Modeling Volumetric Block Types in Residential Building Construction

: The article focuses on the erection of residential buildings from large-sized volumetric blocks as a modern and progressive trend in housing construction. It is noted that one of the major tasks in the development of this promising area of construction is to justify the choice of type of volumetric blocks. The authors propose a method of type formation that, depending on the set ob-jective, can either be composed of large-sized volumetric blocks only, or include combinations of large-sized and smaller-sized blocks. The article details the steps and procedure of modeling the type of volumetric blocks, which comprises three stages. At the first stage, the parameters of boundary blocks are determined, and then, by changing these parameters step by step, the parameters of blocks between the boundary blocks are set. The second stage involves developing options for the placement of blocks in accordance with the space and layout design solutions employed in the residential buildings to be erected. At the third stage, blocks are selected, and their actual type is approved. The stages of modeling of the volumetric blocks type are illustrated by practical examples, tables, and figures.


Introduction
The first residential buildings made of three-dimensional blocks began to be erected in the second half of the twentieth century (Figure 1).Factory-made blocks, as a rule, were designed to accommodate one with at least two rooms.Such reinforced concrete blocks had dimensions in plan from 2.4 × 4.8 m to 3.6 × 6.0 m, and their weight varied between 6 and 10 tons.Since 1961, the mass introduction of residential five-storey buildings made of three-dimensional blocks has begun in Krasnodar, Minsk, Perm, etc.Therefore, in Krasnodar, blocks consisting of three walls and a bottom were used, and in the Minsk version, blocks of four walls were used, but without a bottom.At the same time, in Perm, volumetric-reinforced concrete blocks were divided into residential, sanitary, kitchen, and staircase blocks with the same dimensions of 3.2 × 5.2 × 2.7 m.These reinforced concrete volumetric blocks had a fairly high level of factory readiness.Hence, glazed windows, doors, and wall cabinets were installed in them, and engineering networks with plumbing and electrical appliances were installed.
Bulk blocks were delivered to the construction site using trailers, and installation was carried out, as a rule, from wheels.At the same time, the duration of the construction of an apartment building was reduced by an average of three-four times.From 7 to 10 blocks were installed in one shift, and with three shifts, a 5-storey residential building with 60 apartments was erected in 10-12 working days.Due to the active development of panel and monolithic housing construction, as well as the lack of high-power equipment for construction, block construction has not been engaged for many years.
However, with the development of technology and improvement of the quality of construction, it has become possible to build houses from blocks, and it becomes more technologically advanced, high-quality and economically attractive compared to classical construction methods.
Modern technology for the construction of residential buildings from bulk blocks is characterized by the transition to large-sized bulk blocks of high or full factory capacity [1][2][3].Such blocks are, as a rule, designed to accommodate an apartment with a total area of about 100 square meters.For example, the basic large-sized block manufactured at the MonArch Combine of Innovative Technologies is 15.5 m long, 7.5 m wide and 3.75 m high.Such a block weighs 65 tons and is 98% prefabricated [4,5].Since the majority of the work is transferred to industrial enterprises, building assembly in construction is reduced to three main processes: installation of volumetric blocks, assembly of vertical and horizontal joints, and post-assembly work to connect utility systems [6][7][8][9].
At the same time, there are a wide range of architectural and design solutions for residential buildings, characterized by a broad variety of geometric dimensions [10][11][12][13].For this reason, it is not always feasible to cover such solutions using only large-sized volumetric blocks.Therefore, the type of volumetric blocks for the formation of various series of residential buildings should consist not only of large-sized, but also of other, less dimensional blocks [14][15][16][17].
To determine them, the following method of modeling the type of volumetric blocks is proposed, depending on the planned application of specific series of residential buildings.The formation of such a technique will increase the architectural expressiveness of the building, allow developing a system of mass housing construction and accordingly reduce the cost of construction.

Materials and Methods
Development of the type of volumetric blocks is based on architectural-planning solutions for residential buildings and available technical capabilities of means of mechanization for installation work.
Architectural and design solutions for residential buildings erected in different regions of Russia Federation have their specific features, largely determined by the regional climate and environment.For example, the residential building projects developed by the Parametrica and AMC-project architectural studios (St.Petersburg, Russia) are notable for their diverse range of design solutions for sections.Residential buildings of any configuration can be formed from such sections.However, it should be borne in mind that sections can have multivariant space and layout design solutions for block placement.
At present, installation cranes are typically an uncompetitive choice for the assembly of residential buildings from large-sized blocks due to the limited lifting capacity of existing cranes.
The closest cranes are Liebherr(Switzerland: Buhl (Fribourg)), Terex (Norwalk, Connecticut, USA) Demag(Germany, Dusseldorf), XCMG QY(China: Xuzhou, Jiangsu), Manitowoc(Manitowoc, Wisconsin, USA) , and others (see Table 1).Experience shows that Russian builders prefer Liebherr cranes due to their high operational reliability.For instance, the Liebherr LTM 1650 crane with the maximum lifting capacity of 650 tons is available in two configurations, T3 and T3Y.In the T3Y configuration, the telescopic boom is between 33.9 and 54 m long, and its maximum lifting height is 54 m.With a minimum outreach of 5 m the boom length is 33.9 m, and with a maximum outreach of 52 m the boom length is 54 m.The uniqueness and high cost of installation cranes make it also necessary to supplement the aforesaid indicators (lifting capacity, hook height, boom outreach as well as an economic factor-the machine's working shift cost) with one more-the average daily number of assembled blocks.This indicator is required to calculate the duration of largesized blocks installation.
Production of volumetric blocks involves forming a parallelepiped with wall panels, as its faces and slabs for the upper and lower levels of the blocks.The design of wall panels of blocks assumes built-in pylons (support columns), connected on the top and at the bottom by tie beams.Together, these beams and pylons constitute the frame structure of the building.The technology for the production of inner walls in the space between pylons anywhere in the longitudinal direction makes it possible to build doorways and window apertures and creates space for open plan apartments.
Production of large-sized volumetric blocks on automated conveyor lines is performed in the following technological sequence: molding flat-reinforced concrete products; assembling flat products into large-size blocks on assembly jigs; finishing facade work as well as installation of internal engineering systems.
The structural section of large-sized volumetric blocks is made of self-compacting concrete (grade B70 or lower) and aggregates for heavy and fine-grained concrete.
Each volumetric block is equipped with a set of accessories.For instance, finished apartments are fitted with an in-floor convector with fans, a Radomir bathtub, a wall-hung sink, a semicircular sink, a wall-hung toilet system, a bottle siphon for the washbasin, a bathtub and washbasin mixer, a washing machine, a kitchen sink set, etc.This set of accessories is provided for each apartment.
Volumetric block-type modeling comprises three steps.
The first stage involves the following operations: 1. Determining the baseline parameters of the blocks to be used 1.1.Setting limits on the weight and overall dimensions of blocks: where Q is the weight of the volumetric block in tons; a, b, and c are the overall parameters of the block (length, width, and height, respectively) in meters.
1.2.Choosing the increment of change for the length and width of blocks α is the block length increment of change (the unit: m); β is the block width increment of change (the unit: m).

Modeling block options by incrementally changing the overall dimensions
The dimensional parameters are changed as follows: where j is the block index by length; i is the block index by width.Hence, with the block's overall dimensions being max  =  1 (5) The volume of this block is as follows: where V 11 is the volume of the baseline heaviest and the largest-sized block.
Similarly, the specifications for the baseline lightest block are established, i.e., with the block's overall dimensions being min  =   (10) and its volume equal to where V nm is the volume of the baseline lightest block.The total number of modeled blocks is written as: where u is the total number of modeled blocks.

Construction of the block matrix
To display all n •m blocks, a matrix table is constructed (see Table 2).To display all n•m blocks, a matrix table is constructed (Table 2).Its rows, the number of which is equal to n, register changes in the width of blocks from   to   , and columns, the number of which is equal to m, display incremental changes in the length of blocks from   to   .
Each table cell at the intersection of the jth row and the ith column contains the parameters of the block as a fraction, with the block number in the numerator and its weight in the denominator.
The block number is calculated using the following formula: where   is the block number at the intersection of the jth row and the ith column.The weight of the block is determined using the ratio: where   is the weight of the block at the intersection of the jth row and the ith column;   is the volume of the block at the intersection of the jth row and the ith column.

Results
Having carried out calculations according to the proposed methodology, the calculated types of volumetric blocks were formed.Thus, for each volumetric block, its full specification is given: number in the type, weight, and overall dimensions (Table 3).The second stage involves developing options for space and layout design solutions in residential building sections by placing volumetric blocks based on the calculated block type.Figure 2 shows one of the volumetric blocks floor layout options in a two-section L-shaped rectangular residential building.The range of available volumetric blocks is given in Table 4.To simplify the calculations, it is assumed that one block covers the entire width of the section.Hence, for a 6 m long section, there are 2 possible combinations; for a 10 m long section, there are 97 possible combinations; for a 15 m long section, there are 5503 possible combinations; for a 20 m long section, there are 346295 possible combinations; for a 25 m long section, there are 18537226 possible combinations.
At the third stage the actual types of volumetric blocks are selected from the calculated types of volumetric blocks and approved, depending on the set goal and objectives.
For example, for the initial stage, MonArch Group of Companies plans to produce only a limited range of large-sized blocks (Table 5).For this purpose, an experiment was conducted in New Moscow on the construction of a four-storey building with a plan size of 28.8 × 15.5 m.As a result, the space-planning solutions amounted to seven blocks per floor (Table 6).The location and sequence of installation of the blocks were the same for all floors.The main works included rigging (traverse preparation and slinging) and installation (lifting, aiming, installation, alignment, and fixing).The total installation time of the experimental building was 17.3 h, including the installation of the roof.
The timing results were summarized in a report form (Table 7).
where T is the duration of the construction of the building in the unit of hour and m is the number of large-sized blocks (pcs).At the same time, the complexity of installing large-sized volumetric blocks was defined as the sum of labor costs:  = (  +   ) •  +   + ∑    = (17) where Q is the complexity of the installation of blocks (person-hour); q1 is labor costs for the crane delivery to the facility (person-hour); q2 is labor costs of machinists and crane maintenance workers (person-hour); q3 is labor costs of installers for the preparation of technological equipment (person-hour); q4j is labor costs of installers for the installation of blocks on the jth floor (person-hour); p is the number of taps.
In addition, it became possible to accurately calculate the duration of the installation crane's stay on the construction site, which was expressed as: where T is the duration of the crane's stay at the facility (day); tн is the duration of installation of the aboveground part of a residential building (day); r1 is the duration of installation and dismantling of the crane (day); r2 is the duration of maintenance and repair of the crane (day); r3 is the duration of time loss under adverse meteorological conditions, (day); r4 is the number of weekends and holidays (day).

Discussion
The results of the experiment confirmed the expediency of the adopted stages of modeling the type of volumetric blocks, which makes it possible to form both large-sized and smaller blocks in one system.This combination of blocks ensures reliable and flexible satisfaction of almost any architectural and planning solutions for residential and public buildings.At the same time, in each specific case, taking into account the specifications of the respective regions and manufacturers, it is necessary to approve its nomenclature of volumetric blocks based on the general scheme given (Tables 2 and 3).
It should be particularly noted that, despite the identity of the floor solutions of the experimental building, there was a significant variation in the duration and production of work on each floor during the installation of the blocks.For example, the duration of the first floor was about 5.0 h, and that of the fourth floor was 3.1 h.The analysis showed that the main reason for such a spread of indicators is the lack of practical experience.
The results of the timing of the construction of the experimental building allowed us to substantiate the relevant organizational and technological parameters of the construction of buildings from volumetric blocks-the duration and complexity of installation, the structure of private flows for the installation of blocks, the installation of joints, and the performance of installation work on the connection of engineering communications.As a result, appropriate recommendations were developed on linking the delivery of blocks and the installation of buildings from vehicles, calculating the composition of work crews and drawing up a detailed methodology for the entire complex process of delivery, installation of bulk blocks, and commissioning of facilities.

Figure 2 .
Figure 2. Floor layout of volumetric blocks for L-shaped buildings.

Table 4 .
Calculated types of volumetric blocks (fragment), where LSVB means large-sized volumetric block.

Table 1 .
Technical specifications of heavy-load installation cranes (excerpt).

Table 2 .
Estimated circulation of volumetric blocks.

Table 5 .
Planned range of manufacture of large-sized blocks.

Table 6 .
Parameters of the volumetric blocks of the experimental building.

Table 7 .
Report on the timing of a residential building (fragment).