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Materials 2019, 12(9), 1396; https://doi.org/10.3390/ma12091396

Article
Designing the Composition of Cement Stabilized Rammed Earth Using Artificial Neural Networks
Faculty of Civil Engineering, Warsaw University of Technology, Al. Armii Ludowej 16, 00-637 Warsaw, Poland
*
Authors to whom correspondence should be addressed.
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 (Figure 1).
Striving for the most extensive use of natural materials, buildings made of earth can be an alternative option to other natural materials such as wood, which due to its flammability must be impregnated, whereas earth is non-flammable [3]. On the other hand, building structures made of earth are considered to not be durable. However, it is worth noting that in many regions of the world impressive ancient buildings made of earth can be admired. The best-known example is the Great Wall of China (Figure 2), of which numerous fragments erected in the rammed earth technology about 4000 years ago have survived until the present day.
In the regions of the world with hot and dry climates, there are not only buildings, but whole cities built with technologies using the earth. The most well-known city of this type is Shibam in Yemen (Figure 3). Some buildings of this city, erected in the 19th and 20th centuries, with technologies using the earth, are even 11 stories tall. This confirms that it is possible to use the land as a material for building multi-story residential buildings. Other examples of constructions built with technologies using the earth that belong to the history of architecture, including the proportions of soil, cement, and water that were used in the past, can be found in references [4,5].
Over the centuries, many building technologies that use earth have been developed in various 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 main groups [7]:
-
Techniques that use earth in load-bearing monolithic constructions.
-
Techniques that use earth in load-bearing masonry structures.
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Techniques that use earth as a non-bearing construction material in combination with a supporting structure of another material.
This paper focuses on one of the technologies of erecting load-bearing monolithic earth structures i.e., cement stabilized rammed earth (CSRE). CSRE is a highly sustainable construction technique characterized by low energy demand and a small amount of waste generated during the construction process. The structure consists of rammed layers of moist mixture made in a formwork set on a stable foundation (Figure 4). A basic component of the mixture is the subsoil that lies under the layer of humus usually taken directly from the construction site. The limiting factor determining the suitability of the subsoil for rammed earth technology is the quantity of organic substances. The organic soil is biodegradable, easily absorbs water, and is highly compressible. Therefore, its presence in the soil mixture should not exceed 1% of the total weight of the soil [8]. Depending on the particle size distribution of the soil, the mixture is modified by adding appropriate aggregate fractions and Portland cement. The components are mixed together in an air-dry state, and then water is added to ensure the proper moisture content of the mixture. Layers of the mixture are filled in the formwork and then compacted by mechanical means. After proper compaction of the layer, successive ones are added until the planned height of the element is reached. The formwork is then removed. Since compaction leads to closer packing of soil grains, this process eventually leads to increased mechanical strength [4]. Durability of a monolithic wall made of CSRE with adequate load 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].
A significant part of building project expenses is associated with transport of materials to the construction site. Therefore, one of the ways to reduce those costs is to reduce the need for transportation. Cement stabilized rammed earth technology allows for erecting monolithic load-bearing walls using locally available material, which is a very good solution in less urbanized areas located far from wholesalers.
The compressive strength is a significant mechanical feature of a structural building material. The results of laboratory tests for the compressive strength of cement stabilized rammed earth are presented in numerous publications (Table 1). However, results obtained by individual authors are difficult to compare due to differences in:
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Shapes of the tested samples,
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Energy used in ramming samples and the related volume density of samples,
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Particle size distribution of the earth used in the mixture,
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Mineral and chemical composition of the earth,
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Moisture content of the earth mixture,
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Moisture content of the samples at the time of the test,
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Content and type of Portland cement,
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Duration and conditions of samples storage before strength tests.
The lack of information on some of those parameters is the main challenge in analyzing the results published. For example, from the tests included in Table 1, only article [11] 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.
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 Table 1 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 as particle size distribution, humidity, energy, and the method of ramming, as well as the mineral composition of the applied earth significantly influence the obtained compressive strength. In the absence of standards for the design of cement stabilized rammed earth and the individual approach 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 and the greater the complexity of the process, the more benefits using ANN provides (compared to statistical models, expert systems, Figure 5) [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],
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Level of deterioration of multi-story buildings [32],
-
Loss of a client in the case of collusion [33],
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Energy demand for housing purposes [34,35],
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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 particle-size distribution curves shown in the Figure 6. 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 optimal level.

2.1.2. Preparation of Samples

CSRE samples were prepared in cubic molds, 100 mm × 100 mm × 100 mm. The formation of the samples was carried out by ramming the mixture into three equal layers using a 6.5 kg rammer. The parameters of the rammer were selected on the basis of New Zealand Standard [23]. The samples were formed by freely lowering the rammer from a height of 30 cm to the surface of the moist mixture. For this method of compaction, the optimum moisture content in individual mixtures was 7% to 10% depending on the particle size distribution and the amount of cement.
For each series, 10 samples were made. The authors participated in the preparation of all samples. Therefore, the influence of the sample preparation method on the compressive strength results can be ruled out. The samples to be tested were demolded after 24 h. Then they were cured for 27 days in a condition of relatively high humidity of 95% (±2%) and temperature of 20 °C (±1 °C).

2.1.3. Results of Testing the Samples

Since the rammed earth keeps the layered structure, the samples were loaded in the direction of the ramming. 373 compressive strength results were obtained for the prepared samples. The results of some of these samples are shown in Table 2. The results obtained served as a database for calculations using ANN.
The cement content in the samples of CSRE varied from 3% to 10% and their moisture content from 6% to 14%. The mean compressive strength was 6.00 MPa with a standard deviation of 2.093 MPa. The compressive strength varied from 2.400 to 13.011 MPa (Figure 7).
All tested samples were analyzed and tested. Their features are summarized in Table 3. Appendix A (Table A1) comprises the full set of data.
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 i = a 0 i m a x a 0 i   f o r   1 i 373
where: a i —the standardized value of a (from the i experiments); a 0 i —the original value of a feature observed for i experiment.
The standardization process–done separately for each feature–completed the preparation of data for feeding them to ANN.

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 (Figure 8) 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:
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The amount of Portland cement to be added,
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The amount of water,
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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):
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The amount of cement to be added,
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The density of compacted sample,
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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.

2.2.2. Creating the Artificial Neural Networks

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.
The argument of the activation function is calculated as shown in Formula (2). Inputs are multiplied by weights and summed up.
f ( i n x i w i ) = w y
x i —the value of input i to the neuron; w i —the weight assigned to input i to the neuron; w y —the value of activation function i.e., output from the neuron.
The most commonly applied activation function is a logistic Formula (3).
f ( x ) = 1 1 + e x
e —the base of natural logarithm.
But other functions are applied too e.g., hyperbolic tangent, linear function.
In MLP, ANN neurons are grouped in layers: an input layer, a hidden layer (one or more), and an output layer (see Figure 10).
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. When N sets of data are collected, together with N results, the ANN can be fed with them. The metaheuristic algorithms (built in the software) try to find the set of weights (described above) that minimize the error i.e., the difference between real effect of the phenomenon and the output calculated by ANN for all N cases. The accuracy of predictions achieved from ANN can be verified by comparing them to the observed real cases. The most often applied type of error used for evaluating the accuracy of predictions is the mean squared error (MSE) which is calculated from the Formula (4):
M S E = i = 1 N ( c i r i ) 2 N
c i —predicted value calculated for i sample; r i —real value observed during i observation; N —number of observations.
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 called the test dataset. It provides protection from overtraining (overfitting) ANN. The remaining part of collected data is called a training dataset, as it is used for finding the weights. While the built-in algorithm searches for the best weights, the MSE calculated for training dataset is continuously compared to the MSE for the testing dataset. When the MSE for the testing dataset starts to rise, it defines the end of the training process [42]. If the increasing continues, it could lead to overfitting, as shown in Figure 11.
Then the set of weights found is kept and ANN is ready to use for predictions. The accuracy is evaluated based on the MSE for validating the dataset, which is not used in the training process at all.

3. Results

As 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 content, cement content, density and compressive strength) serves as input–independent variables. The ANN predictions were calculated with the use of STATISTICA software (ver. 13, Dell Inc., Round Rock, TX, USA). The data were randomly divided into three subsets (training, testing, validating) with a proportion of 70:15:15 [43], so in the validating subsets there were 55 samples. The software 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.
The small differences between correlation factors for training, testing and validating datasets (and original values of the moisture content) ensure that the results found are not overfitted. The differences between the original and projected values of the moisture content are shown in Figure 12 (results for all 5 nets and all subsets).
Before the prediction errors were calculated, the prediction values (for the validating dataset) had been back converted to have the original unit i.e., moisture content given in a percentage. The MSE and the square root of it, called the RMSE (root mean squared error), are good for comparing the accuracy achieved by different ANNs. Nevertheless, the three other types of errors can be more 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):
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Mean absolute error (MAE)
M A E = i = 1 N | c i r i | N
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Mean absolute percentage error (MAPE)
M A P E = i = 1 N | c i r i r i | N 100 %
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Maximum absolute percentage error (maxAPE)
m a x A P E = | c i r i r i | 100 %   f o r   1 i N
The values for the above-mentioned errors are shown in Table 5 for all five of the best predicting ANNs found.
The lowest value of error is highlighted for each error type. The ANN No. 2 (7-6-1) was chosen for further predictions as three types of errors calculated (for the validating dataset) are the lowest. The net No. 5 gives the lowest maxAPE. We decided to omit it, based on the fact that the accuracy of predictions made for the lowest and the highest moisture content (as can be seen in Figure 12) are the poorest. Observing the best MSE, MAE and MAPE for ANN No 2, it can be said that extreme moisture content barely influenced the training process. Based on the chosen ANN (7-6-1), the predictions of desired moisture content can be obtained.

4. Discussion

Below is the exemplary process for designing CSRE based on the proposed algorithm and ANN predictions.
STEP I. Let us assume (for the purpose of exemplary calculation) that according to the Figure 8, the soil found at the location of a future structure made of CSRE is characterized by the following aggregate fractions content: clay 10.5%, silt 20.1%, sand 49.4%, gravel 20.0%. The original moisture content checked was 3.00 [%].
STEP II. Real values (from STEP I) are to be extended by assuming the following properties: the compressive strength to achieve (e.g., 7.885 MPa), the addition of cement (e.g., 9%), and the density after the ramming process (e.g., 2238 kg/m3).
STEP III. The chosen ANN (7-6-1) produced the required moisture content at 7.89 [%]. Then, considering the original moisture content of the soil (3%), the addition of the water can be calculated.
STEP IV. Considering the original moisture content of the soil from the construction site (3.00 [%]), the mass of water to be added to obtain the desired moisture content of the CSRE mixture with the assumed cement addition, can be calculated based on the Formula (8):
m x = y 1 y ( m g + m c ) m w
where: m g + m c —the mass of moist subsoil from the construction site, [kg]; m g —the mass of the dried subsoil, [kg]; m w —the mass of water in the subsoil [kg] determined as the difference in mass of the moist subsoil and the dried subsoil, [kg]; m c —the mass of the cement added, [kg]; m x —mass of water that should be added to the CSRE mixture to achieve the desired moisture content specified by the ANN, [kg]; y —predicted moisture content of the CSRE mixture with the use of ANN, [%].
For 100 [kg] of subsoil with a moisture content of 3%, the mass of dry soil and the mass of water in the soil can be calculated from the following Formula (9):
w = m w m g + m w
Thus, the mass of water in this soil is:
3 % = m w 100     m w = 3   [ kg ]
Then, the mass of dry soil can be calculated:
m g + m w = 100     m g = 97   [ kg ]
For this dry soil, the mass of cement to be added is:
m c = 97 × 9 % = 8.73   [ kg ]
To obtain the moisture content of the CSRE mixture containing 100 [kg] of subsoil with a moisture content of 3% and 8.73 [kg] of cement added, the following amount of water should be added:
m x = 7.89 % 1 7.89 % ( 97 + 8.73 ) 3 6.06   [ kg ]
STEP V. As the process of ramming the mixture influences the density of the compacted CSRE, and it is not yet standardized, predictions were made for the set of assumed density, varying from 2118 to 2358 [kg/m3]. The predicted moisture content results are shown in Figure 13.
The above density-moisture curve has been found by predicting the moisture content for a given density through the use of the ANN. The density can be checked after adding all the components of the CSRE and compacting the mixture. If the pair of parameters (density and moisture) fits any point on the curve presented in Figure 13, the assumed compressive strength should be achieved. The algorithm then comes to a stop. The composition of the CSRE based on the site’s subsoil is found. If any combination of the predicted moisture content and the assumed density is not possible to achieve (the pair moisture-density does not fit any point on the curve), the assumptions should be changed–the algorithm comes back to STEP II.
The proposed method requires that, the following simultaneous changes to the assumptions of three values should be made (in STEP II): required compressive strength, cement addition, and the density to achieve. These changes may cause some trouble for the user. The density may be evaluated before the assumption is made based on trial soil compaction where only water is added. The compressive strength and the cement added is positively (but not strongly) corelated, as stated above. The following Table 6—based on the 373 samples prepared and checked—shows the ranges of compressive strength achieved for different portions of cement added.
It is suggested to base the three assumptions on the 373 experiments done by the authors and summarized in Table 6, as well as on the subsoil on site (checking the density after compaction with only water added).

5. Conclusions

The article presents the possibility of using artificial neural networks for designing cement stabilized rammed earth mixtures. Using artificial neural networks, the moisture content of the CSRE mixture was predicted to ensure the assumed compressive strength. The input database was large enough that the artificial neural network found by the software Statistica produced predictions of high accuracy. The mean absolute error MAE was 0.565 [%] of the designed moisture content. It should be emphasized that the prediction errors obtained are smaller than the accuracy when preparing the CSRE mixture under the conditions prevailing at the construction site (e.g., due to changing weather conditions). The algorithm was created for designing cement stabilized rammed earth with the use of subsoil obtained from the construction site. The developed algorithm allows us to determine, using relatively simple soil tests (analysis of grain size and humidity), the composition of the mixture ensuring compressive strength at a level that allows the use of this material in construction. It should be emphasized that the equipment necessary to assess density and particle size distribution is more simple, accessible, and affordable to provide on site, than equipment for compressive strength testing. Software for artificial neural networks (not commonly used in finding a CSRE recipe) that excludes the need of using compressive strength test machinery, is a step toward the real application of CSRE as a structure material. The variety of the soil types that can be found, and—for the time being—the low popularity of CSRE, create some uncertainty in the compressive strength level that can be achieved on a building site. The large size of the database of the samples tested, as well as high accuracy of ANN predictions achieved and presented above, made the authors believe that the created method of designing CSRE will be successfully applied for random soils gathered from variety of locations. The forthcoming research is to be aimed at simplification of the process of designing the CSRE mixture in a way that would hopefully allow builders to prepare the recipe on site.

Author Contributions

Conceptualization, P.N. and H.A.; methodology, P.N. and H.A. validation, P.N.; formal analysis, H.A.; investigation, P.N.; resources, P.N.; data curation, P.N. and H.A.; writing—original draft preparation, P.N. and H.A.; writing—review and editing, P.N. and H.A.; visualization, P.N.; supervision, P.N.; project administration, P.N.; funding acquisition, P.N.

Funding

This research received financial support from the Faculty of Civil Engineering, Warsaw University of Technology.

Acknowledgments

The authors would like to acknowledge the significant help that students of Warsaw University of Technology provided in the preparing and testing of hundreds CSRE samples.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

Table A1. The set of features of 373 samples and the compressive test result are presented in Appendix A.
Table A1. The set of features of 373 samples and the compressive test result are presented in Appendix A.
No.Particle size Distribution [%]Cement Addition [%]Moisture Content [%]Density [kg/m3]Compressive Strength [MPa]
ClaySiltSandGravel
10.1050.1920.4030.3003.09.02296.294.1791
20.1050.1920.4030.3003.09.02300.483.5000
30.1050.1920.4030.3003.09.02277.393.2511
40.1050.1920.4030.3003.09.02270.353.1841
50.1050.1920.4030.3003.09.02309.104.1584
60.1050.1920.4030.3003.09.02295.204.0098
70.1050.1920.4030.3003.09.02311.224.2000
80.1050.1920.4030.3003.09.02277.223.5821
90.1050.1920.4030.3003.09.02295.753.1841
100.1050.2010.4940.2003.09.02252.052.5742
110.1050.2010.4940.2003.09.02273.632.5373
120.1050.2010.4940.2003.09.02168.932.6500
130.1050.2010.4940.2003.09.02284.032.8570
140.1050.2010.4940.2003.09.02260.272.7861
150.1050.2010.4940.2003.09.02275.852.8570
160.1050.2010.4940.2003.09.02280.892.7227
170.1050.2010.4940.2003.09.02282.962.7363
180.1050.2010.4940.2003.09.02258.952.4378
190.1050.2010.4940.2003.09.02267.482.4998
200.1050.2100.5850.1003.09.02252.373.2338
210.1050.2100.5850.1003.09.02246.323.0846
220.1050.2100.5850.1003.09.02221.563.4314
230.1050.2100.5850.1003.09.02248.512.9208
240.1050.2100.5850.1003.09.02267.343.1500
250.1050.2100.5850.1003.09.02288.723.3500
260.1050.2100.5850.1003.09.02275.493.3000
270.1050.2100.5850.1003.09.02251.153.3333
280.1050.2100.5850.1003.09.02250.363.1683
290.1050.2190.6760.0003.010.02232.843.3333
300.1050.2190.6760.0003.010.02212.643.3663
310.1050.2190.6760.0003.010.02238.933.3333
320.1050.2190.6760.0003.010.02252.733.2672
330.1050.2190.6760.0003.010.02250.863.4171
340.1050.2190.6760.0003.010.02237.223.4826
350.1050.2190.6760.0003.010.02254.713.4328
360.1050.2190.6760.0003.010.02225.453.2177
370.1400.2530.5070.1006.011.02271.135.4000
380.1400.2530.5070.1006.011.02294.905.3000
390.1400.2530.5070.1006.011.02306.255.4500
400.1400.2530.5070.1006.011.02313.545.1500
410.1400.2530.5070.1006.011.02317.354.6500
420.1400.2530.5070.1006.011.02293.484.8000
430.1400.2440.4160.2006.011.02285.296.6000
440.1400.2440.4160.2006.011.02303.336.1000
450.1400.2440.4160.2006.011.02393.556.8000
460.1400.2440.4160.2006.011.02283.516.9000
470.1400.2440.4160.2006.011.02314.296.9000
480.1050.1920.4030.3006.08.02258.967.1802
490.1050.1920.4030.3006.08.02235.147.4666
500.1050.1920.4030.3006.08.02271.987.1465
510.1050.1920.4030.3006.08.02263.905.9293
520.1050.1920.4030.3006.08.02292.218.0000
530.1050.1920.4030.3006.08.02219.886.5238
540.1050.1920.4030.3006.08.02229.856.3367
550.1050.1920.4030.3006.08.02220.226.4764
560.1050.1920.4030.3006.08.02249.587.4777
570.1050.1920.4030.3006.08.02245.616.5906
580.1050.1920.4030.3006.08.02197.846.2933
590.1050.1920.4030.3006.08.02269.157.8710
600.1050.1920.4030.3006.08.02297.667.2144
610.1050.1920.4030.3006.09.02250.735.1026
620.1050.1920.4030.3006.09.02309.666.0000
630.1050.1920.4030.3006.09.02295.934.6488
640.1050.1920.4030.3006.09.02315.215.2528
650.1050.1920.4030.3006.09.02281.725.3810
660.1050.1920.4030.3006.010.02325.725.7921
670.1050.1920.4030.3006.010.02348.725.8506
680.1050.1920.4030.3006.010.02406.336.0290
690.1050.1920.4030.3006.010.02294.475.9406
700.1050.1920.4030.3006.010.02196.755.7711
710.1050.1920.4030.3006.010.02209.445.5224
720.1050.1920.4030.3006.010.02343.655.7426
730.1050.1920.4030.3006.010.02320.415.8125
740.1050.1920.4030.3006.010.02324.065.9701
750.1050.1920.4030.3006.010.02311.225.5500
760.1050.1920.4030.3006.010.02183.265.7711
770.1050.1920.4030.3006.010.02252.003.7000
780.1050.1920.4030.3006.010.02339.003.4000
790.1050.1920.4030.3006.010.02264.002.6500
800.1050.1920.4030.3006.010.02348.002.5500
810.1050.1920.4030.3006.08.02240.286.4500
820.1050.1920.4030.3006.08.02281.427.0289
830.1050.1920.4030.3006.08.02292.337.9206
840.1050.1920.4030.3006.08.02228.546.4436
850.1050.1920.4030.3006.08.02307.747.4650
860.1050.1920.4030.3006.08.02235.596.3053
870.1050.1920.4030.3006.08.02248.508.7413
880.1050.1920.4030.3006.08.02301.877.8764
890.1050.1920.4030.3006.08.02272.276.9069
900.1050.2010.4940.2006.010.02259.704.2000
910.1050.2010.4940.2006.010.02284.583.8500
920.1050.2010.4940.2006.010.02283.054.1870
930.1050.2010.4940.2006.010.02274.753.8308
940.1050.2010.4940.2006.010.02264.634.0500
950.1050.2010.4940.2006.010.02273.003.2500
960.1050.2010.4940.2006.010.02249.003.5500
970.1050.2010.4940.2006.010.02361.003.4000
980.1050.2010.4940.2006.011.02254.814.5500
990.1050.2010.4940.2006.011.02270.315.1741
1000.1050.2010.4940.2006.011.02260.674.4058
1010.1050.2010.4940.2006.011.02311.555.2000
1020.1050.2010.4940.2006.011.02274.485.2239
1030.1050.2100.5850.1006.08.02234.806.0990
1040.1050.2100.5850.1006.08.02255.376.5206
1050.1050.2100.5850.1006.08.02227.596.1659
1060.1050.2100.5850.1006.08.02241.756.4026
1070.1050.2100.5850.1006.08.02212.895.0814
1080.1050.2100.5850.1006.08.02217.825.4315
1090.1050.2100.5850.1006.08.02236.036.4734
1100.1050.2100.5850.1006.08.02213.096.0655
1110.1050.2100.5850.1006.08.02212.956.2931
1120.1050.2100.5850.1006.08.02211.135.6034
1130.1050.2100.5850.1006.08.02237.125.7443
1140.1050.2100.5850.1006.09.02314.005.6500
1150.1050.2100.5850.1006.09.02281.955.5000
1160.1050.2100.5850.1006.09.02289.005.0000
1170.1050.2100.5850.1006.09.02276.425.0746
1180.1050.2100.5850.1006.09.02291.715.8000
1190.1050.2100.5850.1006.09.02282.005.3500
1200.1050.2100.5850.1006.09.02284.266.0000
1210.1050.2100.5850.1006.09.02299.255.5500
1220.1050.2100.5850.1006.010.02320.003.9000
1230.1050.2100.5850.1006.010.02192.003.5000
1240.1050.2190.6760.0006.08.02183.924.2440
1250.1050.2190.6760.0006.08.02159.984.0781
1260.1050.2190.6760.0006.08.02137.154.3948
1270.1050.2190.6760.0006.08.02141.433.9237
1280.1050.2190.6760.0006.08.02171.974.0214
1290.1050.2190.6760.0006.08.02226.394.2073
1300.1050.2190.6760.0006.08.02238.214.3331
1310.1050.2190.6760.0006.08.02172.374.0469
1320.1050.2190.6760.0006.09.02264.706.1022
1330.1050.2190.6760.0006.09.02302.166.3000
1340.1050.2190.6760.0006.09.02264.616.1570
1350.1050.2190.6760.0006.09.02257.526.2194
1360.1050.2190.6760.0006.09.02225.895.8424
1370.1050.2190.6760.0006.010.02275.034.9624
1380.1050.2190.6760.0006.010.02265.665.0000
1390.1050.2190.6760.0006.010.02287.005.3250
1400.1050.2190.6760.0006.010.02266.015.0000
1410.1050.2190.6760.0006.010.02216.504.9000
1420.1050.2190.6760.0006.010.02276.695.4094
1430.1050.2190.6760.0006.010.02263.685.3000
1440.1050.2190.6760.0006.010.02265.475.1629
1450.1050.2190.6760.0006.010.02248.715.0746
1460.1050.2190.6760.0006.010.02238.365.1250
1470.1050.2190.6760.0006.010.02201.002.6000
1480.1050.2190.6760.0006.010.02232.002.6500
1490.1050.2190.6760.0006.010.02282.002.4000
1500.1050.2190.6760.0006.010.02174.002.4000
1510.1050.2190.6760.0006.010.02267.002.8500
1520.0700.1490.4810.3006.08.02326.736.0500
1530.0700.1490.4810.3006.08.02324.515.9606
1540.0700.1490.4810.3006.08.02311.446.2000
1550.0700.1490.4810.3006.08.02318.006.0500
1560.0700.1490.4810.3006.08.02330.356.2189
1570.1050.2190.6760.0009.08.02164.575.2740
1580.1050.2190.6760.0009.08.02155.705.3449
1590.1050.2190.6760.0009.08.02184.065.4242
1600.1050.2190.6760.0009.08.02166.345.1267
1610.1050.2190.6760.0009.08.02202.035.9707
1620.1050.2190.6760.0009.08.02178.256.2912
1630.1050.2190.6760.0009.08.02186.326.3192
1640.1050.2190.6760.0009.08.02205.576.2857
1650.1050.2190.6760.0009.08.02189.385.7382
1660.1050.2190.6760.0009.08.02197.356.2262
1670.1400.2530.5070.1009.010.02256.547.0000
1680.1400.2530.5070.1009.010.02258.606.1307
1690.1400.2530.5070.1009.011.02295.838.8000
1700.1400.2530.5070.1009.011.02283.848.2500
1710.1400.2530.5070.1009.011.02276.246.5000
1720.1400.2530.5070.1009.011.02239.786.5000
1730.1400.2530.5070.1009.011.02274.498.2000
1740.1400.2530.5070.1009.011.02269.798.3000
1750.1400.2530.5070.1009.012.02211.055.9901
1760.1400.2530.5070.1009.012.02236.105.9406
1770.1400.2530.5070.1009.014.02128.004.0000
1780.1400.2530.5070.1009.014.02054.003.8500
1790.1400.2440.4160.2009.010.02301.315.9701
1800.1400.2440.4160.2009.010.02310.387.7000
1810.1400.2440.4160.2009.011.02239.185.9500
1820.1400.2440.4160.2009.011.02323.085.7000
1830.1400.2440.4160.2009.011.02324.494.5000
1840.1400.2440.4160.2009.011.02270.834.5500
1850.1400.2440.4160.2009.011.02280.415.1000
1860.1400.2440.4160.2009.011.02251.495.0500
1870.1400.2440.4160.2009.012.02260.916.3000
1880.1400.2440.4160.2009.012.02251.466.3500
1890.1400.2440.4160.2009.014.02206.255.1000
1900.1400.2440.4160.2009.014.02191.885.2500
1910.1400.2440.4160.2009.011.02116.137.0549
1920.1400.2440.4160.2009.011.02310.116.7098
1930.1400.2440.4160.2009.011.02237.367.6312
1940.1400.2440.4160.2009.011.02192.977.3668
1950.1400.2440.4160.2009.011.02345.266.3662
1960.1400.2440.4160.2009.011.02233.407.1221
1970.1050.1920.4030.3009.06.02104.862.8655
1980.1050.1920.4030.3009.06.02089.062.6487
1990.1050.1920.4030.3009.08.02227.178.7604
2000.1050.1920.4030.3009.08.02259.549.4042
2010.1050.1920.4030.3009.08.02294.417.3597
2020.1050.1920.4030.3009.08.02322.9311.6269
2030.1050.1920.4030.3009.08.02271.888.6678
2040.1050.1920.4030.3009.08.02285.4511.9300
2050.1050.1920.4030.3009.08.02245.579.5605
2060.1050.1920.4030.3009.08.02290.1210.8647
2070.1050.1920.4030.3009.08.02292.2610.9991
2080.1050.1920.4030.3009.08.02279.6210.0958
2090.1050.1920.4030.3009.08.02173.606.9767
2100.1050.1920.4030.3009.08.02183.146.9950
2110.1050.1920.4030.3009.08.02207.378.3494
2120.1050.1920.4030.3009.08.02154.725.8439
2130.1050.1920.4030.3009.08.02252.867.8765
2140.1050.1920.4030.3009.08.02240.606.7946
2150.1050.1920.4030.3009.09.02254.316.2593
2160.1050.1920.4030.3009.09.02269.216.5378
2170.1050.1920.4030.3009.09.02280.576.3936
2180.1050.1920.4030.3009.09.02239.865.6135
2190.1050.1920.4030.3009.09.02273.755.9059
2200.1050.1920.4030.3009.09.02295.129.4057
2210.1050.1920.4030.3009.09.02238.069.3703
2220.1050.1920.4030.3009.09.02281.419.6845
2230.1050.1920.4030.3009.09.02343.8710.0381
2240.1050.1920.4030.3009.09.02240.289.2285
2250.1050.1920.4030.3009.09.02255.739.8156
2260.1050.1920.4030.3009.010.02265.426.3434
2270.1050.1920.4030.3009.010.02291.147.5399
2280.1050.1920.4030.3009.010.02284.327.4425
2290.1050.1920.4030.3009.010.02265.537.3845
2300.1050.1920.4030.3009.010.02319.466.5072
2310.1050.1920.4030.3009.010.02267.647.1293
2320.1050.1920.4030.3009.010.02310.576.5271
2330.1050.1920.4030.3009.010.02303.915.9115
2340.1050.1920.4030.3009.010.02295.616.4227
2350.1050.1920.4030.3009.010.02318.056.1133
2360.1050.1920.4030.3009.010.02311.836.7966
2370.1050.1920.4030.3009.010.02321.376.8397
2380.1050.1920.4030.3009.010.02313.686.0139
2390.1050.1920.4030.3009.011.02268.004.9500
2400.1050.1920.4030.3009.011.02256.005.3000
2410.1050.1920.4030.3009.011.02299.004.6500
2420.1050.1920.4030.3009.011.02328.004.6000
2430.1050.1920.4030.3009.012.02219.746.3408
2440.1050.1920.4030.3009.012.02238.885.6287
2450.1050.1920.4030.3009.012.02240.005.5554
2460.1050.1920.4030.3009.012.02224.646.3189
2470.1050.1920.4030.3009.012.02240.675.9166
2480.1050.1920.4030.3009.012.02216.415.5229
2490.1050.1920.4030.3009.014.02084.113.5100
2500.1050.1920.4030.3009.014.02122.173.5559
2510.1050.2010.4940.2009.08.02240.718.3359
2520.1050.2010.4940.2009.08.02151.647.8853
2530.1050.2010.4940.2009.08.02218.899.2350
2540.1050.2010.4940.2009.08.02153.387.6816
2550.1050.2010.4940.2009.08.02206.078.1360
2560.1050.2010.4940.2009.08.02234.698.8511
2570.1050.2010.4940.2009.08.02234.586.4882
2580.1050.2010.4940.2009.08.02195.7610.0693
2590.1050.2010.4940.2009.08.02233.439.8294
2600.1050.2010.4940.2009.011.02328.004.9000
2610.1050.2010.4940.2009.011.02229.005.2000
2620.1050.2100.5850.1009.08.02188.228.5159
2630.1050.2100.5850.1009.08.02287.568.2171
2640.1050.2100.5850.1009.08.02257.549.6211
2650.1050.2100.5850.1009.08.02233.238.8703
2660.1050.2100.5850.1009.08.02239.287.1642
2670.1050.2100.5850.1009.08.02321.508.6692
2680.1050.2100.5850.1009.08.02238.309.9005
2690.1050.2100.5850.1009.08.02277.119.6347
2700.1050.2100.5850.1009.010.02144.385.2550
2710.1050.2100.5850.1009.010.02111.714.6074
2720.1050.2100.5850.1009.010.02100.105.0540
2730.1050.2100.5850.1009.010.02171.445.5863
2740.1050.2100.5850.1009.011.02223.004.2000
2750.1050.2100.5850.1009.011.02291.004.2000
2760.1050.2100.5850.1009.011.02329.003.4000
2770.1050.2100.5850.1009.011.02319.005.5000
2780.1050.2100.5850.1009.011.02206.004.2000
2790.1050.2100.5850.1009.011.02211.003.3000
2800.1050.2190.6760.0009.08.02140.424.9362
2810.1050.2190.6760.0009.08.02129.015.8578
2820.1050.2190.6760.0009.08.02131.595.7112
2830.1050.2190.6760.0009.08.02105.614.9440
2840.1050.2190.6760.0009.08.02147.535.4470
2850.1050.2190.6760.0009.010.02215.526.2493
2860.1050.2190.6760.0009.010.02221.036.5280
2870.1050.2190.6760.0009.010.02239.916.4400
2880.1050.2190.6760.0009.010.02215.536.4599
2890.1050.2190.6760.0009.010.02197.266.5711
2900.1050.2190.6760.0009.011.02173.003.9000
2910.1050.2190.6760.0009.011.02188.005.3000
2920.1050.2190.6760.0009.011.02248.004.8400
2930.1050.2190.6760.0009.011.02234.003.6000
2940.1050.2190.6760.0009.011.02298.003.2500
2950.1050.2190.6760.0009.011.02192.766.3770
2960.1050.2190.6760.0009.011.02252.536.9888
2970.1050.2190.6760.0009.011.02251.156.4942
2980.1050.2190.6760.0009.011.02213.527.3178
2990.1050.2190.6760.0009.011.02256.297.4530
3000.1050.2190.6760.0009.011.02235.506.7844
3010.1050.2190.6760.0009.012.02207.695.0076
3020.1050.2190.6760.0009.012.02185.165.2227
3030.1050.2190.6760.0009.012.02205.324.8635
3040.1050.2190.6760.0009.012.02151.995.0661
3050.1050.2190.6760.0009.012.02195.585.1813
3060.1050.2190.6760.0009.014.02108.363.4827
3070.1050.2190.6760.0009.014.02119.633.0895
3080.1050.2190.6760.0009.014.02161.183.0960
3090.1050.2190.6760.0009.014.02125.803.3113
3100.1050.2190.6760.0009.014.02121.112.9600
3110.1050.2190.6760.0009.014.02114.943.3066
3120.0700.1490.4810.3009.08.02221.0612.3858
3130.0700.1490.4810.3009.08.02189.1213.0106
3140.0700.1490.4810.3009.08.02216.1312.6901
3150.0700.1490.4810.3009.08.02226.0211.6468
3160.0700.1580.5720.2009.08.02334.339.3000
3170.0700.1580.5720.2009.08.02329.239.2574
3180.0700.1580.5720.2009.08.02335.719.2000
3190.0700.1580.5720.2009.08.02362.979.0099
3200.0700.1580.5720.2009.08.02343.219.5002
3210.0700.1580.5720.2009.08.02263.7410.8609
3220.0700.1580.5720.2009.08.02281.878.9811
3230.0700.1580.5720.2009.08.02251.7510.5418
3240.0700.1580.5720.2009.08.02229.0510.4647
3250.0700.1580.5720.2009.08.02166.0910.3287
3260.0700.1580.5720.2009.08.02209.4011.0470
3270.0700.1760.7540.0009.08.02256.729.7500
3280.0700.1760.7540.0009.08.02241.279.6535
3290.0700.1760.7540.0009.08.02221.249.5613
3300.0700.1760.7540.0009.08.02242.528.4158
3310.1050.1920.4030.30010.011.02262.198.2176
3320.1050.1920.4030.30010.011.02325.178.8117
3330.1050.1920.4030.30010.011.02363.259.0547
3340.1050.1920.4030.30010.011.02334.847.6500
3350.1050.1920.4030.30010.011.02240.208.0000
3360.1050.1920.4030.30010.011.02373.007.2500
3370.1050.1920.4030.30010.011.02256.318.7500
3380.1050.1920.4030.30010.011.02386.908.0000
3390.1050.1920.4030.30010.011.02306.129.4500
3400.1050.2010.4940.20010.012.02271.924.8989
3410.1050.2010.4940.20010.012.02256.515.1000
3420.1050.2010.4940.20010.012.02241.565.1000
3430.1050.2010.4940.20010.012.02246.855.3000
3440.1050.2010.4940.20010.012.02241.995.3234
3450.1050.2010.4940.20010.012.02266.675.3250
3460.1050.2010.4940.20010.013.02215.794.3564
3470.1050.2010.4940.20010.013.02231.624.3438
3480.1050.2010.4940.20010.013.02210.204.1500
3490.1050.2010.4940.20010.013.02191.354.1089
3500.1050.2010.4940.20010.013.02208.964.0299
3510.1050.2100.5850.10010.013.02248.504.9749
3520.1050.2100.5850.10010.013.02238.784.9000
3530.1050.2100.5850.10010.013.02203.574.6303
3540.1050.2100.5850.10010.013.02200.764.8776
3550.1050.2100.5850.10010.013.02253.925.7000
3560.1050.2100.5850.10010.013.02251.285.4455
3570.1050.2100.5850.10010.013.02236.764.5048
3580.1050.2100.5850.10010.013.02259.005.3234
3590.1050.2100.5850.10010.013.02253.565.5000
3600.1050.2100.5850.10010.013.02230.586.1000
3610.1050.2100.5850.10010.013.02234.695.6500
3620.1050.1920.4030.30010.013.02278.437.1500
3630.1050.1920.4030.30010.013.02273.107.1500
3640.1050.1920.4030.30010.013.02281.527.0647
3650.1050.1920.4030.30010.013.02264.897.0440
3660.1050.1920.4030.30010.013.02285.717.6000
3670.1050.1920.4030.30010.013.02296.087.1500
3680.1050.1920.4030.30010.013.02302.247.7000
3690.1050.1920.4030.30010.013.02298.517.0647
3700.1050.1920.4030.30010.013.02264.177.5622
3710.1050.1920.4030.30010.013.02252.077.7000
3720.1050.1920.4030.30010.013.02295.417.9703
3730.1050.1920.4030.30010.013.02273.947.3888

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Figure 1. Areas of occurrence of numerous buildings made of earth (yellow color). The black points marked the earth architecture inscribed in the UNESCO World Heritage List [2].
Figure 1. Areas of occurrence of numerous buildings made of earth (yellow color). The black points marked the earth architecture inscribed in the UNESCO World Heritage List [2].
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Figure 2. The Great Wall of China erected with rammed earth technology.
Figure 2. The Great Wall of China erected with rammed earth technology.
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Figure 3. City of Shibam, Yemen. The city whose buildings were mostly erected with construction technologies using earth.
Figure 3. City of Shibam, Yemen. The city whose buildings were mostly erected with construction technologies using earth.
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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 filled with a layer of moist soil-cement mixture. (b) The layer of moist mixture is compressed. (c) The next layer of moist soil-cement mixture is added. (d) Successive layers of moist earth are added and compressed. (e) The formwork is removed leaving the monolithic CSRE wall.
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 filled with a layer of moist soil-cement mixture. (b) The layer of moist mixture is compressed. (c) The next layer of moist soil-cement mixture is added. (d) Successive layers of moist earth are added and compressed. (e) The formwork is removed leaving the monolithic CSRE wall.
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Figure 5. Features of the problems where applying ANN brings more accurate results in solving the problem [26,27].
Figure 5. Features of the problems where applying ANN brings more accurate results in solving the problem [26,27].
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Figure 6. Particle size distribution of soils used for laboratory tests.
Figure 6. Particle size distribution of soils used for laboratory tests.
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Figure 7. Histogram of the compressive strength of the samples.
Figure 7. Histogram of the compressive strength of the samples.
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Figure 8. The algorithm for determining 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 tests.
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Figure 9. The scheme of a neuron (node) with three inputs and one output where x 1 , x 2 , x 3 are input signals from the previous ANN’s layer, w 1 , w 2 , w 3 are their weights, w y 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 1 , x 2 , x 3 are input signals from the previous ANN’s layer, w 1 , w 2 , w 3 are their weights, w y 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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Figure 10. Exemplary ANN (multi-layer perceptron, MLP) with 3 input nodes, 6 nodes in one hidden layer, 1 output node. The ANN of this architecture is marked as (3-6-1).
Figure 10. Exemplary ANN (multi-layer perceptron, MLP) with 3 input nodes, 6 nodes in one hidden layer, 1 output node. The ANN of this architecture is marked as (3-6-1).
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Figure 11. Overfitting predictions and the trend correctly found [28].
Figure 11. Overfitting predictions and the trend correctly found [28].
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Figure 12. Original and predicted values of the moisture content (both standardized).
Figure 12. Original and predicted values of the moisture content (both standardized).
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Figure 13. Predicted final moisture content for given density varied from 2118 to 2358 [kg/m3] for required compressive strength 7.885 [MPa] and assumed 9 [%] addition of cement.
Figure 13. Predicted final moisture content for given density varied from 2118 to 2358 [kg/m3] for required compressive strength 7.885 [MPa] and assumed 9 [%] addition of cement.
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Table 1. Compressive strength results of CSRE from various references [11,14,15,16,17,18].
Table 1. Compressive strength results of CSRE from various references [11,14,15,16,17,18].
ReferenceParticle Size Distribution of Earth Shape and Dimensions of Samples [cm]Moisture Content of the Mixture [%]Compaction MethodDensity of Samples [kg/m3]Cement AdditionCuring ConditionsCompressive Strength [MPa]
[11]Sand 64%
Silt 18%
Clay 18%
cuboid
10 × 10 × 20
9.5hydraulic press
(15 MPa)
Max. 18778%27 days,
70% RH
18.4 (AVG.)
[14]Gravel < 19 mm
Gravel 32%
Sand 66%
Clay + Silt 2%
Cylinder
d = 10,
h = 20
7.8pneumatic rammer-8%2 days in forms,
7 days tightly wrapped,
19 days in an air-dry condition
10 (AVG.)
8.210–12 (AVG.)
8.57–8 (AVG.)
[15]Gravel 26–50%
Sand 46–70%
Silt + Clay 4 %
Cylinder
d = 10/15,
h = 20/30
8.85–9.15
(OMC)
pneumatic rammer209110%28 days in an air-dry condition,
13–25 °C
13.8 (AVG.)
[16]Gravel 45%
Sand 40%
Silt 5%
Clay 10%
wall element 50 × 50 × 115.4
(OMC)
pneumatic rammer2156–21394.5%7 days tightly wrapped, min. 20 days in an air-dry condition6.68 (AVG.)
[17]>19 mm 4.3%
Gravel 32.2%
Sand 59.4%
Clay +Silt 8.4%
wall element 100 × 65 × 169.5–11.0
(OMC)
Mechanized rammer, layers 15 [cm] high1800–20006%
8%
10%
In an air-dry condition2.06 (CH)
2.94 (CH)
3.09 (CH)
>19mm 17.9%
Gravel 56%
Sand 29.6%
Silt + Clay 14.4%
6%
8%
10%
1.69 (CH)
1.64 (CH)
2.35 (CH)
>19mm 6.4%
Gravel 50.5%
P 30.4%
π + I 19.1%
6%
8%
10%
1.52 (CH)
1.72 (CH)
1.92 (CH)
[18]Gravel 20%
Sand 50%
Silt 25% Clay 5%
cylinder
d = 15
h = 30
5.3
(OMC)
pneumatic rammer2005–20124.5%6 days in an air-dry condition5.25 (AVG.)
12 days in an air-dry condition16 (AVG.)
AVG.—average value of compressive strength; CH—characteristic value of compressive strength; OMC—optimum moisture content; RH—relative humidity.
Table 2. Results of compressive strength for some chosen samples.
Table 2. Results of compressive strength for some chosen samples.
Sample NumberParticle Size Distribution [%]Cement Addition
[%]
Moisture Content
[%]
Density of the Sample
[kg/m3]
Compressive Strength
[MPa]
Clay
ϕ > 0.002
[mm]
Silt
ϕ ≥ 0.002
ϕ < 0.063
[mm]
Sand
ϕ ≥ 0.063
ϕ < 2.0
[mm]
Gravel
ϕ ≥ 2.0
ϕ < 4.0
[mm]
60.1050.1920.4030.3003922954.01
810.1050.1920.4030.3006822406.45
1080.1050.2100.5850.1006822185.43
1250.1050.2100.5850.10061022995.55
1440.1050.2190.6760.00061022655.16
1790.1400.2440.4160.20091023015.97
2190.1050.1920.4030.3009922745.91
2450.1050.1920.4030.30091222405.55
3280.0700.1760.7540.0009822419.75
3640.1050.1920.4030.300101322827.06
Table 3. The summary of the features’ values calculated for all 373 samples.
Table 3. The summary of the features’ values calculated for all 373 samples.
FeatureMinimumMaximumMean AverageStandard Deviation
Clay [% of the total weight of aggregates]0.0700.1400.1070.015
Silt [% of the total weight of aggregates]0.1490.2530.2060.021
Sand [% of the total weight of aggregates]0.4030.7540.5160.109
Gravel [% of the total weight of aggregates]0.0000.3000.1720.117
Cement addition [% of the total weight]3.0010.007.572.11
Moisture content [% of the total weight]6.0014.009.861.74
Density [kg/m3]2054.002406.332250.3356.43
Compressive strength [MPa]2.4013.016.002.09
Table 4. The best predicting ANN found.
Table 4. The best predicting ANN found.
ANN NumberNo. of Neurons in the Hidden LayerCorrelation of the Training DatasetCorrelation of the Testing DatasetCorrelation of the Validating DatasetActivation Function in the Hidden LayerActivation Function in the Output Layer
1130.91040.88770.8557tanhlinear
260.90310.87980.8831tanhlinear
3100.92330.88170.8522tanhtanh
440.90530.86260.8503tanhlinear
5230.94310.91830.8579tanhexponential
Table 5. The errors of predictions calculated.
Table 5. The errors of predictions calculated.
ANN No.12345
MSE0.9960.7960.9510.9760.928
MAE0.7440.5650.6570.7220.668
MAPE [%]8.196.527.348.037.16
maxAPE [%]46.0373.2873.7561.7943.38
Table 6. Results of compressive test of 373 samples of CSRE.
Table 6. Results of compressive test of 373 samples of CSRE.
Cement Addition [%]Number of SamplesCompressive Strength [MPa]
MinMaxMean av.Standard dev.
3362.4384.2003.2150.456
61202.4008.7415.4391.304
91742.64913.0116.8742.232
10434.0309.4506.3571.557

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