Elsevier

Applied Mathematics and Computation

Volume 267, 15 September 2015, Pages 108-118
Applied Mathematics and Computation

Probabilistic assessment of failure risk of the building envelope thermally insulated from the inside

https://doi.org/10.1016/j.amc.2015.05.080Get rights and content

Highlights

  • Modelling the static behaviour of representative building insulated from the interior.

  • Analysing of temperature changes in exterior as damage risk of structures.

  • Using Monte Carlo method for probabilistic assessment of the failure risk.

  • Comparing probabilistic and deterministic method of static reliability assessment.

Abstract

Thermal insulation of external walls is designed in particular to reduce energy performance of buildings. Insulation placed on the outer side of walls act as an effective protection against the external environment. On the contrary placing the thermal insulation layer on the inner side of the building envelope is quite hazardous as the internal insulation does not fulfil the protective function. It actually exposes the bearing layer of the building envelope to the immediate effect of the environment and therefore it enhances the negative impacts of the cyclic temperature changes on structural system of the building. This paper focuses on probability risk of development of failures on such construction depending on variable boundary conditions (rigidity of the structure, strength of the materials, and range of the temperature load). Besides this there is also comparison of probability and deterministic approach to the evaluation of static reliability of the building constructions. Using of probabilistic approach in this context is still very rare. The aim of this paper is to analyse the effects of internal insulation on load bearing system of buildings, and to verify the applicability of probabilistic methods in the analysis of structural reliability. Like the deterministic approach, it draws attention to the high risk of failure of the structures insulated from the inside. At the same time, however, it shows the high demands of the probabilistic method on the amount of input data. If the data are not available, it is possible to replace some of them results of deterministic method; this approach has negative consequences in mutual dependency of accuracy of achieved results.

Introduction

Structural system of each building is exposed to influence of individual external effects. Among the most important and with the highest risk there is load of temperature changes of the external environment. Its intensity depends mainly on the geographical location of the building. The construction is usually sufficiently protected from such effects by thermal insulation parameters of the perimeter structure. If the perimeter structure consists from more functional layers (e.g. bearing and thermal-insulating layer) the ideal structural solution is to place the thermal insulation layers from outside. Such arrangement protects the whole building from temperature changes of the exterior including the bearing layer of the building envelope.

Construction solution of the building envelopes can be divided to single-layer and multi-layer – so called sandwich. At the single-layer perimeter walls the required functions of the construction are merged into one layer made from one material, e.g. brick or block masonry, light concrete, wood, etc. The sandwich structure consists of two or more layers of which each usually fulfils one specific function – e.g. bearing, thermal insulation, protection etc.). The most common sandwich is two-layer perimeter wall composed of bearing layer (masonry, concrete etc.) and thermal insulation layer (polystyrene, mineral wool). The perimeter walls are completed with plaster or tiling as required.

The structural arrangement of the perimeter walls influences significantly the course of temperatures inside the construction. Fig. 1 shows the limit curves of distribution of the internal temperatures in cross section of single-layer perimeter wall (A) and two-layer sandwich constructions, where in one case the thermal insulation is placed from outside of the building (B) and in the second case it is from inside (C) [1]. The limit range of the temperatures in construction was determined assuming that there is a constant temperature of the interior +20 °C during the whole year cycle; the range of the temperatures of the surrounding environment or more precisely of the temperatures on the outside surface of the construction is considered as −15 °C for winter period and +50 °C for the summer (e.g. on the surface of the sunlit façade). In this context it is necessary to say that depending on the local intensity of the solar radiation in the relevant geographical location of the building and the saturation of the colour solution of the surface the surface temperatures on south or south–west oriented perimeter walls may exceed even the value +80 °C. The annual temperature variance inside the construction will increase accordingly.

In the Fig. 1 it is clear that there is significant influence of the position of thermal insulation of the perimeter wall on the intensity of the thermal exposure of its bearing layer. If we use as comparison criterion the extend of the temperatures during the annual cycle in the middle of this thickness depending on the construction solution of each variety there might be even many-times higher exposure of the wall insulated from the interior compared to the construction insulated from the side of the exterior. The location of the thermal insulation layer on the interior surface of the wall even causes significantly higher stress of the bearing layer of the wall compared to the wall without any insulation. Based on the Fig. 1 it is possible to state that location of the thermal insulation on the interior surface of the perimeter wall eliminated the positive interaction of the temperature inside the wall with the temperature of the interior environment, which with its stable annual regime stabilizes positively the temperature regime of the wall.

Cyclic temperature changes of the perimeter structures cause their dilatation movements – they extend when heated or more precisely they shrink when cooled. If they were free dilatation movements this phenomenon would not have to mean any significant consequences of the construction. The problem is however that the free movement of the perimeter structures is limited – e.g. by connection with other structures, which are not subject to such movements. Such structures are mainly the foundations or interior walls or ceilings. These structures occur in environment with approximately stable temperature for the whole life cycle so the extend of the dilatation movements is near to zero or more precisely lower than the dilatation of the perimeter wall. The structures limit through the contact the dilatation movement of the perimeter walls. Due to this phenomenon there is stress in all co-effecting elements – perimeter walls, connected structures, as well as in contact between those two.

Internal thermal insulation of the external walls brings 2 main problems into buildings. The first one is already described above and is further analysed in this paper. Second, the internal insulation negatively changes the hygrothermal regime of perimeter walls, causes condensing of humidity, and increases the risk of damage of these structures by moisture. This is a matter of building physics, which the relatively extensive research is dedicated to. On the other hand, the question of statics is very neglected, despite the objective factors, such as cracks in joints between internal and external walls insulated from inside. The research presented in this paper is one of the few who are more detailed focussed on this problem. Application of probabilistic method is also unique.

Section snippets

Numeric analysis of the problem

During the research of the consequences of interior insulation of the perimeter walls on the construction’s system static reliability there was a numeric analyses of the static behaviour made for the representative building. It was a five-storey construction with perimeter and interior bearing walls made from full bricks on lime mortar with concrete foundation strips and discontinuous wooden beamed ceilings. With height of one floor equal to 3 m the total height of the construction is 15 m, the

Probability analysis of the problem

Following step of the problem analysis was to evaluate the probability of formation of failures in brick perimeter walls and on contact areas with adjacent structures. For this reason program AntHill was chosen; it uses simulation method SBRA (Simulation Based Reliability Assessment) [4]. The function of the reliability of constructions is analysed using method Monte Carlo based on histograms with nonparametric dividing of the input variable probability. It is a very suitable tool for

Comparison of deterministic and probability approach

At the beginning of comparison of both used methods it is necessary to say that in case of insufficient input data for the probability analysis the results of simulation by finite element method is one of possibilities how to acquire data. This is a reason why there is potential dependency of the method SBRA on numerical analysis FEM which has influence on the final demandingness, time consumption of the probability analysis, and final accuracy of the acquired results. This problem is often

Conclusions

Target of the performed analyses was to determine level of probability of risk of damage on the construction of traditional building provided with additional insulation from interior side of the perimeter walls. With regards to the insufficiency of necessary input data a supporting analysis by finite elements method was made. This circumstance was used for mutual comparison of both approaches – the probabilistic one and the deterministic one. Based on the performed analyses it is possible to

Acknowledgement

The research work was supported by the Project SGS-2013-036.

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    The internal insulation

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Cited by (3)

  • Avoiding mould growth in an interiorly insulated log wall

    2016, Building and Environment
    Citation Excerpt :

    Ibrahim et al. [14] have shown that interior thermal insulation systems can cause several moisture problems: inability to dry out over the years, condensation risk, etc. Pasek and Kesl [13] have shown that the interior insulation of the perimeter building envelope in the climatic conditions of Central Europe is quite unsuitable because of a high probability of damage to the structural system of the building compared to other possible varieties of perimeter wall designs. Pašek has also shown that stress increases in external walls and adjacent structures caused by non-forced effects of temperature changes in the environment after the application of internal insulation [17].

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