materials
Article Designing the Composition of Cement Stabilized Rammed Earth Using Artificial Neural Networks
Hubert Anysz * and Piotr Narloch *
Faculty of Civil Engineering, Warsaw University of Technology, Al. Armii Ludowej 16, 00-637 Warsaw, Poland * Correspondence: [email protected] (H.A.); [email protected] (P.N.); Tel.: +48-606-668-288 (H.A.); +48-691-660-184 (P.N.) Received: 30 March 2019; Accepted: 26 April 2019; Published: 29 April 2019
Abstract: Cement stabilized rammed earth (CRSE) is a sustainable, low energy consuming construction technique which utilizes inorganic soil, usually taken directly from the construction site, with a small addition of Portland cement as a building material. This technology is gaining popularity in various regions of the world, however, there are no uniform standards for designing the composition of the CSRE mixture. The main goal of this article is to propose a complete algorithm for designing CSRE with the use of subsoil obtained from the construction site. The article’s authors propose the use of artificial neural networks (ANN) to determine the proper proportions of soil, cement, and water in a CSRE mixture that provides sufficient compressive strength. The secondary purpose of the paper (supporting the main goal) is to prove that artificial neural networks are suitable for designing CSRE mixtures. For this purpose, compressive strength was tested on several hundred CSRE samples, with different particle sizes, cement content and water additions. The input database was large enough to enable the artificial neural network to produce predictions of high accuracy. The developed algorithm allows us to determine, using relatively simple soil tests, the composition of the mixture ensuring compressive strength at a level that allows the use of this material in construction.
Keywords: rammed earth; cement stabilized rammed earth; artificial neural networks; sustainable building material
1. Introduction Technologies for erecting buildings using raw earth were popular in all civilizations of the world until the beginning of the 20th century. Nowadays, every third person in the world lives in a house built from the earth while in the developing countries the number is more than half of the population [1]. Thanks to the widespread availability of earth, numerous objects made from it are located on every inhabited continent (Figure1).
Materials 2019, 12, 1396; doi:10.3390/ma12091396 www.mdpi.com/journal/materials Materials 2019, 12, x FOR PEER REVIEW 2 of 27 Materials 2019, 12, 1396 2 of 27 Materials 2019, 12, x FOR PEER REVIEW 2 of 27
Figure 1. Areas of occurrence of numerous buildings made of earth (yellow color). The black Figure 1. Areas of occurrence of numerous buildings made of earth (yellow color). The black points pointsFigure marked 1. Areas the of earthoccurrence architecture of numerous inscribed buildings in the made UNESCO of earth World (yellow Heritage color). ListThe black[2]. markedpoints marked the earth the architecture earth architecture inscribed in inscribed the UNESCO in the World UNESCO Heritage World List [2 ].Heritage List [2]. StrivingStriving for for the the most most extensive extensive use use of of natural materials,materials, buildingsbuildings mademade of of earth earth can can be be an an Striving for the most extensive use of natural materials, buildings made of earth can be an alternativealternative option option to to other other natural natural materials materials such such as wood, whichwhich duedue to to its its flammability flammability must must be be alternative option to other natural materials such as wood, which due to its flammability must be impregnated,impregnated, whereas whereas earth earth is is no non-flammablen-flammable [3]. [3]. On the otherother hand,hand, building building structures structures made made of of impregnated, whereas earth is non-flammable [3]. On the other hand, building structures made of earthearth are are considered considered to to not not be be durable. durable. However, However, it is worth notingnoting that that in in many many regions regions of of the the world world earth are considered to not be durable. However, it is worth noting that in many regions of the world impressiveimpressive ancient ancient buildings buildings made made of of earth earth can be admired.admired. TheThe best-knownbest-known example example is is the the Great Great impressive ancient buildings made of earth can be admired. The best-known example is the Great WallWall of of China China (Figure (Figure2 ),2), of of which which numerous numerous fragments fragments erected erected in the in rammed the rammed earth technology earth technology about Wall of China (Figure 2), of which numerous fragments erected in the rammed earth technology about4000 4000 years years ago haveago have survived survived until theuntil present the present day. day. about 4000 years ago have survived until the present day.
Figure 2. The Great Wall of China erected with rammed earth technology. FigureFigure 2. 2.TheThe Great Great Wall Wall of of China China erected erected with rammedrammed earth earth technology. technology.
InIn thethe regionsregions ofof thethe worldworld withwith hothot andand drydry climates,climates, therethere areare notnot onlyonly buildings,buildings, butbut wholewhole In the regions of the world with hot and dry climates, there are not only buildings, but whole citiescities builtbuilt withwith technologiestechnologies usingusing thethe earth.earth. The mostmost well-knownwell-known citycity ofof thisthis typetype isis ShibamShibam inin cities built with technologies using the earth. The most well-known city of this type is Shibam in YemenYemen (Figure (Figure3). 3). Some Some buildings buildings of this of city, this erected city, inerected the 19th in andthe 20th19th centuries, and 20th with centuries, technologies with Yemen (Figure 3). Some buildings of this city, erected in the 19th and 20th centuries, with usingtechnologies the earth, using are eventhe earth, 11 stories are even tall. This11 stories confirms tall. that This it confirms is possible that to useit is the possible land as to a use material the land for technologiesas a material using for thebuilding earth, multi-story are even 11 residential stories tall. buildings. This confirms Other thatexamples it is possible of constructions to use the built land as a material for building multi-story residential buildings. Other examples of constructions built
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Materials 2019, 12, x FOR PEER REVIEW 3 of 27 building multi-story residential buildings. Other examples of constructions built with technologies withusing technologies the earth that using belong the toearth the that history belong of architecture, to the history including of architecture, the proportions including of soil, the cement, proportions and of watersoil, cement, that were and used water in the that past, were can used be found in the in past, references can be [ 4found,5]. in references [4,5].
FigureFigure 3. 3.CityCity of of Shibam, Shibam, Yemen. Yemen. The The ci cityty whose buildings wereweremostly mostly erected erected with with construction construction technologiestechnologies using using earth. earth.
OverOver the the centuries, centuries, many many building building technologies technologies that useuse earthearth have have been been developed developed in in various various regions of the world. Their variety results, among other factors, from the type of land and climate regions of the world. Their variety results, among other factors, from the type of land and climate conditions prevailing in the area [6]. Construction techniques using earth can be divided into three conditions prevailing in the area [6]. Construction techniques using earth can be divided into three main groups [7]: main groups [7]: − - TechniquesTechniques that that use use earth earth in in load-b load-bearingearing monolithic constructions.constructions. − - TechniquesTechniques that that use use earth earth in in lo load-bearingad-bearing masonry structures.structures. − - TechniquesTechniques that that useuse earth earth as aas non-bearing a non-bearing construction construction material material in combination in combination with a supporting with a supportingstructure ofstructure another of material. another material. ThisThis paper paper focuses onon one one of theof technologiesthe technologies of erecting of erecting load-bearing load-bearing monolithic monolithic earth structures earth structuresi.e., cement i.e., stabilized cement stabilize rammedd earthrammed (CSRE). earth CSRE (CSRE). is a highlyCSRE sustainableis a highly constructionsustainable construction technique techniquecharacterized characterized by low energy by low demand energy and demand a small an amountd a small of waste amount generated of wast duringe generated the construction during the constructionprocess. The process. structure The consists structure of rammed consists layers of ra ofmmed moist layers mixture of mademoist inmixture a formwork made set in ona formwork a stable foundation (Figure4). A basic component of the mixture is the subsoil that lies under the layer of set on a stable foundation (Figure 4). A basic component of the mixture is the subsoil that lies under humus usually taken directly from the construction site. The limiting factor determining the suitability the layer of humus usually taken directly from the construction site. The limiting factor determining of the subsoil for rammed earth technology is the quantity of organic substances. The organic soil the suitability of the subsoil for rammed earth technology is the quantity of organic substances. The is biodegradable, easily absorbs water, and is highly compressible. Therefore, its presence in the organic soil is biodegradable, easily absorbs water, and is highly compressible. Therefore, its presence soil mixture should not exceed 1% of the total weight of the soil [8]. Depending on the particle size in distributionthe soil mixture of the should soil, the not mixture exceed is modified1% of the by total adding weight appropriate of the soil aggregate [8]. Depending fractions andon the Portland particle sizecement. distribution The components of the soil, are the mixed mixture together is modified in an air-dry by adding state, and appropriate then water aggregate is added to fractions ensure the and Portlandproper cement. moisture The content components of the mixture. are mixed Layers together of the in mixture an air-dry are filledstate, in and the then formwork water andis added then to ensurecompacted the proper by mechanical moisture means.content Afterof the proper mixture. compaction Layers of of the the mixture layer, successive are filled onesin the are formwork added anduntil then the compacted planned height by mechanical of the element means. is reached. After proper The formwork compaction is then of the removed. layer, successive Since compaction ones are addedleads until to closer the packingplanned of height soil grains, of the this element process eventuallyis reached. leads The to formwork increased mechanicalis then removed. strength Since [4]. compactionDurability ofleads a monolithic to closer wall packing made ofof CSREsoil withgrains, adequate this process load capacity eventually depends leads on theto particleincreased mechanicalsize of the strength soil used [4]. and Durability the addition of a of monolithic Portland cementwall made [9]. Withof CSRE CSRE with technology adequate it load is possible capacity depends on the particle size of the soil used and the addition of Portland cement [9]. With CSRE technology it is possible to construct monolithic walls that contain communication openings, since erecting walls in layers provides the possibility of easy assembly of reinforcement [10].
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Materialsto construct 2019, 12, x monolithic FOR PEER REVIEW walls that contain communication openings, since erecting walls in layers4 of 27 provides the possibility of easy assembly of reinforcement [10].
Figure 4. A scheme for erecting a wall using rammed earth technology. Different layers of the CARE Figure 4. A scheme for erecting a wall using rammed earth technology. Different layers of the CARE monolithic wall are marked with different colors. Steps when erecting a wall: (a) Formwork is built and monolithicfilled with wall a layer are marked of moist soil-cementwith differen mixture.t colors. (b) Steps The layer when of moisterecting mixture a wall: is compressed. (a) Formwork (c) The is built andnext filled layer with of a moist layer soil-cement of moist soil-cement mixture is added.mixture. (d) ( Successiveb) The layer layers of moist of moist mixture earth areis compressed. added and (c) Thecompressed. next layer of (e )moist The formwork soil-cement is removed mixture leaving is added. the monolithic(d) Successive CSRE layers wall. of moist earth are added and compressed. (e) The formwork is removed leaving the monolithic CSRE wall. A significant part of building project expenses is associated with transport of materials to theA significant construction part site. of Therefore, building oneproject of theexpenses ways to is reduce associated those with costs transport is to reduce of thematerials need for to the constructiontransportation. site. CementTherefore, stabilized one rammedof the earthways technology to reduce allows those for erectingcosts is monolithic to reduce load-bearing the need for walls using locally available material, which is a very good solution in less urbanized areas located far transportation. Cement stabilized rammed earth technology allows for erecting monolithic load- from wholesalers. bearing walls using locally available material, which is a very good solution in less urbanized areas The compressive strength is a significant mechanical feature of a structural building material. locatedThe far results from of wholesalers. laboratory tests for the compressive strength of cement stabilized rammed earth are presentedThe compressive in numerous strength publications is a significant (Table1). However,mechanical results feature obtained of a bystructural individual building authors material. are Thedi resultsfficult toof comparelaboratory due tests to di ffforerences the compressive in: strength of cement stabilized rammed earth are presented in numerous publications (Table 1). However, results obtained by individual authors are difficult- toShapes compare of the due tested to samples,differences in: - Energy used in ramming samples and the related volume density of samples, − - ShapesParticle of the size tested distribution samples, of the earth used in the mixture, − - EnergyMineral used and in chemicalramming composition samples and of thethe earth,related volume density of samples, − - ParticleMoisture size distribution content of the of earth the mixture,earth used in the mixture, − - MineralMoisture and contentchemical of thecomposition samples at of the the time earth, of the test, − - MoistureContent content and type of the of Portland earth mixture, cement, − - MoistureDuration content and conditions of the samples of samples at the storage time of before the test, strength tests. − Content and type of Portland cement, − DurationThe lack and of conditions information of on sample somes of storage those parameters before strength is the tests. main challenge in analyzing the results published. For example, from the tests included in Table1, only article [ 11] lists the chemical compositionThe lack of of information the earth. In references on some [ 12of,13 those] it is presentedparameters that is di fftheerences main in thechallenge chemical in composition analyzing the resultsof the published. clay used For can haveexample, a significant from the impact tests onincluded the obtained in Table value 1,of only compressive article [11] strength. lists the chemical composition of the earth. In references [12,13] it is presented that differences in the chemical composition of the clay used can have a significant impact on the obtained value of compressive strength.
Table 1. Compressive strength results of CSRE from various references [11,14–18].
Moisture Particle Size Shape and Density of Compressive Content of Compaction Cement Curing Reference Distribution of Dimensions of Samples Strength the Mixture Method Addition Conditions Earth Samples [cm] [kg/m3] [MPa] [%} Sand 64% cuboid hydraulic press 27 days, [11] Silt 18% 9.5 Max. 1877 8% 18.4 (AVG.) 10 × 10 × 20 (15 MPa) 70% RH Clay 18% Gravel < 19 mm pneumatic 2 days in [14] 7.8 - 8% 10 (AVG.) Gravel 32% rammer forms,
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Table 1. Compressive strength results of CSRE from various references [11,14–18].
Shape and Moisture Density of Particle Size Compaction Cement Compressive Reference Dimensions of Content of the Samples Curing Conditions Distribution of Earth Method Addition Strength [MPa] Samples [cm] Mixture [%] [kg/m3] Sand 64% cuboid hydraulic press 27 days, [11] Silt 18% 9.5 Max. 1877 8% 18.4 (AVG.) 10 10 20 (15 MPa) 70% RH Clay 18% × × Gravel < 19 mm 7.8 10 (AVG.) Cylinder 2 days in forms, [14] Gravel 32% pneumatic - d = 10, 8.2 8% 7 days tightly wrapped, 10–12 (AVG.) Sand 66% rammer h = 20 19 days in an air-dry condition Clay + Silt 2% 8.5 7–8 (AVG.) Gravel 26–50% Cylinder 28 days in an air-dry 8.85–9.15 pneumatic [15] Sand 46–70% d = 10/15, 2091 10% condition, 13.8 (AVG.) (OMC) rammer Silt + Clay 4 % h = 20/30 13–25 ◦C Gravel 45% Sand 40% wall element 50 5.4 pneumatic 7 days tightly wrapped, min. [16] 2156–2139 4.5% 6.68 (AVG.) Silt 5% 50 11 (OMC) rammer 20 days in an air-dry condition × × Clay 10% >19 mm 4.3% 6% 2.06 (CH) Gravel 32.2% 8% 2.94 (CH) Sand 59.4% 10% 3.09 (CH) Clay +Silt 8.4% >19mm 17.9% Mechanized wall element 9.5–11.0 6% 1.69 (CH) [17] Gravel 56% rammer, layers 1800–2000 In an air-dry condition (OMC) 8% 1.64 (CH) Sand 29.6% 100 65 16 15 [cm] high × × 10% 2.35 (CH) Silt + Clay 14.4% >19mm 6.4% 6% 1.52 (CH) Gravel 50.5% 8% 1.72 (CH) P 30.4% 10% 1.92 (CH) π + I 19.1% Gravel 20% cylinder 5.25 (AVG.) 5.3 pneumatic 6 days in an air-dry condition [18] Sand 50% d = 15 2005–2012 4.5% (OMC) rammer Silt 25% Clay 5% h = 30 12 days in an air-dry condition 16 (AVG.) AVG.—average value of compressive strength; CH—characteristic value of compressive strength; OMC—optimum moisture content; RH—relative humidity. Materials 2019, 12, 1396 6 of 27
Determining the proper moisture content of the soil-cement mixture is one of the key issues in rammed earth technology. The moisture content determines its workability and, as a result, affects the most important properties of the material, including its compressive strength. The optimum moisture content (OMC) for a rammed earth mixture is critical in achieving maximum dry density through dynamic compaction [19]. If too little water is in the mixture, then the soil cannot achieve the same level of compaction due to the greater degree of friction between the soil particles [20]. If too much water is added, then capillary water occupies the soil pore spaces reducing the level of achievable compaction and increasing the level of porosity in ready dried wall [20]. The optimum moisture content of a CSRE mixture depends on the particle size of the soil [19,21], as well as the cement content and compaction method used [22]. The data presented in the Table1 shows that for a similar method of sample compaction, the optimum moisture content increases along with the amount of the cement added. The density of the samples made of CSRE mixtures with a similar moisture and cement content depends primarily on the soil particle size. Although it is possible to determine precisely the optimum moisture content of the mixture under conditions found during construction, the problem is that these conditions are highly variable for longer periods of time. They are influenced by, among other factors, atmospheric conditions, that are usually unpredictable. It is worth noting that this phenomenon has been noticed in the standards. Currently, the largest accumulation of knowledge in modern rammed earth construction is thought to exist within Australia and New Zealand [19]. The New Zealand Standard [23] allows for moisture content to differ by 3% from the planned optimum. According to the authors of the article, the range of a soil mixture’s moisture content allowed by this standard is too wide. This can be confirmed by the test results [24], where the compressive strength values of samples from soil mixtures with a moisture content of 2% lower or 2% higher than the optimal value differ from each other by 50%. As a consequence of the high tolerance in the moisture content of the CSRE mixture, the compressive strength to be used in the design of a standard earth wall construction is only 0.5 MPa [25], regardless of the compressive strength results of the CSRE samples obtained in laboratory tests. It is worth noting that according to reference [23], for a series with a minimum of 5 samples with a ratio of height to width of 1:1, the lowest value of compressive strength should be greater than 1,3 MPa, and therefore more than 260% of the design compressive strength value. Designing concrete is itself a complex process. However the methods of design and factors critical for the compressive strength are well known. Applying CSRE as a structural material is, for the time being, an experimental process. The amount of cement is much lower in CSRE than in concrete and therefore a difference of, e.g., 5 kg of cement for 1 m3, influences the properties of CSRE much more than the properties of concrete. In general, CSRE seems to be a construction material that is very sensitive to changes in composition, where the aggregate skeleton and the way of compaction play very important in reaching the required compressive strength. The correlation factors for the compressive strengths of samples calculated for water content and cement to be added show that these variables are weakly or not at all correlated with compressive strength. Even the Spearman’s correlation factor calculated for the w/c ratio and compressive strength (for 373 CSRE samples described further in this paper) is not significant ( 0.622). − As the absolute value of the correlation factor with a single component of CSRE (water or cement) is below 0.5, its influence on the compressive strength is meaningless. The absolute value of the correlation of the water-to-cement ratio is higher than 0.5, so the influence of compressive strength can be observed, but is still not a strong one. The higher w/c is, the lower the compressive strength. These Spearman’s correlation values confirm that the other properties of CSRE mixtures also have a significant influence on the compressive strength. A possible way of finding a composition of a CSRE mixture that meets compressive strength criterion is a prediction based on the obtained results of the samples’ tests. In concrete, the type and amount of cement used are of crucial importance to the compressive strength obtained. In the case of CSRE, the amount of cement is smaller, so that the remaining properties of the mixture, such Materials 2019, 12, x FOR PEER REVIEW 6 of 27
a consequence of the high tolerance in the moisture content of the CSRE mixture, the compressive strength to be used in the design of a standard earth wall construction is only 0.5 MPa [25], regardless of the compressive strength results of the CSRE samples obtained in laboratory tests. It is worth noting that according to reference [23], for a series with a minimum of 5 samples with a ratio of height to width of 1:1, the lowest value of compressive strength should be greater than 1,3 MPa, and therefore more than 260% of the design compressive strength value. Designing concrete is itself a complex process. However the methods of design and factors critical for the compressive strength are well known. Applying CSRE as a structural material is, for the time being, an experimental process. The amount of cement is much lower in CSRE than in concrete and therefore a difference of, e.g., 5 kg of cement for 1 m3 , influences the properties of CSRE much more than the properties of concrete. In general, CSRE seems to be a construction material that is very sensitive to changes in composition, where the aggregate skeleton and the way of compaction play very important in reaching the required compressive strength. The correlation factors for the compressive strengths of samples calculated for water content and cement to be added show that these variables are weakly or not at all correlated with compressive strength. Even the Spearman’s correlation factor calculated for the w/c ratio and compressive strength (for 373 CSRE samples described further in this paper) is not significant (−0.622). As the absolute value of the correlation factor with a single component of CSRE (water or cement) is below 0.5, its influence on the compressive strength is meaningless. The absolute value of the correlation of the water-to-cement ratio is higher than 0.5, so the influence of compressive strength can be observed, but is still not a strong one. The higher w/c is, the lower the compressive strength. These Spearman’s correlation values confirm that the other properties of CSRE mixtures also have a significant influence on the compressive strength. Materials 2019A, 12possible, 1396 way of finding a composition of a CSRE mixture that meets compressive strength 7 of 27 criterion is a prediction based on the obtained results of the samples’ tests. In concrete, the type and amount of cement used are of crucial importance to the compressive strength obtained. In the case of as particleCSRE, size the distribution,amount of cement humidity, is smaller, energy, so that and the the remaining method properties of ramming, of the as mixture, well as such the mineralas compositionparticle ofsize the distribution, applied earth humidity, significantly energy, and influence the method the obtainedof ramming, compressive as well as the strength. mineral In the absencecomposition of standards of the for applied the design earth ofsignificantly cement stabilized influence rammedthe obtained earth compressive and the individualstrength. In approachthe of researchersabsence of to standards this problem, for the design the authors of cement propose stabilized the rammed use of artificialearth and the neural individual networks approach (ANN) to of researchers to this problem, the authors propose the use of artificial neural networks (ANN) to determine the desired composition of a mixture. The more the nature of the process is unknown determine the desired composition of a mixture. The more the nature of the process is unknown and and thethe greater greater thethe complexitycomplexity of of the the process, process, the the more more benefits benefits using using ANN ANN provides provides (compared (compared to to statisticalstatistical models, models, expert expert systems, systems, Figure Figure5)[ 5)26 [26,27].,27].
Figure 5. Features of the problems where applying ANN brings more accurate results in solving the problem [26,27].
According to the aforementioned figure, Artificial Neural Networks (ANN) are widely applied as a predictive tool in the construction industry. They have been applied for predicting:
- Delays in the completion date of construction works [28,29], - Construction costs [30,31], - Level of deterioration of multi-story buildings [32], - Loss of a client in the case of collusion [33], - Energy demand for housing purposes [34,35], - Financial results of construction companies [36].
Properties of construction materials can be predicted with the use of ANN [37,38]. There are successful examples of ANN use in designing specific concrete where recycled aggregates were also considered [39]. The above mentioned application of ANN is also a solid base for expecting good results in the CSRE mixture designing.
2. Materials and Methods
2.1. Database of CSRE Test Results
2.1.1. Materials Hall and Djerbib [19] point out that for sample production, if soils obtained from different locations were to be used, it would be difficult to analyze the laboratory test results due to the large number of variables introduced, including but not limited to the mineralogical composition. Therefore, in laboratory tests inorganic soil mixture of clay, sand, and gravel was obtained from the construction site. Each of these components were then dried to a constant mass and mixed in ten proportions to obtain Materials 2019, 12, 1396 8 of 27 particle-size distribution curves shown in the Figure6. Each soil was named numerically in relation to its sand: gravel: silty clay ratio out of a total 10 components. For example, symbol 613 means that the mixture consists of 6 parts sand, 1 part gravel, and 3 parts clay by weight. For each of these mixtures, 3 to 10% by weight of Portland cement CEM I 42.5R was added. Afterwards, water was added to these mixtures to ensure an optimum moisture content, i.e., the moisture of the mixture, which, guaranteed the highest dry density for the adopted method of ramming the samples. For comparative purposes, the tests were also carried out on mixtures with a moisture content 2% higher and 2% lower than the optimalMaterials level. 2019, 12, x FOR PEER REVIEW 8 of 27
FigureFigure 6. 6.Particle Particle size size distributiondistribution of so soilsils used used for for laboratory laboratory tests. tests.
2.1.2.2.1.2. Preparation Preparation of of Samples samples CSRE samples were prepared in cubic molds, 100 mm 100 mm 100 mm. The formation of CSRE samples were prepared in cubic molds, 100 mm × 100× mm × 100× mm. The formation of the the samplessamples was was carried carried out out by by ramming ramming the themixture mixture into three into threeequal equallayers layersusing a using6.5 kg arammer. 6.5 kg rammer.The Theparameters of of the the rammer rammer were were selected selected on on the the basis basis of ofNew New Zealand Zealand Standard Standard [23]. [23 The]. Thesamples samples werewere formed formed by freelyby freely lowering lowering the the rammer rammer fromfrom a he heightight of of 30 30 cm cm toto the the surface surface of the of themoist moist mixture. mixture. For thisFor this method method of compaction,of compaction, the the optimum optimum moisture content content in in individual individual mixtures mixtures was was 7% to 7% 10% to 10% dependingdepending on theon the particle particle size size distribution distribution andand thethe amount of of cement. cement. ForFor each each series, series, 10 samples 10 samples were were made. made. The authorsThe authors participated participated in the in preparationthe preparation of all of samples. all Therefore,samples. the Therefore, influence the of theinfluence sample of preparationthe sample preparation method on method the compressive on the compressive strength results strength can be results can be ruled out. The samples to be tested were demolded after 24 h. Then they were cured ruled out. The samples to be tested were demolded after 24 h. Then they were cured for 27 days in a for 27 days in a condition of relatively high humidity of 95% (± 2%) and temperature of 20 °C (±1 °C). condition of relatively high humidity of 95% ( 2%) and temperature of 20 C( 1 C). ± ◦ ± ◦ 2.1.3. Results of testing the samples 2.1.3. Results of Testing the Samples Since the rammed earth keeps the layered structure, the samples were loaded in the direction of theSince ramming. the rammed 373 compressive earth keeps strength the layered resultsstructure, were obtained the samplesfor the prepared were loaded samples. in the The direction results of the ramming.of some of 373 these compressive samples are strength shown resultsin Table were 2. The obtained results for obtained the prepared served samples. as a database The results for of somecalculations of these samples using ANN. are shown in Table2. The results obtained served as a database for calculations using ANN. Table 2. Results of compressive strength for some chosen samples.
Particle Size Distribution [%] Silt Sand Gravel Cement Moisture Density of Compressive Sample Clay φ ≥ 0.002 φ ≥ 0.063 φ ≥ 2.0 Addition Content the Sample Strength Number φ > 0.002 φ < 0.063 φ < 2.0 φ < 4.0 [%] [%] [kg/m3] [MPa] [mm] [mm] [mm] [mm] 6 0.105 0.192 0.403 0.300 3 9 2295 4.01 81 0.105 0.192 0.403 0.300 6 8 2240 6.45 108 0.105 0.210 0.585 0.100 6 8 2218 5.43 125 0.105 0.210 0.585 0.100 6 10 2299 5.55
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Table 2. Results of compressive strength for some chosen samples.
Particle Size Distribution [%] Cement Moisture Density of Compressive Sample Silt Sand Gravel Clay Addition Content the Sample Strength Number φ 0.002 φ 0.063 φ 2.0 φ > 0.002 ≥ ≥ ≥ [%] [%] [kg/m3] [MPa] φ < 0.063 φ < 2.0 φ < 4.0 [mm] [mm] [mm] [mm] 6 0.105 0.192 0.403 0.300 3 9 2295 4.01 Materials81 2019, 12, x 0.105FOR PEER REVIEW 0.192 0.403 0.300 6 8 2240 6.45 9 of 27 108 0.105 0.210 0.585 0.100 6 8 2218 5.43 125 0.105 0.210 0.585 0.100 6 10 2299 5.55 144144 0.105 0.105 0.219 0.219 0.6760.676 0.0000.000 66 1010 22652265 5.16 5.16 179179 0.140 0.140 0.244 0.244 0.4160.416 0.2000.200 99 1010 23012301 5.97 5.97 219219 0.105 0.105 0.192 0.192 0.4030.403 0.3000.300 99 9 9 2274 2274 5.91 5.91 245245 0.105 0.105 0.192 0.192 0.4030.403 0.3000.300 99 1212 22402240 5.55 5.55 328328 0.070 0.070 0.176 0.176 0.7540.754 0.0000.000 99 8 8 2241 2241 9.75 9.75 364 0.105 0.192 0.403 0.300 10 13 2282 7.06 364 0.105 0.192 0.403 0.300 10 13 2282 7.06
The cement content in the samples of CSRE varied from 3% to 10% and their moisture content from 6%6% toto 14%.14%. The The mean mean compressive compressive strength strength was was 6.00 6.00 MPa MPa with with a standard a standard deviation deviation of 2.093 of 2.093 MPa. TheMPa. compressive The compressive strength strength varied varied from 2.400from to2.400 13.011 to 13.011 MPa (Figure MPa ( 7Figure). 7)
Figure 7. HistogramHistogram of of the compressive strength of the samples.
All testedtested samples samples were were analyzed analyzed and tested.and tested. Their featuresTheir features are summarized are summarized in Table3. Appendixin Table A3. (TableAppendix A1) A comprises (Table A1) the comprises full set of the data. full set of data. Previous analysis [28,40,41] was the basis of the decision to standardize the input data with the linear method. TheTable following 3. The summary Formula of (1)the wasfeatures’ used: values calculated for all 373 samples.
a0i Mean Standard Feature ai = Minimumf or 1 i 373Maximum (1) maxa0i ≤ ≤ Average Deviation Clay [% of the total weight of aggregates] 0.070 0.140 0.107 0.015 where:Silt [%ai—the of the standardizedtotal weight of aggregates] value of a (from the 0.149i experiments); 0.253a0i—the original 0.206 value of 0.021a feature observedSand [% for of thei experiment. total weight of aggregates] 0.403 0.754 0.516 0.109 GravelThe [% standardization of the total weight process–done of aggregates] separately 0.000 for each feature–completed 0.300 0.172 the preparation 0.117 of data for feedingCement addition them to [% ANN. of the total weight] 3.00 10.00 7.57 2.11 Moisture content [% of the total weight] 6.00 14.00 9.86 1.74 Density [kg/m3] 2054.00 2406.33 2250.33 56.43 Compressive strength [MPa] 2.40 13.01 6.00 2.09
Previous analysis [28,40,41] was the basis of the decision to standardize the input data with the linear method. The following Formula (1) was used:
𝑎 𝑎 = 𝑓𝑜𝑟 1 𝑖 373 (1) 𝑚𝑎𝑥𝑎
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Table 3. The summary of the features’ values calculated for all 373 samples.
Feature Minimum Maximum Mean Average Standard Deviation Clay [% of the total weight of aggregates] 0.070 0.140 0.107 0.015 Silt [% of the total weight of aggregates] 0.149 0.253 0.206 0.021 Sand [% of the total weight of aggregates] 0.403 0.754 0.516 0.109 Gravel [% of the total weight of aggregates] 0.000 0.300 0.172 0.117 Cement addition [% of the total weight] 3.00 10.00 7.57 2.11 Moisture content [% of the total weight] 6.00 14.00 9.86 1.74 Density [kg/m3] 2054.00 2406.33 2250.33 56.43 Compressive strength [MPa] 2.40 13.01 6.00 2.09
2.2. Proposed Solution
2.2.1. Algorithm The authors propose an algorithmic procedure consisting of five steps that make it possible to design the composition of the CSRE. In laboratory tests, it is possible to determine the moisture of the CSRE mixture by adding an appropriate amount of water to the mixed dry ingredients of the mixture. Practically, CSRE requires adaptation of the mix design method to the real conditions prevailing at the construction site. The unique parameters of a construction site include its soil particle-size distribution and the moisture content in the soil. The authors propose the algorithm (Figure8) in which the laboratory test results can be used to determine the composition of the soil mixture through the use of field tests. From these tests, the particle-size distribution of the soil (content of clay, silt, sand and, gravel fractions) and its moisture content are obtained (STEP I). In the process of preparation of the mixture on the construction site, it should be considered that the addition of water depends on the natural moisture of the soil. In order to design CSRE mixture with a certain compressive strength based on the subsoil used, it is necessary to determine:
- The amount of Portland cement to be added, - The amount of water, - The ramming energy needed to obtain a specific dry density of the compacted soil mixture.
The following features are assumed in the proposed calculation algorithm (STEP II):
- The amount of cement to be added, - The density of compacted sample, - The compressive strength.
The density of the compacted mixture is a function of the energy used for compaction. The study of this obvious relation is not the subject of this article, however, such a relationship was observed during the experiments. Therefore the density of the compacted sample is used as one input of the ANN and it represents the energy used for the compaction process. Next (STEP III), the moisture content of the mixture intended for compaction is calculated using the artificial neural network (ANN). The inputs to the ANN are: the particle-side distribution (percentage content of clay, silt, sand, and gravel fractions), and the values of the three aforementioned assumed parameters. In STEP IV, the addition of water is calculated based on the determined amount of cement, the assumptions, and the local moisture of the soil. In the next step (STEP V), the method requires the preparation of a CSRE sample with a designed composition and checking if it can be compacted to the assumed dry density. If so, the recipe for preparing the CSRE element with the assumed compressive strength is determined. If the assumed density cannot be achieved, then the calculation of the moisture content should be repeated (back to STEP II), taking the density obtained in STEP V. The procedure between STEP II and STEP V should be repeated until the assumed density is achieved. If it cannot be obtained as a result of the procedure repetition, the assumed amount of cement to be added to the mixture should be modified. Then, the artificial neural network will predict a different moisture content. Materials 2019, 12, x FOR PEER REVIEW 11 of 27 MaterialsMaterials 2019, 201912, x, 12FOR, 1396 PEER REVIEW 11 of 2711 of 27
Figure 8. The algorithm for determining the composition of the soil mixture based on field tests.
2.2.2. CreatingFigure 8. theThe artificial algorithm neural for determining networks the composition of the soil mixture based on field tests. Figure 8. The algorithm for determining the composition of the soil mixture based on field 2.2.2.A Creating multi-layer the Artificialperceptron Neural (MLP) Networks ANN consists of neurons (nodes)–see Figure 9–where input tests.values are transformed by a so-called activation function giving the value as an output from the neuron.A multi-layer perceptron (MLP) ANN consists of neurons (nodes)—see Figure9—where input 2.2.2.values Creating are transformedthe artificial by neural a so-called networks activation function giving the value as an output from the neuron. A multi-layer perceptron (MLP) ANN consists of neurons (nodes)–see Figure 9–where input values are transformed by a so-called activation function giving the value as an output from the neuron.
Figure 9. The scheme of a neuron (node) with three inputs and one output where x1, x2, x3 are input signals from the previous ANN’s layer, w1, w2, w3 are their weights, wy the value of activation function Figure 9. The scheme of a neuron (node) with three inputs and one output where 𝑥 ,𝑥 ,𝑥 are input i.e., outgoing signal from the node to consecutive layer or output of the net [28]. signals from the previous ANN’s layer, 𝑤 ,𝑤 ,𝑤 are their weights, 𝑤𝑦 the value of activation function i.e., outgoing signal from the node to consecutive layer or output of the net [28].
Figure 9. The scheme of a neuron (node) with three inputs and one output where 𝑥 ,𝑥 ,𝑥 are input
signals from the previous ANN’s layer, 𝑤 ,𝑤 ,𝑤 are their weights, 𝑤𝑦 the value of activation function i.e., outgoing signal from the node to consecutive layer or output of the net [28].
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The argument of the activation function is calculated as shown in Formula (2). Inputs are multipliedThe argument by weights of and the summed activation up. function is calculated as shown in Formula (2). Inputs are multiplied by weights and summed up.
𝑓 n 𝑥 ∗𝑤 =𝑤𝑦 (2) X f x w = wy (2) i ∗ i i
𝑥 —the value of input 𝑖 to the neuron; 𝑤 —the weight assigned to input 𝑖 to the neuron; 𝑤𝑦—the xi—the value of input i to the neuron; wi—the weight assigned to input i to the neuron; wy—the value value of activation function i.e., output from the neuron of activation function i.e., output from the neuron. The most commonly applied activation function is a logistic Formula (3). The most commonly applied activation function is a logistic Formula (3). 1 ( ) 𝑓 𝑥 = 1 (3) f (x) = 1+𝑒 (3) 1 + e x − e𝑒—the—the basebase ofof naturalnatural logarithm.logarithm But other functions are applied too e.g., hyperbolichyperbolic tangent,tangent, linearlinear function.function. In MLP, ANNANN neuronsneurons are are grouped grouped in in layers: layers: an an input input layer, layer, a hiddena hidden layer layer (one (one or or more), more), and and an outputan output layer layer (see (see Figure Figure 10). 10).
Figure 10. Exemplary ANN (multi-layer perceptron, MLP) with 3 input nodes, 6 nodes in one hidden layer, 11 outputoutput node.node. The ANN ofof thisthis architecturearchitecture isis markedmarked asas (3-6-1).(3-6-1).
The activation function is not applied in the nodes of the input layer. Observing a given The activation function is not applied in the nodes of the input layer. Observing a given phenomenon, the data (parameters accompanying the phenomenon) is collected, as well as the results. phenomenon, the data (parameters accompanying the phenomenon) is collected, as well as the When N sets of data are collected, together with N results, the ANN can be fed with them. The results. When 𝑁 sets of data are collected, together with 𝑁 results, the ANN can be fed with them. metaheuristic algorithms (built in the software) try to find the set of weights (described above) that The metaheuristic algorithms (built in the software) try to find the set of weights (described above) minimize the error i.e., the difference between real effect of the phenomenon and the output calculated that minimize the error i.e., the difference between real effect of the phenomenon and the output by ANN for all N cases. The accuracy of predictions achieved from ANN can be verified by comparing calculated by ANN for all 𝑁 cases. The accuracy of predictions achieved from ANN can be verified them to the observed real cases. The most often applied type of error used for evaluating the accuracy by comparing them to the observed real cases. The most often applied type of error used for of predictions is the mean squared error (MSE) which is calculated from the Formula (4): evaluating the accuracy of predictions is the mean squared error (MSE) which is calculated from the Formula (4): PN 2 i=1(ci ri) MSE = − (4) ∑ (𝑐 −𝑟 ) 𝑀𝑆𝐸 = N (4) 𝑁 ci—predicted value calculated for i sample; ri—real value observed during i observation; N—number of observations. 𝑐 𝑖 𝑟 𝑖 𝑁 —predictedTo do so, avalue portion calculated of cases for from sample; the collected —real dataset value should observed be excluded during forobservation; the verification — ANNnumber accuracy of observations. (so called validation). Another portion from the dataset that should be excluded is the
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Materials 2019, 12, 1396 13 of 27 To do so, a portion of cases from the collected dataset should be excluded for the verification ANN accuracy (so called validation). Another portion from the dataset that should be excluded is the part calledcalled the the test test dataset. dataset. It provides It provides protection protection from overtrainingfrom overtraining (overfitting) (overfitting) ANN. The ANN. remaining The remainingpart of collected part of datacollected is called data ais trainingcalled a training dataset, dataset, as it is as used it isfor used finding for finding the weights. the weights. While While the thebuilt-in built-in algorithm algorithm searches searches for the for best the weights, best weight the MSEs, calculatedthe MSE calculated for training for dataset training is continuously dataset is continuouslycompared to compared the MSE for to the MSE testing for dataset. the testing When dataset. the MSEWhen for the the MSE testing for the dataset testing starts dataset to rise,starts it todefines rise, it the defines end of the the end training of the process training [42 ].process If the increasing [42]. If the continues, increasing it couldcontinues, lead toit overfitting,could lead to as overfitting,shown in Figure as shown 11. in Figure 11.
FigureFigure 11. 11. OverfittingOverfitting predictions predictions and and th thee trend trend correctly found [28]. [28].
Then the set of weights found is kept and ANN is ready to use for predictions. The accuracy is evaluated based onon thethe MSEMSE forfor validatingvalidating the the dataset, dataset, which which is is not not used used in in the the training training process process at all.at all. 3. Results 3. ResultsAs an output from the ANN, the moisture content was chosen as the dependent variable. The other seven types of data checked for each sample (i.e., clay content, silt content, sand content, gravel As an output from the ANN, the moisture content was chosen as the dependent variable. The content, cement content, density and compressive strength) serves as input–independent variables. other seven types of data checked for each sample (i.e., clay content, silt content, sand content, gravel The ANN predictions were calculated with the use of STATISTICA software (ver. 13, Dell Inc., Round content, cement content, density and compressive strength) serves as input–independent variables. Rock, TX, USA). The data were randomly divided into three subsets (training, testing, validating) with The ANN predictions were calculated with the use of STATISTICA software (ver. 13, Dell Inc., Round a proportion of 70:15:15 [43], so in the validating subsets there were 55 samples. The software allows Rock, TX, USA). The data were randomly divided into three subsets (training, testing, validating) the application of only one hidden layer. The features of five of the best predicting ANN (MLP type) with a proportion of 70:15:15 [43], so in the validating subsets there were 55 samples. The software found are presented in Table4. allows the application of only one hidden layer. The features of five of the best predicting ANN (MLP type) found are presented in Table 4. Table 4. The best predicting ANN found.
No. of CorrelationTable 4. The bestCorrelation predicting ANNCorrelation found. Activation Activation ANN Neurons in of the of the of the Function in Function in No. of Neurons Correlation of Correlation of Correlation of Activation Activation ANNNumber the Hidden Training Testing Validating the Hidden the Output in the Hidden the Training the Testing the Validating Function in the Function in the Number Layer Dataset Dataset Dataset Layer Layer Layer Dataset Dataset Dataset Hidden Layer Output Layer 1 113 130.9104 0.9104 0.8877 0.8877 0.8557 0.8557 tanh tanh linearlinear 2 26 60.9031 0.9031 0.8798 0.8798 0.8831 0.8831 tanh tanh linearlinear 3 310 100.9233 0.9233 0.8817 0.8817 0.8522 0.8522 tanh tanh tanh tanh 4 44 40.9053 0.9053 0.8626 0.8626 0.8503 0.8503 tanh tanh linearlinear 5 523 230.9431 0.9431 0.9183 0.9183 0.8579 0.8579 tanh tanh exponentialexponential
The small differences between correlation factors for training, testing and validating datasets The small differences between correlation factors for training, testing and validating datasets (and (and original values of the moisture content) ensure that the results found are not overfitted. The original values of the moisture content) ensure that the results found are not overfitted. The differences differences between the original and projected values of the moisture content are shown in Figure 12 between the original and projected values of the moisture content are shown in Figure 12 (results for (results for all 5 nets and all subsets). all 5 nets and all subsets).
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FigureFigure 12. 12. OriginalOriginal and and predicted predicted values values of the moisture contentcontent (both (both standardized). standardized).
BeforeBefore the the prediction prediction errors errors were were calculated, calculated, the predictionprediction valuesvalues (for (for the the validating validating dataset) dataset) hadhad been been back back converted converted to to have have the the original original unit i.e.,i.e., moisturemoisture content content given given in in a percentage.a percentage. The The MSEMSE and and the the square square root root of of it, it, called called the the RMSE (root meanmean squaredsquared error), error), are are good good for for comparing comparing thethe accuracy accuracy achieved achieved by by different different ANNs. ANNs. Neverthele Nevertheless,ss, thethe threethree otherother types types of of errors errors can can be be more more informative for a researcher who would like to use predicting features of ANN for a new set of data informative for a researcher who would like to use predicting features of ANN for a new set of data where the result is unknown. These types of errors are as follows (5,6,7): where the result is unknown. These types of errors are as follows (5,6,7): - - MeanMean absolute absolute error error (MAE) (MAE) PN ∑|i=𝑐 1−𝑟ci |ri 𝑀𝐴𝐸MAE = = | − | (5)(5) 𝑁 N - - MeanMean absolute absolute percentage percentage error error (MAPE) (MAPE)