following. Various dam safety guidelines equations presented to compute the uplift pressures according to the position of the drain from the upstream (u/s) face, the drain effectiveness and the elevation of the drainage gallery have been implemented (Fig. 5). It is interesting to note that Federal agencies in the US (FERC, USACE and USBR) are currently evaluating the need for unified Federal criteria for the calculation of uplift pressures as well as crack initiation and propagation criteria in the stability of concrete gravity dams [17]. It is believed that a computational tool like CADAM could be of great assistance to conduct extensive parametric analyses for various dam geometry and drainage conditions to study the effects of modelling assumptions on computed performance indicators. During a severe flood, it is possible that a section of the dam be overtopped. In this case, water pressure may be considered on the crest surface as well as floating debris.

5. Seismic and post-seismic safety analysis Some original features that have been included for seismic and post-seismic safety analyses are presented below. Existing cracks computed from the initial static conditions may close depending on the intensity and orientation of the earthquake forces. Separate analyses could be performed successively with the base acceleration

409

pointing u/s and d/s to estimate the cumulative damage by reducing the cohesion that could be mobilised along the joint considered. The cohesion is considered null along the seismically induced crack length to compute the SSFs in seismic and post-seismic conditions. Since the pseudo-static method does not recognise the oscillatory nature of earthquake loads CADAM performs the safety evaluation in two phases: (a) a stress analysis using peak ground acceleration (or spectral acceleration) values to compute the crack length, and (b) a stability analysis using sustained acceleration values to compute SSFs. A single acceleration peak might be sufficient to induce a crack but it may not be of sufficient duration to induce significant sliding displacement. For stability evaluation an ‘effective’ acceleration equals to 0.67 – 0.5 the peak value has often been used in practice [18]. The stress analysis is therefore used to determine the length over which cohesion will be applied in the stability analysis. 5.1. Pseudo-static analysis In a pseudo-static seismic analysis, the inertia forces induced by the earthquake are computed from the product of the mass and the acceleration. The dynamic amplification of inertia forces along the height ...