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The first assessed factor was workability classes (Fig.4) that are in the case studies evaluated using the classification model of according to Standard CSN 73 305015,16. These are rock classification systems used for earthwork during construction work and serve for earthwork pricing. However, apart from the price, they also influence the construction project and earthwork realization.

Classification table of soil and rock workability classes.

Soils and rocks are divided into 7 workability classes (Fig.4). Various classification criteria are used there, and they are predominantly related to the fact whether it is the case of fine-grained or coarse-grained soils, semi-rock or hard rocks. Workability classes are used to document all engineering-geological boreholes, excavations, earthwork pricing, but also to choose suitable mechanisms for earthwork.

The first group are cohesive soils (Fig.4). Cohesive soils are classified into workability classes based on plasticity index and consistency index. Workability classes 1, 2 and 3 in fine-grained soils mean that plasticity index is below 17, while consistency index is 0.050.75 for workability class 1 (soil can be worked by a shovel), 0.751.00 for workability class 2 (soils can be worked with a spade) or consistency index over 1.00 for workability class 3 (soil can be loosened by a pickaxe). Or, in case fine-grained soils have a plasticity index equal to or higher than 17 and the consistency index 0.051.20, such soils are ranked into workability class 3. In case the consistency index is over 1.20, it is workability class 4.

In cohesionless soils we distinguish 2 groups of criteria (Fig.4). In the first group we have the combination of relative compaction (density index) and grain-size distribution. If the density index is below 0.33 and grains are smaller 20mm, it is workability class 1. If the density index is from 0.33 to 0.67, and grain-size is smaller than 20mm, it is workability class 2. The third option are cohesionless soils of density index over 0.67, and grain-size distribution below 50mm, which is workability class 3.

In the second group of criteria, it is the case of a combination volume percentage and certain grain-size distribution. Workability class 1 is characterized by grain-size below 20mm and volume percentage over 10%. The remaining volume percentage below 10% is characterized by grains over 20mm. The same applies for workability classes 2 and 3the majority volume percentage over 10% is made up by grains 2050mm (workability class 2) and 50100mm (workability class 3). The minority volume percentage (below 10%) is constituted by grain-size over 50mm (workability class 2) and over 100mm (workability class 3). In workability class 4, the volume percentage below 10% is characterized by grain-size over 250mm, volume percentage 1050% for grain-size distribution 100250mm, and the remaining volume is characterized by lower workability class 4. The workability class 5 is characterized by gran-size distribution of 250580mm (0.1m3) mm and volume percentage 1050%, and grain-size 100250mm in the volume percentage over 50%. A similar principle of volume percentages applies in workability classes 6 and 7, where the workability class 6 has grain-size distribution of 250580mm (0.1m3) for a larger percentage volume (over 50%), while workability class 7 is characterized by grain-size distribution below 580mm (0.1m3). Smaller volume percentage (below 50%) is characteristic of grain-size below 580mm (0.1m3) in workability class 6, and workability class 7 it is expressed by the remaining occurrence of hard rocks of lower workability class than 7. The grain-size mean of 580mm has the value 0.1m3 in the standard.

The occurrence of hard rocks (Fig.4) is typical for higher workability classes as the higher strength of rocks mean they are not easily broken or loaded. The assessment criterion is discontinuity spacing. The workability class 5 is characterized by discontinuity spacing below 150mm. In the workability class 6 the discontinuity spacing is 150250mm, and in workability class 7 it is over 250mm.

The least important criterion for workability class assessment is the use of manual tools or machinery. Manual tools (Fig.4) are used only in the first four workability classes, where workability class 1 is workable by a shovel. In workability class 2 we need to use a spade, and in class 3, we need to use a pickaxe. Ruling out shovels, spades or pickaxes, in workability class 4 we need to employ a wedge and sledgehammer. For the remaining workability classes, we need to use machinery.

As for machinery (Fig.4) in connection with workability classes, there are the following rules. For workability classes 1 and 2 we can use a wheel loader, for workability class 3 and 4 we use an excavator, and for workability class 5 we use a ripper or a heavy excavator, or explosives. For workability class 6 we use a heavy ripper or explosives. For workability class 7 only explosives are used. In line with technological progress, new mechanisms may be applied for the different workability classes. At the same time, for some workability classes we use identical mechanisms, but the difference is in the spent energy on loosening and loading. Also, there will be different extent of wear. All this must be reflected in the selected workability class and corresponding price of earthwork.

Out of all the properties we assess within engineering-geological investigations, the most economically significant24,25 for construction works is soil and rock workability as it is used for earthwork pricing. This mainly applies in construction projects with dominant volume of earthwork. In sewer system construction projects, earthwork plays the decisive role.

The first assessment criterion is the influence of a particular workability class on the price of 1m3 of earthwork. We produced graphs for each workability class (Fig.5ah), where the last Fig.5h shows the minimum, maximum and average values of all graphs describing the workability class prices.

Graphs of the workability class prices (17) and a summarized graph; (a) workability class 1; (b) workability class 2; (c) workability class 3; (d) workability class 4; (e) workability class 5; (f) workability class 6; (g) workability class 7; (h) minimum, maximum and average price of each workability class.

The first and second graphs of workability classes 1 and 2 (Fig.5a,b) show the lowest prices when compared to the remaining ones. This is logical because workability classes 1 and 2 have the easiest breakability. The prices in the two workability classes are identical due to a somewhat conventional averaging of prices in the two classes.

As for workability class 1 and 2 costs (Fig.5a,b), it showed that the minimum cost of earthwork is Eur 1.7 per 1m3, which corresponds to 1.8% of the maximum price of all workability classes. This is because the simplest excavation technologies are used (road trench). Another reason is the highest volumes (over 5000m3), which are always cheaper (in higher volumes, machinery and staff are already on site, which makes the price of 1m3 cheaper). The calculation of percentages is made up by comparing the maximum price out of all the workability classes. On the contrary, the maximum price of earthwork in workability classes 1 and 2 is Eur 17.3 (18.6%), which is related to the most demanding excavation technology (shielded pit) and the lowest cubic volume (below 100m3). The average price is Eur 6.4 (6.8%).

Workability class 3 (Fig.5c) is priced at Eur 2.2 (2.4%) per 1m3, which means a rise of 0.6% in comparison with the two previous workability class minimum prices. Similarly to the previous case it was a road trench of high cubic capacity (over 5000m3). On the contrary, the maximum price in this workability class is Eur 31.0 (33.3%) with an increase of 14.7%. Also, in this case a similar technology (shielded pit) was used, and the cubic capacity was below 100m3. The average price was Eur 9.9 (10.6%).

The minimum price of workability class 4 (Fig.5d) rose by 1.0%, when compared to the previous workability class, to Eur 3.2 (3.4%) per 1m3. The maximum value rose by 9.442.7% (Eur 39.8). As for the correlation of price minimum and maximum related to excavation technology and cubic volumes, the relationship is compatible with the previous cases; only in the maximum price the excavation technology of shielded pit changed to shielded trench. This category has an average cost of Eur 14.9 (16.0%) within whole workability class 4.

In connection with the minimum price of workability class 5 (Fig.5e) there was the highest increase (11.4%), when compared to the previous class, to 14.8% (Eur 13.8 per 1m3). As for the maximum price, there was also an increase in comparison with the previous workability class 4 (of 25.1%) to 67.8% (Eur 63.1). As for the correlation with the previous cases, the technology changed for the minimum price. Instead of road trench, the technology was unshielded trench. Talking of the maximum price, it is similar to the previous caseinstead of the shielded pit, shielded trench was used. As for the cubic volume, the minimum price is related to volumes over 5000m3 and maximum price differs to previous cases (all volumesbelow 100m3, 1001000m3, 10005000m3, over 5000m3), while in workability classes 14 the cubic volume was always below 100m3. The average price in this class is Eur 32.9, and thus represents 35.4% of the maximum price in all workability classes.

In workability class 6 (Fig.5f) the minimum price is Eur 21.2 (22.8%) per 1m3, which corresponds to an increase of 8.0% when compared with workability class 5. The minimum price is this workability class is identical to the previous one (unshielded trench), but the minimum price also concerns unshielded pit. The maximum price is Eur 75.6 (81.2%) and corresponds to a rise of 13.4%. The same technology is used, i.e., shielded trench. As for the volume, the situation is identical to the previous case, both as for the minimum and maximum price. The average value is Eur 41.2, which is 44.2%.

The workability class 7 (Fig.5g) is priced at Eur 26.7 (28.7% for road trench) per 1 m3, which constitutes a rise of 5.9% when compared with the minimum price of the previous workability class. As for technology, road trench was used. The maximum price in this workability class is Eur 93.1 for shielded trench, which is 100% of the maximum price for all the workability classes (an increase of 18.8% when compared with workability class 6). As for the excavation technology, the maximum price did not change. As for the cubic volume, the correlations of the minimum and maximum price remained unchanged. In the minimum values, the earthwork cubic volume is below 5000m3 and in the maximum value, the cubic volume is below 100 m3, 1001000m3, 10005000m3, or over 5000m3. The average price is Eur 50.0 (53.7%).

Figure5 gives the frequencies of the 6 case studies, in which the column price is complemented with frequencies and order number of assessed layers. This means that the column with a price is visually highlighted in unshielded trench, which was implemented in the case studies. The case studies will be described in detail below.

The second assessed criterion (factor) will be the influence of the excavation technology (Fig.6af). To produce Fig.6, data from Fig.5 were used, but Fig.6 is presented separately to independently assess the factor mentioned above.

Graphs of the different types of excavations and technologies used; (a) shielded trench; (b) shielded pit; (c) unshielded pit; (d) road trench; (e) unshielded trench; (f) minimum, maximum and average price of each excavation type and technology.

Comparing all the five technologies (shielded trench, unshielded trench, shielded pit, unshielded pit and road trench) it shows that the most costly excavation type is shielded trench (Fig.6a). It is important to take into account that the price reflects the costs, and the costs reflect the factors at play. Shielded trench has a linear character, and when excavating it, the performance of the machinery cannot be optimised as in the case of other types of excavations with a more spatial character. It is logical that in this most expensive technology, the workability class 7 is the most costly (at cubic volume below 100m3) as this concerns the geological structure that is most difficult to loosen and load. On the contrary, the cheapest is the workability class 1 and 2, which are the easiest to loosen and load (at cubic volumes over 5000m3). The ratio between the cheapest and most expensive workability class is 15-fold (93.1/6.3=14.8).

The second most costly excavation type is shielded pit (Fig.6b). Using shielded pit, it is more likely to optimise the gradual excavation spatially. The most costly is workability class 7 at cubic volumes below 100m3, and the cheapest workability classes 1 and 2 at cubic volumes over 5000m3. The ratio of the cheapest and most expensive option is sixfold (52.6/8.2=6.4).

The third most costly excavation type is unshielded pit (Fig.6c). Supports need not be erected when compared with the previous technology. Aa for the most expensive and cheapest value, the situation is identical to shielded pit, but the ratio is 20-fold (46.8/2.3=20.4).

Road trench is the fourth most expensive type of excavation (Fig.6d). It is relatively low demanding and easy to optimise when compared with the previous excavation types. The ratio of the cheapest and most expensive option is the highest (35-fold; 60.0/1.7=35.3). This means that the engineering-geological structure is the most important in this type of excavation (apart from cubic volume). The difference is caused by the differences between the most expensive workability classes 6 and 7 (at cubic volume below 100m3) and the cheapest workability classes 1 and 2 (at the cubic volume over 5000m3).

The least expensive type of excavation is unshielded trench (Fig.6e), in which the costs are reduced by the absence of trench supports. The ratio between the minimum price (workability class 7 and cubic volume below 100 m3 and 1001000m3) and the maximum price (workability class 1 and 2 at the cubic volume over 5000m3) is 19-fold (36.9/2.0=18.5), which points at the importance of the geological structure.

The third assessed criterion (factor) is the influence of excavated cubic volume per price of 1m3 within earthwork. We produced four graphs with four excavated cubic volumes, namely below 100m3 (Fig.7a), 1001000m3 (Fig.7b), 10005000m3 (Fig.7c) and over 5000m3 (Fig.7d). At the same time, Fig.7e shows the minimum, maximum and average prices with respect to the four excavated cubic volumes.

Graphs of assessed excavated cubic volumes; (a) excavated cubic volume below 100m3; (b) excavated cubic volume 1001000m3; (c) excavated cubic volume 10005000 m3; (d) excavated cubic volume over 5000m3; (e) maximum, minimum and average price of excavated cubic volumes.

As for the assessment of cubic volume below 100m3 (Fig.7a) there is a clear dependency in the sense that the prices rise from the cheapest workability classes 1 and 2 to the most expensive workability class 7 in each type of excavation and technology. It is also clear that the lowest price at such cubic volume is in workability classes 1 and 2 using unshielded trench. On the other hand, the most expensive is the complicated technology of shielded trench. In all workability classes, the prices rise in the order: unshielded trench, road trench, unshielded pit, shielded trench and shielded pit). There are only three exceptions. In workability class 3 the most costly technology is shielded pit and the next-to-last is shielded trench. The order of these two types changes in workability classes 4 and 5. In workability classes 6 and 7, the second most expensive technology is road trench because of reduced capacity to optimise earthwork (linear excavations are more difficult to optimise in hard rocks).

When comparing the cubic volume below 100 m3 (Fig.7a) with other cubic volumes (1001000m3; Fig.7b, 10005000m3; Fig.7c and over 5000m3; Fig.7d), the order is the almost identical. The rule is that the prices rise along with an increase in the workability class and more demanding technology of excavation.

When comparing the ratio between the price minimum and maximum (Fig.7e) in connection with the four assessed cubic volumes, it shows, for example, the ratio between the minimum and maximum at the smallest cubic volume below 100m3 (Eur 89.6), which constitutes a 27-fold ratio (93.1/3.5=26.6). In other volumes, the ratio is even up to 55-fold (93.1/1.7=54.8) at cubic volume over 5000m3. This factor is clearly important. If we assess the average prices for the excavated cubic volumes, the ratio between the most expensive price for cubic volume below 100m3 and the minimum average price for excavated cubic volume over 5000m3 is Eur 12.3 (13.2%).

The following text will describe the results of the influences of all important parameters that participated in the implementation of earthworks and are therefore also part of their pricing. Therefore, in the final result, this influence is reflected in the cost of earthworks. For many buildings, earthworks are one of the most important items in the total construction costs. Especially it concerns those structures that work with large volumetric changes, such as the displacement of rock masses (soil or rock). The influence of the workability class will be evaluated first because this parameter reflects the amount of work needed to break and load rock masses. This means that more easily breakable rocks (such as soil) will have a smaller share of the total price than harder-to-breakable rocks such as rock. The second evaluated influence is the influence of excavated cubic volume. Here, more volume cubic meters will have a greater impact on the overall price than smaller cubic meters. However, this amount is also considered in the fact that one cubic meter will be cheaper in the total amount for more volume than for fewer volume earthworks. The third evaluation will be the influence of the type of excavation and its technology. Such as unshielded trench, road trench, shielded pit, unshielded pit, and shielded trench. In this case, simpler and less demanding types of excavation and their technology are cheaper than more complex and demanding types (in the previous sentence they are sorted ascending according to this statement).

To compare the different factors (workability classes, excavated cubic volume and type of excavation and its technology) affecting the price of 1m3 of earthwork, we used the comparison of average prices and the factors (Fig.8). The most influence on the pricing was observed with the engineering-geological structure represented by workability class, i.e., 46.8% (Eur 43.6; Fig.8a). The influence was calculated as a percentage ratio between the minimum and maximum average price of the lowest and highest workability classes. The second most prominent influence was observed with the type of excavation and its technology, i.e., 29.9% (Eur 27.8; Fig.8b). This influence was obtained as a percentage ratio between the minimum and maximum price of the cheapest and most expensive technologies. The third was the excavated cubic volume, i.e., 13.2% (Eur 12.3; Fig.8c). This was calculated as a percentage ratio between the minimum and maximum average price of the cheapest cubic volume category over 5000m3 and the most costly cubic volume category below 100m3.

Graphs of the influence of the different earthwork factors on the price of 1m3 earthwork (evaluation approachstudy 1); (a) workability class factor; (b) type of excavation and its technology; (c) excavated cubic volume factor.

When we compare all these influences, it shows that the influence of 46.8% in engineering-geological structures represented by workability classes has almost double (1.6) influence than the type of excavation (29.9%). Therefore, when planning earthwork, it is most important to pay attention to engineering-geological investigations to determine the geological structure precisely as for workability classes. This has a fundamental influence on the determination of earthwork prices (46.8%). The remaining part of the price is determined by the type of excavation and its technology (29.9%) and excavated cubic volumes (13.2%).

The six sewer system case studies assessed in engineering-geological sections and described in this subsection (Fig.3) are localized on the geological map Fig.2. The different sewer systems were technologically implemented as unshielded trench (Study 2a), while their pricing is given per each locality in Fig.9af. The pricing is summarized in Figs.9g and 10. Each sewer system 16 (case study) was implemented using the technology of unshielded trench but there is also a calculation for the technology of shielded trench (Study 2b), which was not implemented.

Graph comparing the excavated cubic volumes (m3) in the different case studies and the price (EUR) using the technology of unshielded trench (evaluation approachstudy 2a) and shielded trench (evaluation approachstudy 2b); (a) locality 1; (b) locality 2; (c) locality 3; (d) locality 4; (e) locality 5; (f) locality 6; (g) summary values for all the localities.

Graph of total prices for all case studies in dependence on workability classes and different layers, including their genesis; (a) the implemented option 2aunshielded trench; (b) hypothetical option 2bshielded trench.

When we compare the case studies (Fig.9af), the highest excavated cubic volume was in the first locality, i.e., 77.0% (2751.1m3) out of all the localities. Although the first case study (Fig.9a) was implemented in 6 layers, there were only three workability classes (2, 3 and 4). The most dominant was the fourth layer (489.7m3), which represented Eur 4943.0 (24.6%) in unshielded trench. The second option of shielded trench was 2.7 times more expensive (Eur 13,416.7).

The second case study (Fig.9b) represented 1.9% (68.5m3) of all excavated cubic volume in all case studies. It was implemented in four layers and two workability classes (2 and 3). The most voluminous was the second layer from the ground surface (44.2m3), which amounted at Eur 268.4 (1.3%) using the technology of unshielded trench. The non-implemented technology of shielded trench was 3.3 times more expensive (Eur 889.6).

When compared with all the assessed localities, the third case study (Fig.9c) represented 3.5% (124.0m3) of the excavated cubic volume. In this case study, only three layers were assessed (workability classes 2, 3 and 4). The most voluminous (72.1m3) was the second layer with the price for unshielded trench of Eur 727.5 (3.6%) and for shielded trench of Eur 2864.9 (5.0%). This means that shielded trench was 3.9 times more expensive than unshieldedtrench.

The fourth case study (Fig.9d) represented 7.1% (254.5m3) of the excavated cubic volume out of all the localities. The fourth case study was implemented in 3 layers as above, but only under one workability class (3). The most voluminous was the second layer from the ground surface (148.9m3). This volume costs Eur 905.0 (4.5%) to be excavated using the technology of unshielded trench, and Eur 2088.3 if the technology of shielded trench was used (2.3 times more expensive).

The fifth case study (Fig.9e) represents 5.7% (204.1m3) of all the excavated cubic volume. Three layers of two workability classes (2 and 3) were excavated. The most voluminous was the second layer (103.5m3), which cost Eur 629.4 (3.1%) in unshielded trench and Eur 1452.4 in shielded trench (2.3 times more expensive).

As for the total excavated cubic volume, the sixth case study (Fig.9f) represents 4.7% (168.6m3). Four layers were assessed there of workability classes 3, 4, 5 and 6. The most voluminous was the first layer (55.6m3), which cost Eur 337.9 (1.7%) in unshielded trench, and Eur 1119.9 (2.0%) in shielded trench. It is interesting that in this case study, the first layer (workability class 3) had the highest volume but cost the least to excavate when compared with higher workability classes. This did not occur in other case studies.

The overall excavated cubic volume in all the six localities was 3570.6m3 (Fig.9g). The total price was Eur 20,073.4 using the technology of unshielded trench, while the hypothetical option would cost Eur 57,219.8 (2.9 time more).

If we assess all the case studies in one graph (Fig.10), it is possible to observe the following. Out of the seven workability classes, we managed to identify only five in the six studied localities (workability classes 2, 3, 4, 5 and 6), leaving thus classes 1 and 7 out. The most abundant was workability class 3 with 39.6% (Eur 7 942.8 for unshielded trench; Fig.10a). Interestingly, this class is made up by the highest number of genetic types of soil (glaciolacustrine, proluvial, anthropogenic, fluvial and eolian sediments), while glaciolacustrine sediments dominated (20.5%). The second most abundant class was workability class 4 with 30.6% (Eur 6134.2) constituted by 3 different genetic types (glaciolacustrine, fluvial and eluvial sediments). The third came workability class 2 with 22.4% (Eur 4498.8) with 2 genetic types (glaciolacustrine and eolian sediments). All the three most dominant classes were most abundant for the genetic type of glaciolacustrine sediments. The last two workability classes 5 (4.3%) and 6 (3.1%) only had a small share, and were represented by eluvial and marine sediments.

For better visibility and comparison, we made a graph for the pricing of shielded trench (Fig.10b) too. We may observe changes in the total prices in relation to the workability classes in all case studies, and at the same time, there are also the different layers and their genesis. The ratio of the total price of study 2a using the technology of unshielded trench is 2.9 times cheaper than in study 2b using the technology of shielded trench.

In conclusion of this Section (Studies 2a and b), we identified the influence of the three examined factors on the price of the sewer system earthwork implementation. If we assess the influence of workability classes, average prices were used for the assessment. Figure11 gives the graphs comparing the excavated cubic volumes and their prices in the 6 case studies as a sum.

Graphs of different earthwork factor influence on the price of excavations (study 2aunshielded trench, the first column; study 2bshielded trench, the second column), (a) workability class factor; (b) excavated cubic volume factor; (c) type of excavation and its technology.

The first assessed factor was the workability classes (Fig.11a). We found that the most dominant classes (for unshielded trenchstudy 2a) were workability classes 2 (22.4%), 3 (39.6%) and 4 (13.7%). On the contrary, the least dominant were workability classes 5 (4.3%) and 6 (3.1%). The ratio between the minimum and maximum average price was 36.5% considering the technology of unshielded trench. There is an analogy with the second option of shielded trench (study 2b) but the ratio between the minimum and maximum average price amounted to 31.2%. Clearly, the extreme workability classes (1 and 7) were not excavated within the 6 case studies and thus were not included in the price.

The second assessed factor was excavated cubic volume (Fig.11b). The most dominant group (in unshielded trenchstudy 2a) was cubic volume from 100 to 1000m3 (63.8%) and, the least dominant group are excavated cubic volume from 1000 to 5000m3 (17.6%). The difference in the average price between the cheapest and most expensive cubic volume was 46.2%. The order of the assessed cubic volumes for shielded trench (study 2b) was identical to the second assessed group of unshielded trench (study 2a), while the difference between the cheapest and the most expensive cubic volume was 33.3% considering the average prices. The cubic volume over 5000m3 is missing as it made part of the study 1 only.

The third assessed factor was to compare the implemented technology of unshielded trench with the cost of shielded trench (Fig.11c). The difference in the average prices of the two technologies was 161.1%.

In conclusion of studies 2a and 2b, we can state we identified a structured influence of factors (Fig.12). To compare the results of the second study, we also state the results of study 1 (Fig.12a). As for the second study, in the technology of unshielded trench (study 2a) the most decisive factor was the type of excavation and its technology with 66% (Fig.12b); the second factor was the excavated cubic volume with 19%, and the third was the influence of workability class with 15%. In the technology of shielded trench (Fig.12c; study 2b) the influence was analogous: 49% (the type of excavation and its technology), 26% (excavated cubic volume) and 25% (workability class).

Graph of study results with quantified levels of influence of the different factors on the price of earthwork (workability class, type of excavation and its technology, excavated cubic volume), (a) study 1; (b) study 2a; (c) study 2b.

These results are affected by the different number of types of excavations. In study 2, we compared only two technologies (shielded and unshielded trench), while in the study 1, we compared five types of excavations. Next, the 6 localities (case studies) did not include the extreme workability classes 1 (loose, unconsolidated soils workable by a shovel) and 7 (healthy hard rocks). The last reason is that the cubic volume over 5000m3 was not assessed in the case studies. Having combined these boundary conditions, the factors were influenced significantly.

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