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The mechanical property characterization of dam concrete is a challenging task mainly due to the use of large aggregate sizes. The properties of dam concrete are often evaluated from wet-screened concrete tests using standard specimen sizes. A physically-based relationship between dam concrete and wet-screened concrete strength properties is currently unavailable.A prediction methodology is proposed which can be used to obtain the compressive and the splitting tensile strength of dam concrete by taking into account the wet-screened strength results, the effect of the specimen dimensions and the effect of the maximum size of aggregate. The predicted results are compared with test results available in the literature and with test results recently obtained during the construction of the Baixo Sabor dam. It is shown that the proposed prediction tool can be used to obtain accurate estimates of dam concrete strength.

The explicit formulation of a small displacementmodel for the coupled hydro-mechanical analysis of concretegravity dam foundations based on joint finite elementsis presented. The proposed coupled model requires athorough pre-processing stage in order to ensure that theinteraction between the various blocks which representboth the rock mass foundation and the dam is always edgeto edge. The mechanical part of the model, though limitedto small displacements, has the advantage of allowing anaccurate representation of the stress distribution along theinterfaces, such as rock mass joints. The hydraulic part andthe mechanical part of the model are fully compatible. Thecoupled model is validated using a real case of a dam inoperation, by comparison of the results with those obtainedwith a large displacement discrete model. It is shown that itis possible to assess the sliding stability of concrete gravitydams using small displacement models under both staticand dynamic conditions.

This paper proposes a methodology for the prediction of the compressive creep strains of dam concrete based on wet-screened experimental results at constant elevated temperature conditions measured in situ. Due to its large aggregate dimensions, the experimental characterization of dam concrete has particular constraints. The wet-screened concrete, obtained by sieving the aggregates larger than a given dimension, after mixing, is used to cast standard specimens and to embed monitoring devices. An experimental in situ installation using creep cells was used to obtain the compressive creep strain development over time for the maturing conditions of the dam core. The study of the effect of wet-screening procedure on creep in compression considers three types of concrete, dam concrete and two wet-screened concretes tested at three loading ages, 28, 90 and 365 days. The comparison between different types of concrete at different maturing conditions requires the definition of a reference state given by the maturity method, using the equivalent age, and relies on the fit of compressive creep strains to the RILEM recommended model B3. To take into account the effect of the aggregate content on the deformability properties of dam concrete, an equivalent two-phase composite model was applied. The equivalent composite model considered the equivalent matrix as the wet-screened concrete and the inclusions as the larger aggregates that are removed during the wet-screening procedure. Predictions obtained with the composite model are close to the dam concrete experimental results, for the tested loading ages.

This paper proposes the use of the maturity method and of a two-phase composite models for the prediction of dam concrete modulus of elasticity.The methodology was validated with test results obtained from experimental in situ setup using creep cells placed in the dam's body, subjected to variable environmental conditions. It is shown that composite models can be used to predict the modulus of elasticity of in situ dam concrete based on the modulus of elasticity of the wet-screened concrete.

The reduced lifetime of geothermal wells is one of the main issues facing the geothermal industry, with cement durability being one of the main causes for shortening of a well's life. While most wells are cemented with American Petroleum Institute (API) class cements, alternative cementing systems are currently being considered. In this paper, the interactions of two alternative cement formulations with a typical geothermal rock formation are compared with a class A cement. This allows understanding of the most critical zone in the geothermal cement, which is the outermost layer where the cement encounters and, consequently, interacts with the exterior harsh environment, including the volcanic formation and brine. The faster setting of white cement and high-alumina cement compared with the well Portland cement seems to reduce the reaction extent with the rock. For all the cements tested, both the increased curing temperature (from 150°C to 290°C) and the use of bentonite as drilling mud significantly decreased the bond between the cement and the rock.

The application of the limit state design (LSD) in the geotechnical area has increased over the last two decades, but this approach is not yet widely used in dam safety evaluation. This study aims to widen the use of the LSD application for large dams, in particular concrete gravity dam foundations. This paper starts with a brief reference to the LSD approach in recently published guidelines for dam design, followed by a detailed description of the LSD formulation when applied to the foundation of concrete dams. The relevance of the joint application of the concepts of ultimate limit states and of numerical methods is highlighted. Comments are made regarding the criteria adopted in order to determine the characteristic values of the material mechanical properties, with an emphasis on discontinuities, taking into account the spatial variability. The sliding safety assessment of the foundation of a concrete gravity dam using the LSD and a discrete element model, both in persistent and in an accidental design situation, is presented. Results led to the conclusion that the LSD methodology may be followed for dam foundation design with the partial factor values prescribed in Eurocode 7.

To improve the effectiveness of concrete dam safety control in real time, a method is presented for theconstruction of decision rules for the early detection of developing failure scenarios. The decision rulesare based on the use of linear discriminant models developed with data obtained through mathematicalmodels of the dam

In its lifetime, a dam can be exposed to significant water level variations and seasonal environmental temperature changes. The structural safety control of a concrete dam is supported by monitoring activities and is based on models.In practice, the interpretation of recorded concrete dam displacements is usually based on HST (hydrostatic, seasonal, time) statistical models. These models are widely used and consider that the thermal effect can be represented by a seasonal function. The main purpose of this paper is to present an HTT (hydrostatic, thermal, time) statistical model to interpret recorded concrete dam displacements. The idea is to replace the seasonal function with the use of recorded temperatures that better represent the thermal effect on dam behavior.Two new methodologies are presented for constructing HTT statistical models, both based on principal component analysis applied to recorded temperatures in the concrete dam body. In the first method, principal component analysis is used to choose the thermometers for the construction of the HTT model. In the second method, the thermal effect is represented by the principal components of temperature of selected thermometers.The advantage of these methods is that the thermal effect is represented by real temperature measured in the concrete dam body. The HTT statistical models proposed are applied to the 110m high Alto Lindoso arch dam, and the results are compared with the HST displacement model.

The purpose of this research work is to identify the effect of the daily variation of the air temperature on the structural response of a concrete dam. It is intended to obtain a better knowledge about structuralbehaviour of concrete dams. In current day to day activities, quantitative interpretation models are used for the assessment of structural dam behaviour of concrete dams. Most models ignore the temperature effect of a wave with a daily variation. However, in dams with automated data acquisition systems this daily effect can be used to anticipate the detection of abnormal behaviour.In this paper, the Short Time Fourier Transform analysis of the residuals is used, obtained by the quantitative interpretation models and measurement data, to identify the signature that the daily variation of the air temperature has on the structural behaviour of a concrete dam. A case study is presented based on the analysis of a horizontal displacement measured on a pendulum, in the Alto Lindoso concrete dam. As a result, the relation between magnitudes of daily variations of the horizontal displacement analysed and the air temperature was defined. The relation obtained can be used to assess if there is alterations or not in the dam response to short period loads corresponding to the daily variations analysed.

This paper presents the application of a methodology which can be used to assess arch dam foundation stability, using the discrete element method (DEM) and the code 3DEC. A global three-dimensional model of a dam foundation was developed, in which some discontinuities were simulated and both the grout and drainage curtains were represented. The model, calibrated taking into account recorded data, was used to carry out non-linear mechanical analysis. The same model was employed to perform a hydraulic analysis, based on equivalent continuum concepts, which allowed the water pressure pattern within the foundation to be obtained. These water pressures were applied on discontinuities involved in the possible sliding mechanism along the dam/foundation interface, and the safety of the dam/foundation system was evaluated using a process of reduction of strength characteristics, with the aim of calculating the minimum safety factors that ensure stability. Results were compared with those obtained with the usual bi-linear uplift pressure distribution at the base of the dam, commonly used in concrete dam design. The relevance of carrying out hydraulic analysis in arch dam foundation failure studies is highlighted.

A monitorização de estruturas em Portugal tem sofrido desenvolvimentos significativos nas últimas décadas, na sequência da valorização das vantagens, a curto e longo prazo, da observação e do controlo da segurança das obras. Com esse fim, têm sido introduzidos no mercado dispositivos que recorrem à tecnologia de fibra ótica para a monitorização de obras de engenharia civil.O objetivo deste estudo foi a comparação do desempenho de diferentes dispositivos de medição de extensões do betão. Para isso foram moldados provetes de betão de pontes e de betão de barragens, nos quais foram inseridos diferentes tipos de extensómetros disponíveis no mercado. A comparação foi feita através da diferença entre as extensões medidas em cada extensómetro e as extensões calculadas a partir das medições realizadas em trandutores de deslocamento dispostos nas faces durante ensaios de módulo de elasticidade.Os dispositivos em estudo foram extensómetros de corda vibrante, extensómetros do tipo FSG (resistência elétrica - full-bridge) e extensómetros de fibra ótica, embebidos em betão de pontes e extensómetros do tipo Carlson e extensómetros de fibra ótica, inseridos em em betão de barragens.A utilização de extensómetros de fibra ótica para os dois tipos de betão revelou o bom funcionamento e fiabilidade destes sensores face a diferentes condições, viabilizando uma futura utilização em obra, tanto em pontes como em barragens.

Antes da sua aplicação, tanto em obra como em provetes laboratoriais, requere-se a calibração dos dispositivos de resistência elétrica do tipo Carlson, nomeadamente extensómetros e medidores do movimento de juntas, a embeber no seio do betão. Essa calibração é realizada com recurso a sistemas mecânicos, correntemente designados por prensas de teste e calibração, constituindo padrões de referência que asseguram a rastreabilidade das medições. Atualmente não são conhecidas soluções comerciais fiáveis adequadas a este fim, pelo que houve necessidade de desenvolver um equipamento específico para o efeito.Em termos de desempenho pretende-se, no caso dos extensómetros correntes de 254 mm (10

This paper presents a study on seepage in a gravity dam foundation carried out with a view to evaluating dam stability for the failure scenario of sliding along the dam/foundation interface. A discontinuous model of the dam foundation was developed, using the code UDEC, and a fully coupled mechanical-hydraulic analysis of the water flow through the rock mass discontinuities was carried out. The model was calibrated taking into account recorded data. Results of the coupled hydromechanical model were compared with those obtained assuming either that the joint hydraulic aperture remains constant or that the drainage system is clogged. Water pressures along the dam/foundation interface obtained with UDEC were compared with those obtained using the code DEC-DAM, specifically developed for dam analysis, which is also based on the Discrete Element Method but in which flow is modelled in a different way. Results confirm that traditional analysis methods, currently prescribed in various guidelines for dam design, may either underestimate or overestimate the value of uplift pressures. The method of strength reduction was used to estimate the stability of the dam/foundation system for different failure scenarios and the results were compared with those obtained using the simplified limit equilibrium approach. The relevance of using discontinuum models for the safety assessment of concrete dams is highlighted.

The safety of the system formed by the dam, its foundation, the reservoir, and the downstream area of the dam should be evaluated on its structural, hydraulic, operational and environmental components.In particular, the structural safety assessment of an existing dam is based on the establishment of correlations between the main loads, its structural properties, and its structural responses. The values of observed responses are compared to predicted values obtained by structural behaviour models or by historical observations.Over the years, new developments in technological devices have been introduced in this field, namely through the implementation of automated data acquisition systems. This evolution, associated with very important progresses in information systems technology, has raised new challenges, but has also provided new opportunities, such as the development of data management systems that allow the person responsible for dam safety to access data, interpret the information, and make decisions, as quickly as possible.The National Laboratory for Civil Engineering (LNEC) has developed the GestBarragens system, which was designed and developed using a modular approach, based on a common data architecture that can be accessed through a Web interface.This paper intends to show the improvements that the GestBarragens system provides to the activities related to the safety control of more than one hundred large concrete and embankment dams, including the observation of several physical quantities measured by the monitoring systems, the interpretation of the information and the transmission of warnings to the entities responsible for the dam

A Nova Barragem do Alto Ceira, atualmente em construção, é uma barragem abóbada, em betão, com 41m de altura e 133m de comprimento no coroamento, situada na zona centro de Portugal. A necessidade de construção da nova barragem prende-se com a substituição da existente, situada cerca de 200m a montante, a qual se encontra significativamente degradada devido a fenómenos de expansão do betão. Como é usual, o projeto da nova barragem engloba um plano de observação elaborado de acordo com o Regulamento de Segurança de Barragens, sendo a instrumentação embebida no betão baseada em sensores elétricos convencionais, em utilização há várias décadas.Os recentes desenvolvimentos da monitorização estrutural com base na fibra ótica, beneficiando nãosó da elevada precisão, durabilidade, e possibilidade de multiplexagem dos sensores óticos, mastambém da facilidade de transmissão do sinal e comunicação da fibra ótica, evidenciam grandespotencialidades na sua aplicação a barragens. Com esse objetivo, novos transdutores em fibra óticaforam desenvolvidos e instalados, numa base experimental, na Nova Barragem do Alto Ceira. Tendoem consideração que os sensores embebidos no betão em massa são dos mais expostos à agressividadedos métodos construtivos de barragens, foram selecionados para implementação novos transdutores dedeformação, de temperatura e de juntas, baseados nas redes de Bragg em fibra ótica, com o objetivo deavaliar o seu desempenho, fiabilidade e requisitos de instalação. Assim, de um modo pioneiro, foramconcebidos e construídos em laboratório, e instalados em obra um número limitado destes sensores.Neste artigo, são apresentados os novos sensores e as condições de instalação na barragem, bem comoresultados da calibração e de comparação com os sensores elétricos tradicionais, quer em condiçõescontroladas de laboratório, quer em condições de obra.

The New Alto Ceira Dam is a concrete arch dam, 41 m high and 133 m long at the crest, located in the middle region of Portugal. Its objective is the replacement of the existing dam located about 200 m upstream, which is highly deteriorated due to swelling phenomena.The dam is actually under construction and its monitoring safety plan is in accordance with the Portuguese Safety Regulations on Dams. The instrumentation embedded into the concrete is based on traditional electrical devices developed several decades ago and with proved durability characteristics.Considering the recent improvements in fiber optic based instruments for structural monitoring, benefiting of multiplexing technique, great reliability and accuracy, it was decided, in an experimental frame, to develop and to install in the New Alto Ceira Dam a set of fiber optic devices.Assuming the instruments embedded into the concrete mass as those exposed to the most aggressiveness of the construction methodologies, strain meters, thermometers and joint meters were selected to the development and implementation of fiber Bragg grating based transducers in order to appraise their performance, reliability, and installation requirements. After laboratory testing and validation, a limited number of these type of transducers were installed in the New Alto Ceira Dam.In this paper, the results from calibration tests are presented, and then a comparison of performance between new fiber optic sensors and the traditional electric sensors is made under controlled conditions, in laboratory. Some preliminary results of the experimental monitoring of the dam are also illustrated.

The current study has investigated the interactions betweenwell cements and one of the most common types of rocks foundin geothermal environments, under hydrothermal conditions.Holes were drilled in blocks of ignimbrite rock and API classG cement with 0, 20 and 40% added silica flour, was poured intothe cavities. The whole assemblage was autoclaved, under typicalgeothermal conditions at 150° and 300°C for 28 days.The results show that chemical reactions occur in the intertransition zone, which are dependent on both drilling fluid andtemperature. The use of bentonite as a drilling fluid and the exposure to higher temperatures (300°C) when compared to 150°C,seem to exacerbate the reactions occurring in the ITZ. Consequently, there is formation of new crystalline products, whichhave worse performance when the physical bonding between thecement and the rock is considered.The effect of other variables such as CO2 exposure, the hydrothermal alteration of the rock and the curing time are currentlybeing investigated within this research project.

Dam safety control activities require an accurate knowledge of each specific dam, with the purpose ofdefining and justifying the judgment about its safety. This task is mainly supported by the cross validationbetween simulation models, measurements provided by the monitoring systems, and the parameters thatcharacterize the dam's behaviour. The main issue is the assessment of the actual structural behaviour in realconditions, which can be used to detect any anomaly and/or malfunction in advance.Over the years, we can verify a significant evolution in the process of interpreting the physical quantitiesprovided by dam monitoring systems. Nowadays, automated data acquisition systems have become a realityin several dams. These systems can be used to support the analysis for dam safety assessment in real time,but also lead to the increase of requirements related to the management, processing and analysis of largeamounts of data.With the development of information systems to support the activities related to dam safety control,particularly the management of a large quantity of information, new challenges related to the managementand analysis of information in real time are raised.The implementation of an Internal Early Warning System (IEWS) based on the automatic analysis of a largequantity of data in real time allows the early identification and notification of potential abnormal situations andmakes the person responsible able to focus on other activities related with the dam safety control of dams.This paper addresses a proposal for an IEWS able to generate warnings in real time when non-accordancebetween observed and predicted values is verified. Subjects related to the definition of the thresholds forquantities measured by the monitoring system, as well as the notification process to the person responsiblefor the dam's safety control, are also discussed.This paper presents the actual Portuguese experience. Aspects related with the requirements for the IEWSare approached. Threshold definition with quantitative interpretation models based on statistical methods,such as multiple linear regression models, and artificial neural network models, is discussed.

This paper presents the most relevant monitoring data and the interpretation of the structural behaviour of Alqueva dam during the first filling of the reservoir, which took place between February 2002 and January 2010.The safety control and the interpretation of the dam

This paper presents the application of a methodology which can be used to assess arch dam foundation stability, using the discrete element method (DEM) and the code 3DEC. A global three-dimensional model of a dam foundation was developed, in which some discontinuities were simulated and both the grout and drainage curtains were represented. The model, calibrated taking into account recorded data, was used to carry out non-linear mechanical analysis. The same model was employed to perform a hydraulic analysis, based on equivalent continuum concepts, which allowed the water pressure pattern within the foundation to be obtained. These water pressures were applied on discontinuities involved in the possible sliding mechanism along the dam/foundation interface, and the safety of the dam/foundation system was evaluated using a process of reduction of strength characteristics, with the aim of calculating the minimum safety factors that ensure stability. Results were compared with those obtained with the usual bi-linear uplift pressure distribution at the base of the dam, commonly used in concrete dam design. The relevance of carrying out hydraulic analysis in arch dam foundation failure studies is highlighted.

Nowadays, organizations are embracing digital transformation, investingin the integration of information and communication technology (ICT) toolsand solutions. Advanced ICT technologies converge with operations technologies(OT), allowing machines, processes, employees, and products to be part ofa single data framework, from data collection to analysis, interpretation, and assessment,which are the foundation for informed decision-making. Industry 4.0takes advantage of emergent ICT to make the right decisions, at the right time,optimizing processes, minimizing risks and improving value chains. The mainaim of the structural safety assessment and control of critical infrastructures, suchas dams and bridges, is to protect people, property and the environment fromharmful effects of failure or misoperation of infrastructures. This goal is achievedthrough Structural Health Monitoring and Control (SHMC) activities to monitorand track the life-cycle of critical infrastructures in such a way that it can providesufficient information for long- and short-term decisions regarding structuralsafety assessment. The objective of this work is to present a reflection of the impactof the industry 4.0 trends on the structural safety assessment of critical infrastructuresand, more specifically, to understand the level of maturity and toshow how the leveraging of enabling technologies such as augmented reality,Internet of Things (IoT), additive manufacturing, cloud computing, big data andanalytics are impacting the SHMC activities on critical infrastructures, which aretraditional cyber-physical systems with complex sensor networks used to assessand control structural safety and health.

As atividades de controlo de segurança de barragens de betão têm um caráter preventivo, com o intuito de facilitar a tomada de decisões de forma atempada para evitar ou minimizar as consequências resultantes de um acidente ou incidente de uma barragem. No controlo de segurança de barragens com sistemas de monitorização automática, a análise de uma grande quantidade de dados ainda pode tornar-se uma tarefa difícil. Por um lado, pretende-se garantir o controlo de segurança, em tempo real, mas, por outro lado, a capacidade humana de processar a informação de dados é limitado. No entanto, os desenvolvimentos tecnológicos em termos de capacidade de processamento de informação têm permitido o desenvolvimento de ferramentas para a análise de grandes quantidades de dados. A necessidade de rever os procedimentos de análise de dados adequados para a extração de informação tornou-se um aspeto importante para a tomada de decisão em tempo útil. Por estas razões, é fundamental proporcionar às entidades responsáveis pela segurança das barragens um sistema de apoio à gestão da informação que facilite o acesso aos dados, a interpretação da informação e a tomada de decisão, de forma atempada. Neste contexto, o principal objetivo desta dissertação é a definição de metodologias para: i) melhorar a qualidade das grandezas medidas pelo sistema recolha automática de dados, através da implementação de procedimentos para o controlo da sua qualidade e para a validação dos resultados, tendo em conta a incerteza de medição dos sistemas de medição; ii) melhorar os procedimentos relacionadas com a análise de dados e a sua interpretação, através de uma abordagem baseada nos dados da observação, a fim de apoiar a decisão de quais as grandezas que devem ser incluídas na sistemas de recolha automática de dados, quantificar o efeito da onda térmica diária na resposta da estrutura e reconhecer padrões de comportamento da barragem; iii) a definição de avisos relacionados com a identificação de comportamento anómalo, e de potenciais cenários de rotura. A aplicação das metodologias propostas num sistema de apoio à gestão da informação será um passo sólido para a melhoria dos processos de controlo de segurança em tempo real.

Apresenta-se um estudo sobre o comportamento de fundações de barragens de betão na fase de exploração normal das obras desenvolvido com o objectivo de validar e fundamentar a aplicação de modelos numéricos de análise do comportamento hidromecânico de maciços rochosos, tendo em vista generalizar a sua utilização e tornar mais eficaz a observação e controlo de segurança destas obras. Foi estudada a representação em modelos numéricos da cortina de impermeabilização e do sistema de drenagem e das condições geológico-geotécnicas concretas das zonas de fundação analisadas, tendo em conta, nomeadamente, os problemas computacionais associados a modelos tridimensionais. Foram realizados ensaios de afluência de água em duas grandes barragens portuguesas, uma gravidade e uma abóbada, que se verificou serem fundamentais para caracterizar o escoamento no maciço, complementando a informação obtida com o sistema de observação. Desenvolveram-se modelos hidráulicos e hidromecânicos do comportamento das fundações destas barragens, que no caso da barragem gravidade foram utilizados no estudo de cenários de rotura. Apresentam-se conclusões sobre a adequação e limitação dos modelos numéricos utilizados, sobre os parâmetros essenciais para calibrar e aplicar esses modelos, e propõem-se métodos de planeamento e utilização dos sistemas de observação de fundações de barragens, de modo a melhorar o controlo de segurança.

O presente trabalho pretende contribuir para o aperfeiçoamento dos modelospara análise do comportamento de barragens de betão ao longo do tempo, submetidasa processos expansivos devidos a reacções químicas de origem interna. Odesenvolvimento destas reacções expansivas, determinado pela composição do betãoe influenciado pelos campos térmico, higrométrico e de tensões, pode provocarfissuração e contribuir para a deterioração precoce das obras.O trabalho aborda, na parte inicial, a fenomenologia dos processos expansivos,salientando-se os factores de natureza física e química que mais os influenciam. Deseguida apresentam-se os aspectos relacionados com a identificação e acaracterização das reacções expansivas, no que respeita às evidências físicas e aosseus efeitos estruturais. Analisam-se, entre outras obras, as barragens portuguesasafectadas por esta patologia.A influência dos factores que regulam o desenvolvimento do processoexpansivo (composição do betão, temperatura, humidade e estado de tensão) équantificada com base num modelo de interacção químico-mecânico, permitindo umaestimativa das expansões à escala das obras de engenharia. Este modelo foiintegrado num código computacional de elementos finitos que considera ocomportamento diferido do betão, através de um modelo viscoelástico com maturação,e o surgimento e propagação da fendilhação, por meio de uma formulação de dano.Utiliza-se uma técnica incremental na discretização das acções que permite simular aevolução do comportamento ao longo do tempo, tendo em conta os fenómenosdiferidos e o progressivo desenvolvimento da fissuração.Apresentam-se dois estudos de aplicação a barragens portuguesas afectadaspor processos expansivos. O primeiro estudo refere-se à barragem de Santa Luzia,uma abóbada construída entre 1939 e 1943, em que a magnitude das expansões émoderada. O segundo estudo reporta-se à barragem de Pracana, uma obra decontrafortes cuja albufeira foi mantida vazia durante mais de uma década após trintaanos de exploração, devido à fendilhação generalizada da sua estrutura provocada porgrandes expansões diferenciais, que depois foi reabilitada, encontrando-se desdeentão em exploração normal há cerca de quinze anos. Os resultados destes estudosdemonstram o interesse e as potencialidades das metodologias desenvolvidas naquantificação do processo expansivo, na interpretação do comportamento observado ena avaliação das condições de segurança das obras.

This work deals with the estimation of the parameters of mixtures of beta variables. The work is organized in four main sections preceded by an introduction and succeeded by conclusions. The second section summarizes the properties of the beta distribution and describes two methods to estimate its parameters from observed samples, the method of moments and the maximum likelihood method. The third section presents the general concept of a mixture of random variables, presents the likelihood function of a sample of a beta mixture, finally, describes the EMA