Effects of elevated temperature on physical and mechanical properties of carbonate rocks in South-Southern Nigeria

Purpose. Limestone and marble are carbonate rocks with several structural and engineering applications. The physical and mechanical properties of the rocks are fundamental as they determine their suitability for various use. Temperature is one of the critical factors that could affect the properties of the rocks and consequently their engineering application. Therefore, a better understanding of how the temperature, especially when it is higher than ambient, will affect the properties of the rocks is essential. In this work, the effects of the elevated temperature on some physical and mechanical properties of the carbonate rocks have been studied. Methods. Cubic samples of the rocks were prepared and heated in a furnace to different temperatures up to 900°C at an interval of 100°C and then cooled to the room temperature for testing. Porosity, dry density and uniaxial compressive strength (UCS) of the samples were determined under the effect of the elevated temperature. The porosity and dry density were determined using the saturation and buoyancy method while the UCS was estimated from the point load index tests performed on the samples. Findings. The results of this work indicate that the elevated temperature has significant effects on the physical and mechanical properties of the rocks. The porosity of the rocks showed an increasing trend as the temperature was increased while the density steadily decreased especially at the temperature above 300°C. The UCS of the rocks also declines with increased temperature but with an intermittent increase in their strength at a specific heating temperature. Originality. Most of the available studies on Nigerian carbonate rocks are focused on the estimation of physical and mechanical properties of the rocks without considering changes in these properties when the rocks are subjected to high temperatures. This study therefore aims to fill the gap by investigating the effects of the elevated temperatures on the physical and mechanical properties of some of the Nigerian carbonate rocks. Practical implications. The results of this study further increase understanding of the effect of high temperature on carbonate rocks, and also help to identify the critical temperature at which the properties of carbonate rocks undergo significant and irreversible changes. This information is very important for restoration of valuable fire-damaged structures made of carbonate rocks.Мета. Вивчення впливу високих температур на фізико-механічні властивості карбонатних порід на основі експериментальних термічних досліджень їх зразків для проектування будівель і споруд, стійких до руйнувань від пожеж. Методика. Кубічні зразки порід нагрівалися в печі до 900°C з інтервалом у 100°C, а потім охолоджувалися до кімнатної температури. Пористість, об’ємна маса в сухому стані, міцність на одноосьовий стиск (МОС) зразків визначалися при різних високих температурах. Пористість та об’ємна маса в сухому стані вимірювалися шляхом визначення насичення й плавучості зразків, у той час як МОС оцінювалася при випробуванні зразків на зосереджене навантаження. Результати. Результати дослідження свідчать про те, що високі температури чинять суттєвий вплив на фізико-механічні властивості карбонатних порід. З підвищенням температури пористість порід має стійку тенденцію до збільшення, а об’ємна маса – до зменшення, особливо при температурах вище 300°C. МОС також в цілому знижується при підвищенні температури, однак при деяких температурах спостерігається тимчасове збільшення міцності. Наукова новизна. Вперше для карбонатних порід Нігерії встановлено характер впливу високих температур на їх фізико-механічні властивості, що раніше не досліджувалось. Дане дослідження проведено з метою заповнення прогалини у вивченні цього питання. Практична значимість. Розширено уявлення щодо впливу високих температур на карбонатні породи та визначено критичні значення температури, при яких їх властивості зазнають суттєвих і незворотніх змін. Ці дані є досить важливими для відновлення значущих споруд із карбонатних порід, які піддалися руйнуванню під час пожежі.Цель. Изучение влияния высоких температур на физико-механические свойства карбонатных пород на основе экспериментальных термических исследований их образцов для проектирования зданий и сооружений, устойчивых к разрушениям от пожаров. Методика. Кубические образцы пород нагревались в печи до 900°C с интервалом в 100°C, а затем охлаждались до комнатной температуры. Пористость, объемная масса в сухом состоянии, прочность на одноосное сжатие (ПОС) образцов определялись при различных высоких температурах. Пористость и объемная масса в сухом состоянии измерялись путем определения насыщения и плавучести образцов, в то время как ПОС оценивалась при испытании образцов на сосредоточенную нагрузку. Результаты. Результаты исследования свидетельствуют о том, что высокие температуры оказывают значительное влияние на физико-механические свойства карбонатных пород. С возрастанием температуры пористость пород имеет устойчивую тенденцию к увеличению, а объемная масса – к уменьшению, особенно при температурах выше 300°C. ПОС также в целом снижается при повышении температуры, однако при некоторых температурах наблюдается временное увеличение прочности. Научная новизна. Впервые для карбонатных пород Нигерии установлен характер влияния высоких температур на их физико-механические свойства, что ранее не исследовалось. Данное исследование проведено для заполнения пробела в изучении этого вопроса. Практическая значимость. Расширены представления о влиянии высоких температур на карбонатные породы и определены критические значения температуры, при которых их свойства претерпевают существенные и необратимые изменения. Эти данные очень важны для восстановления значимых сооружений из карбонатных пород, которые подверглись разрушению при пожаре.The author wish to express his appreciation to Mr. J.O. Ayeni, Mr. M.B. Jamiu, Mr. I.O. Olanrewaju and Mr. T.V. Oluwafemi for their contribution in acquiring the data used for this study

Pointwise convergence of averages along cubes

Let $(X,\mathcal{B},\mu, T)$ be a measure preserving system. We prove the pointwise convergence of the averages $$\frac{1}{N^2}\sum_{n,m= 0}^{N-1} f_1(T^nx)f_2(T^mx)f_3(T^{n+m}x)$$ and of similar averages with seven bounded functions.Comment: 18 pages, latex, We have replaced Lemma 2 with a new one. We also have added a referenc

Introduction

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Malaysia’s relations with Saudi Arabia under Tun Dr. Mahathir era, 1981-2003

Malaysia’s early formal relation with Saudi Arabia begun since the late Tunku Abdul Rahman Putra al-Haj era (the first Malaysian Premier, 1957-1970) until present. During the reign of Tun Dr. Mahathir, the fourth Malaysian Premier, the relation has changed dynamically. Several initiatives have been taken by the Tun Dr. Mahathir regime to shift the pattern of relations from one to two way communication. Apart from successfully securing economic opportunities from the kingdom, this study attempts to relate the significance of the relations to the Tun Dr. Mahathir regime with its efforts to portray religious commitment, both at domestic and international level. The promotion of Islam by Malaysian leaders, both at home, and at the international level, is vital for the continuation of their political survival. Equipped with more liberal-pragmatic Islamic approach has, to some extent, prolonged the survival of the Tun Dr. Mahathir’s political regime interests

Optimal Switching in Finite Horizon under State Constraints

We study an optimal switching problem with a state constraint: the controller is only allowed to choose strategies that keep the controlled diffusion in a closed domain. We prove that the value function associated with this problem is the limit of value functions associated with unconstrained switching problems with penalized coefficients, as the penalization parameter goes to infinity. This convergence allows to set a dynamic programming principle for the constrained switching problem. We then prove that the value function is a solution to a system of variational inequalities (SVI for short) in the constrained viscosity sense. We finally prove that uniqueness for our SVI cannot hold and we give a weaker characterization of the value function as the maximal solution to this SVI. All our results are obtained without any regularity assumption on the constraint domain.Comment: 32 page