Quantitative methods for predicting underground construction waste considering reuse and recycling

The construction industry has been greatly developed in the past few decades, especially in the extensive use of underground space. The increasing amount of waste (e.g., soil, sludge, and rock) generated in the underground construction constitutes an important part of construction and demolition waste (CDW), but the related problems are rarely addressed in an independent quantitative study. In order to facilitate recycling of underground construction waste (UCW), quantitative methods for predicting UCW are proposed based on mass conservation in this study. Through on-site investigation and literature review, the source characteristics of UCW and corresponding recycling potential are firstly analyzed. Secondly, the corresponding quantitative method is proposed for predicting each type of UCW according to the principle of mass conservation. Finally, the proposed quantitative methods are applied in two real underground infrastructure projects to verify the accuracy. The results show that the accuracy of quantitative methods for predicting shield sludge and engineering soil is 82.03–95.79% and 94.49% respectively. The quantitative methods for predicting the amount of UCW proposed in this study is effective. In both cases, underground construction produced a large amount of construction waste with great recycling potential. UCW can theoretically reach 100% recycling, and full reuse and recycling of UCW will bring huge benefits and be conducive to the sustainable development of the construction industry.


Introduction
Because of the large-scale underground construction in the recent years and the inevitable earthwork in the construction process, a large amount of waste excavated in underground construction has become a problem that cannot be ignored (Shang et al. 2013). Excavated waste is inert material that is not normally considered to cause a major problem on environment and society. However, more and more studies prove that excavated waste has a strategic impact on resource efficiency and the sustainable environment. Construction industry is a major contributor to the decrease of natural resources, especially the resources of sand and rocks (Kirthika et al. 2020). With the increasing demand of protecting the environment and building a sustainable society, the constraints on the exploitation of natural sand and rock are becoming increasingly tight (Magnusson et al. 2015;Rana et al. 2016). Therefore, it is of practical significance to supplement the channels of acquiring construction sand and gravel by means of various wastes recycling (Rana et al. 2016). Disorderly disposal and invalid utilization of an enormous amount of excavated waste will add to the cost of the project (Bellopede et al. 2011). Numerous untreated engineering soils will encroach on land and pollute soil and water (Kalbe et al. 2008;Lee et al. 2008). The random dumping of soil may also threaten the safety of human life and bring serious social problems, for example, a landslide killed 77 people and engulfed an industrial park of over 100,000 m 3 in Shenzhen in 2015 (The Xinhua News Agency 2016).
It is of great significance for the whole construction industry to realize safe and sustainable development to fully recycle the excavated waste. Different from the practices of developed countries, excavated waste are mainly buried at landfill sites in China (Zhang et al. 2020a, b), while the recycling rate of the excavated soil and rock in western countries such as Ireland is more than 90% and that in Germany is more than 80% (European Commission 2016). Information such as classification and quantity of excavated waste cannot be accurately obtained in the early stages of construction, which is not conducive to the orderly and coordinated development of excavated waste reuse, recycle, and disposal (Diana et al. 2015;Riviera et al. 2014).
Methodologies for estimating CDW fall into six major categories (Guerra et al. 2019;Masudi et al. 2010;Wu et al. 2014): site visit (SV), generation rate calculation (GRC), material flow analysis (MFA), classification system accumulation (CSA), variables modeling (VM), and other methods. The relevant studies on quantifying CDW are summarized and analyzed (Table 1). Due to the complexity and uncertainty of construction waste production, scholars usually combine various methods to achieve better results. The recent trend is that more and more computer technologies have been applied to the quantification of CDW. The amount of UCW is related to geotechnical properties and construction conditions, so its calculation requires a combination of multiple quantitative methods to calculate like those of mass conversation, site visit, material flow analysis, and principal factor analysis. Traditionally, the prediction of the amount of sludge production was mainly through experience method, for example, 1:4 (sand)~1:7 (cohesive soil) of the excavated volume being used as the predictive generation rate of the amount of sludge generated in sludge shield. The method of experience generation rate for predicting the volume of shield sludge usually has great uncertainty, which brings difficulties for the subsequent development of detailed waste planning.
Large underground construction projects often overlap with civil and infrastructure projects. Civil and infrastructure construction will produce a lot of CDW (de Magalhães et al. 2017), but previous researchers have paid little attention to it because of such difficulties as incomplete data and the huge workload. Wu et al. (2014) summarized 57 papers related to the quantification of CDW, of which only 5 papers are related to civil and infrastructure work. Less research focus on civil and infrastructure construction, ignoring a very important part of the construction industry, not to mention ignoring the quantification of inert construction waste excavated from underground construction. The focus of scholars on the quantification of civil and infrastructure waste is usually at a regional level. Macro-level quantification cannot accurately estimate the quantity of a specific type of UCW.
In order to bring convenience to the precise management of UCW and promote the clean and sustainable development of the whole construction industry, this study proposes a relatively accurate quantitative methodology to predict the amount of UCW considering its reuse and recycling. The quantitative methods enable project stakeholders to predict the amount of UCW at the design and the early construction stage and provide effective data support for the source reduction, consumption, transfer, and resource utilization of construction waste. In this study, two tunnel infrastructure construction cases are used to validate the proposed quantitative methods, which also provides reference data for estimating the amount of waste produced by other tunnel construction.
The remainder of this paper is as follows. After the "Introduction" section is the "Material and methods" section used in this study. The related work (the source characteristics, factors affecting the yield, and the possible recycling direction of UCW) are also involved in the "Material and methods" section. Two case studies are then presented in the "Case study" section. The "Result" section shows findings of the study. It is followed by the "Discussion" section, which is an in-depth discussion on both quantitative methods and cases study. Conclusions covering the further research are given in the "Conclusions" section.

Material and methods
Although it is widely accepted that CDW includes excess material from construction, demolition, and renovation, not all countries include excavated waste in their definition of CDW (Lu et al. 2011). In China, CDW is the general term for engineering soil, engineering sludge, construction waste, demolition waste, decoration waste, etc. (MOHURD 2019), and engineering soil and engineering sludge generated in underground construction are what we focus on in this study.
The whole research method and process of this study are shown in Fig. 1. Firstly, the source characteristics, factors affecting output, potential recovery value, and recycling directions of UCW were analyzed through on-site investigation and literature review. Secondly, the quantitative methods for predicting various UCWs are put forward according to the principle of mass conservation. Based on the geological data and geotechnical information, two cases are finally used to verify the accuracy of the quantitative methods of typical UCW.

Related work
All underground construction will inevitably produce engineering soil and engineering sludge. In China, engineering soil includes abandoned soils generated during foundation excavation of all kinds of buildings, structures, and pipe networks. Engineering sludge includes the sludge generated during the construction of bored cast-in-situ pile foundation, underground diaphragm wall, sludge shield, horizontal directional drilling, etc. Engineering sludge is required differently in different constructions. In this study, shield construction, underground diaphragm wall construction, and pile foundation construction are selected as the typical underground construction.

Source characteristics of UCW
Shield waste Shield construction refers to the method of tunneling and dredging by using shield tunneling machine while controlling the excavation face and surrounding rock without collapse and instability. Because of its advantages of fast digging speed, excellent quality, and relatively high construction safety , in the case of poor stratum conditions and complex geological conditions, etc., the shield method has become the preferred construction method for tunnel construction in China (Yu et al. 2020).The types of shield machines can be divided into open face shield machine, sludge shield machine, EPB shield machine, etc. The waste products of EPB shield construction are mainly engineering soil, and the products of sludge shield are mainly engineering sludge and soil. The shield tunneling machine builds the tunnel without disturbing the surrounding rock due to the linings assembled from the pipe pieces on the machine, and the wall The waste generation rate for the underground construction stage was the highest among the three stages (underground stage, superstructure stage, and finishing stage).
a MFA material flow analysis, GRC generation rate calculation, SV site visit, CSA classification system accumulation, VM variables modeling, BIM building information modeling, FST fuzzy set theory behind which grouting is implemented. The residue under the knife disc is dissolved into the sludge, and the sludge discharge system continuously discharges the sludge from the sludge tank to ensure that the pressure of the sludge film is in equilibrium.
Pile foundation waste Pile foundation passes the superstructure loads to the deep stability soil or rock, reducing the nonuniform settlement of ground and foundation. Pile foundation can be classified into precast-driven piles and bored cast-insitu piles (Luo et al. 2019). Construction of bored cast-in-situ piles will generate hole-wall-protecting sludge, which is made by artificial pulping with original soil. Through circulating sludge, the earth blocks cut by the drill bit are carried out of the hole, and then the steel cage tied up is installed in the hole, and concrete piles are poured underwater by the catheter method. During the drilling process, the hole-wall-protecting sludge shall meet the requirements (relative density of sludge is 1.1~1.3, viscosity is 10~25s, sand content <6%, etc.) to play the role of wall protection and fixation, preventing caving hole.
Underground diaphragm wall waste An underground diaphragm wall is a narrow and deep underground trench formed by grouting, which has the functions of waterproof, seepage proof, bearing, and retaining (Li et al. 2013). Sludge and soil are produced in the construction process of the underground diaphragm wall. The sludge plays the role of wall protection, and the soil is produced at the bottom of the sludge with the digging of the mechanical grab, and the sludge is used in circulation during the whole construction process. Geological exploration is also needed for underground diaphragm wall construction. For the different conditions of sandy soil and cohesive soil in the construction stratum, the allocation index of sludge is different, and the specific data should be prepared according to the actual situation of the project.

Factors affecting yield
The amount of UCW depends mainly on the construction scale. Underground construction usually passes through one or more strata; the geological conditions and geotechnical properties of different strata will affect the yield of waste. The operating parameters of machine and special construction requirements also affect the actual output of excavated waste. Construction scale and geological conditions are the main factors affecting the amount of UCW.
Geological and geotechnical conditions For engineering soil, the looseness coefficient is the main factor. The soil mass in the construction area is a compact volume, and the volume of engineering muck after loosening (i.e., transport volume) is greater than its dense volume. According to the source characteristics of shield sludge, and the principle of the residue separation in the separation system, the cohesive muck is partly separated from circulating sludge in the form of chunks during the cutting process. The sand-gravel that can be recovered for use as reclaimed aggregate is also separated. So, the amount of shield sludge is related to the content of cohesive soil and sand-gravel in stratum. According to the key physical parameters of stratum selected from geotechnical survey data for quantification, the transformation indexes of shield sludge are summarized and  Table 2. Table 2 can be used to calculate the proportion of sand-gravel, sludge soil, and other soil.
Construction scale and strata volume The construction depth of pile foundation is determined by the bearing capacity. Generally, the construction area is below 40 m underground. The construction depth of the underground diaphragm wall is determined by the water table and is generally less than 20 m underground. The two types of construction will go through a variety of strata. The construction area of shield tunneling is generally below 10 m underground. The diameter of most shield tunnels is larger than 10 m, so the tunnels will pass through one stratum or more during the shield construction. Geotechnical properties of different strata have a great impact on the type and amount of waste to be generated. Therefore, we should not only know the overall scale of construction, but also calculate the volume of each geological layer that goes through. For the variety and instability of the terrain, we can adopt an idealized model and then use integral method to calculate the volume of each layer.

Reuse and recycling of UCW
The high valued composition and characteristics of UCW make it necessary to have the waste reused and recycled in place of natural resources like sand, gravel, and rock (Haas et al. 2020). Excavated waste can be used directly on site (reused) or transported off-site for either recovery (recycled) or disposal. Excavated waste can be used as substitute for other earthworks (landfill covers, trench works, dam works, paving layers, etc.) materials in accordance with construction requirements (Griffiths and Radford 2012).
In light of the source characteristics of the engineering sludge, the composition of the pile foundation sludge and the underground diaphragm wall sludge have constant low sand-gravel content; both types of sludge can be directly reduced to be dry soil (water content less than 35%) with the use of the sludge-water separation system. Shield sludge will carry a large amount of high economic value sand-gravel during the production process. Sand-gravel will be separated with using the sand-slurry separation system, and sludge will be dehydrated into dry soil and transported out of the field. Sand-gravel can be used as recycled aggregate for the construction site and other recycled building products (e.g., reclaimed mortar, recycled cement, recycled concrete) (Zhao et al. 2010). Dry soil can be used as raw material for roadbed, sintered wall materials and sintered aggregate, etc (Weng et al. 2003;Zhang et al. 2020b). Parameters that may affect management of UCW include geographic characteristics, geotechnical properties, facility capacity, demand for recycled materials, etc (Magnusson et al. 2015). According to the primary recycling ways of UCW, quantitative methods of sludge, sand-gravel, and other soil (material other than sludge, sandgravel) are established respectively, which will greatly facilitate the management and recycling of UCW.

Quantitative methods based on principle of mass conservation
Calculating the volume of waste has more practical significance for CDW management. According to the principle of mass conservation, the excavated material eventually becomes waste before it can be reused and recycled. Construction can lead to changes in the physical state of these materials, which will lead to changes in density. Therefore, the calculation of the volume of UCW converted by raw soil inevitably uses the principle of mass conservation.
Quantitative method for predicting production of engineering sludge Shield sludge The formation of shield sludge has a complex mechanism. The construction of shield tunneling is carried out according to the ring. After each tunneling ring, the work such as pipe paving and sludge adjustment will be carried out. We use the ring as the basic unit of derivation, and the volume of soil that can form sludge (V sl , m 3 ) produced during each ring driving is calculated as is shown below: where V i is the volume of i soil layer in each tunneling ring (m 3 ), λ i is the proportion of soil that can form sludge (named sludge soil in later chapter) in i soil layer (%), and ε is the loss coefficient.
In the shield sludge system, the total volume and specific gravity of the sludge in the pool are determined and thus set the initial specific gravity of the sludge as ρ 0 (kg/m 3 ) and the volume of sludge in the pool as V 0 (m 3 ). The sludge after being driven has a specific high gravity, part of the sludge needs to be abandoned and adjusted with water to the value of ρ 0 , and the process also requires keeping the sludge volume equal to the pre-driven gross volume. The average density of the sludge soil particle is ρ s , and the density of water is ρ w . Mass conservation calculation is carried out within the system of sludge tank: where V S is the volume of sludge added after shield driving (m 3 ), Vw is the volume of added water (m 3 ), and α is the correction coefficient determined by the sedimentation time of sludge pool and the change of sludge viscosity, etc.
Finally, we get the total shield sludge output of the whole shield project (V TS1 , m 3 ) as is shown below: where n≥1, N ≤ the total number of driving rings.
Bored cast-in-situ piles sludge The amount of sludge converted from the pile foundation itself (V 1 , m 3 ) should be equal to the volume of pile foundation (V, m 3 ). The calculation formula is as follows: Pore broadening coefficient (μ) refers to the ratio of the actual volume of pouring concrete and theoretical volume (the volume calculated according to the design pile diameter).
The amount of sludge in the hole before being concretepoured (V 2 , m 3 ) is equal to the amount of sludge formed by the pile foundation itself, and the total amount is calculated as follows: Additional V 3 m 3 sludge needed to turn 10 m 3 excavated soil into sludge is calculated as follows: Therefore, the total amount of sludge of bored cast-in-situ piles foundation (V TS2 , m 3 ) is calculated as follows: Underground diaphragm wall sludge The index of underground diaphragm wall sludge is closely related to the geotechnical properties of the soil layer it is in. The production of underground diaphragm wall sludge (V TS3 , m 3 ) is: As it passes through the clay layer, the pore broadening coefficient is small, usually 1.1. When the excavated stratum is sandy soil, the pore broadening coefficient is 1.3. V is the construction volume (m 3 ).

Quantitative method for predicting production of engineering soil
The major factors to predict the yield of engineering soil are the loose coefficient.
The volume of engineering soil (V TS , m 3 ) is calculated as follows: The loose coefficient σ refers to the ratio between the volume of excavated soil and the natural volume, which can be obtained by field measurement. V is the construction volume (m 3 ).

Quantitative method for predicting production of sand-gravel
Sand-gravel is the most economically valuable material in excavated waste, and the volume of sand-gravel (V sg , m 3 ) which can be separated as reclaimed aggregate is calculated as follows: τ i is the proportion of sand-gravel that can be screened out during pre-treatment in i soil layer.

Engineering verification based on geological and geotechnical analysis
The geology of the construction site has a great influence on the yield of UCW. In actual engineering analysis, the overall geological conditions are evaluated according to the geological prospecting report, and the quantity and proportion of all kinds of soil layer involved in the actual project are preliminarily counted. Targeted analysis of the physical and mechanical properties and particle analysis are carried out on the relatively large soil layers, through geological and geotechnical analysis to obtain the amount of slurry soil, sand-gravel, and other soil.
The following formula is used to measure the accuracy of the quantitative prediction methods: V r is the actual value of waste volume (m 3 ) and V p is the predicted value of waste volume (m 3 ). Basic data are derived from construction design drawings, geological information reports, Chinese construction standards, and the experience of field staff to ensure the reliability of the prediction results. The real waste output datasets of the cases study are provided by the waste transporters and on-site workers.

Case study
Among all types of excavated waste, shield waste constitutes the largest part, and its occurrence source characteristics and prediction methods are more representative. Therefore, two typical shield construction projects are analyzed to validate the quantitative method of shield sludge and the quantitative method of engineering soil.

Project overview of Hangzhou Boao Tunnel
The total length of Boao Tunnel is 2800 m, and the length of the cross-river tunnel is about 1680 m. The slurry shield of 11.7 m in diameter is adopted to excavate Hangzhou Boao Tunnel. The sludge-water treatment site is arranged on the west side of the structure, covering an area of about 5000 m 2 , with 1200 m 3 sludge in the pool of an initial density of 1.3×10 3 kg/m 3 . The propulsion distance of each ring is 5 m.
In the preliminary work, we have obtained the actual production of part of the shield sludge in the Boao Tunnel, the data of which are respectively those of ring 551, ring 563, and ring 572 on the western line and ring 243, ring 250, and ring 255 on the eastern line. These six rings will verify the quantitative method of shield sludge.
During the site investigation prior to construction, constructors will perform geotechnical and/or geophysical tests. Before construction, drilling samples should be analyzed to obtain basic information about complex geological conditions. The detailed geological survey report is illustrated in Fig. 2.
We can see from Fig. 2 that ring 551, ring 563, and ring 572 of the western line mainly involve the stratums of gravel layer and silty clay layer, among which the gravel layer takes up a large proportion. Ring 243, ring 250, and ring 255 on the eastern line mainly include silty clay layer, sand layer, and gravel layer. The physical properties of the soil layers involved in the six rings are listed in Table 3.
In the separation system of shield slurry and sand-gravel, the screen mesh is 0.25 mm in size. Particles larger than 0.25 mm in the soil will be screened out. The sludge consists of 1 volume of soil and 1.1 volume of water, and the average density of the slurry soil is 2.7×10 3 kg/m 3 . The loss coefficient ε is 0.95 in this study.

Project overview of Changsha Metro Line 5
The construction method of earth pressure balance (EPB) shield is adopted for the tunneling of Changsha Metro Line 5. The diameter of the tunnel is 6.3 m and the length of EPB shield construction area is 1600 m. The geotechnical properties and construction information of two tunnel projects were provided by the construction party. The loose coefficient σ is 1.04.

Accuracy of quantitative methods for predicting shield sludge
In combination with the geological and geotechnical datasets of Boao Tunnel in Hangzhou and the calculation formula of slurry soil ratio listed in Table 2, we obtained the volume of sand-gravel, cohesive soil, and slurry soil in the unexcavated strata in ring 551, ring 563, and ring 572 of the western line and ring 243, ring 250, and ring 255 of the eastern line. The results are shown in Table 4 and Table 5.
By comparing Table 4 and Table 5, we can see that even the same project will have a big difference due to the large geological span. For example, the excavated waste produced by the rings in the western line contains more sand-gravel, which can obtain huge economic value through simple screening, while the rings in the eastern line will produce more sludge, which will increase the difficulty of excavated waste treatment. Therefore, detailed geological and geotechnical analysis is the key to accurate management in underground civil and infrastructure projects.
The forecast yield of the 6 rings was calculated, and the accuracy of quantitative method for predicting shield sludge was calculated by Formula (12). The comparison between the actual sludge production and predicted production is as shown in Table 6.
According to the data in Table 5, the accuracy of quantitative method for predicting shield sludge is between 82.03 and 95.79%.

Accuracy of quantitative methods for predicting engineering soil
The amount of shield soil generated by Changsha Metro Line 5 could be calculated according to Formula (10). With L=1600 m, α=1.04, and R =3.15 m in the formula, the yield of engineering soil was 103936.35 m 3 . In the shield construction process, all the engineering soil was trucked away. We could calculate the actual output of the engineering soil according to the volume of soil truck; the actual output was about 110470 m 3 . According to the precision calculation Formula (12), the accuracy of the quantitative method for predicting engineering soil is 94.49%.

The stock of potential secondary resources in cases
According to the overall geological survey report and construction plan of Boao Tunnel, the volume of sand-gravel, cohesive soil, and sludge soil in the whole line was calculated.
According to the data in Table 7, we calculated that the total volume of sand-gravel produced during the tunnel construction was 168009.90 m 3 , the amount of cohesive muck was 95889.95 m 3 , and the amount of sludge soil was 178267.90 m 3 . The shield sludge yield was 520542.2 m 3 . After the completion of the project, the sludge in the sludge pool was also treated and disposed, so the total disposal amount was 521742.2 m 3 .
According to the engineering verification results summarized above, the amount of engineering soil generated by the shield part of Changsha Metro Line 5 was 103936.35 m 3 .
According to the geological report of Changsha Metro Line 5, we could calculate that the soil contained 51363.12 m 3 of sand-gravel.
UCW is the resource placed in wrong place and can theoretically be 100% recycled. Sand-gravel can be used as recycled aggregate for building materials; dry soil can be used as low-level material for roadbed, pressed brick, etc.; other soil can be used for planting, backfill, etc. UCW will bring great economic value, social benefits, and environmental improvements if they are fully recycled.

Accuracy specification
The accuracy of quantitative method for predicting shield sludge is between 82.03 and 95.79%, and the accuracy of quantitative method for predicting engineering soil is 94.49%. According to the current status of construction waste control and management, if the accuracy is ≥80%, we consider the quantitative methods is effective. The principle of various UCW prediction methods proposed in this study is essentially the same, and they are all based on their source characteristics and mass conservation to predict the possible waste output. The accuracy of quantitative methods of engineering soil and shield sludge has certain representative significance. We can conclude that the quantitative methods for predicting the amount of UCW proposed in this study are effective.  The average accuracy of quantitative method for predicting shield sludge is 89.67%. The accuracy of the methods proposed in this study is also good compared with other literatures. Maués et al. (2020) used fuzzy set theory to establish a quantitative model for predicting residential building construction waste. The model obtained an accuracy of 64.29% in the development phase and 66.67% in the validation phase. Guerra et al. (2019) developed algorithms to quantify concrete and drywall waste streams using BIM. The concrete algorithm had a variation of 11%. Yuan et al. (2021) developed a big data-probability (BD-P) model to estimate construction waste composition based on bulk density. A validation experiment using 604 ground truth data entries indicated a model accuracy of 90.2%. The quantitative methods proposed in this study can accurately estimate the production of UCW, which will greatly facilitate the follow-up management.
The accuracy of quantitative method for predicting shield sludge has certain fluctuation under the various reasons. One of the reasons is the lack of data of additives (e.g., bentonite, cellulose, foaming agent) added in construction process. Various additives are added into the sludge to maintain its functions and properties during shield sludge circulation. On the other hand, the sludge in the pool is not completely uniform, and sludge density can be affected by sedimentation and other reasons. The uncertainty of time may lead to a large error in the calculation of water addition. Last but not the least, the operating parameters of shield machine also affect the actual output of excavated waste. The quantitative methods proposed in this study do not consider the machine operation parameters and some special requirements, but only consider the two main factors: construction scale and geological conditions.

Economic value
The amount of UCW produced by underground civil and infrastructure projects is huge, and the reasonable and full utilization of these UCW will obtain huge economic value. For example, the treatment process of the excavated sand-gravel is relatively simple, and its reuse and recycling ways are wide, which can obtain great economic value if all the excavated sand-gravel could be fully reused and recycled. Because the quality of the sand-gravel produced by these two projects is slightly worse than that of the sand-gravel in the market, the price of the sand-gravel recycled in cases is 150 yuan /m 3 . The total value of the sand-gravel produced by the Boao Tunnel Project is about 25 million yuan. The net profit is about 22 million yuan after removing transportation cost of about 1 million yuan and the follow-up treatment cost of about 2 million yuan. The net profit of sand-gravel separated from Changsha Metro Line 5 is estimated above 7 million yuan. Enhance research on sorting and aggregate strengthening technology can bring more benefits to relevant stakeholders.  Sludge dewatering has always been the difficulty and key point of sludge treatment. Generally, the type of shield construction is chosen according to the geological properties. When the permeability coefficient of the geological layer is greater than 1×10 −4 , sludge shield is adopted; when the permeability coefficient of geological layer is less than 1×10 −7 , EPB shield is adopted; when the permeability coefficient is between the above two numbers, both types can be adopted. Accelerating the improvement of the construction method of shield tunneling machine to minimize sludge production is the sensible solution for sludge treatment. Dry soil produced by dewatering sludge can be used as low-level raw materials; other soil will be partially backfilled or transported for offsite use. A huge economic value can be obtained if all the waste could be fully reuse and recycled.

Environmental improvements
Full reuse and recycling of UCW have great potential for carbon emission reduction. On the one hand, it can partially offset the carbon emissions generated by landfill. On the other hand, the recycled building materials from UCW will offset the carbon emissions generated by ordinary building materials.
The reuse and recycling of UCW will reduce the dust generated from random stacking or landfills and improve air quality. At the same time, it also will reduce the land occupation and maintain water and soil balance, which is conducive to the maintenance of ecological stability.

Social benefits
Quantitative methods proposed in this study are the sum of the quantitative data of each construction section, which can provide effective data for the precise on-site management of the excavation waste, such as determining the volume and location of the sludge pool, the quantity and distribution scheme of the soil separator, crusher, etc., and the reasonable allocation of transport personnel and vehicles.
If a large amount of UCW is not reused or recycled, it will not only waste resources, but also cause safety problems such as landslides and affect the image of the city.

Conclusions
Underground construction produces a large amount of waste with high reuse and recycling value, but few quantitative studies focus on it. In order to bring convenience to the management and recycling of UCW, this study established quantitative methods to predict the amount of UCW based on the principle of mass conservation. The source characteristics, factors affecting the yield, and the possible recycling direction of UCW were analyzed to provide sufficient theoretical support for the establishment of the methods. Through the engineering verification of the actual project, it is concluded that the quantitative method for predicting shield sludge has a valid accuracy with the accuracy range from 82.03 to 95.79%. The accuracy of the quantitative method for predicting engineering soil is 94.49%. Meanwhile, the stock of potential secondary resources in cases was calculated.
It proves that the quantitative methods proposed in this study are effective and workable. It is feasible to use the mass conservation principle combined with geological and geotechnical data to predict UCW production.
Two cases demonstrate that underground construction can produce huge amounts of construction waste. Due to its own special properties, UCW can reach a recovery rate of 100%. UCW is a huge hidden resource. Recyclable sand-gravel make up a large part of the excavated waste, and the reasonable and full utilization of this UCW will obtain huge economic value, social benefits, and environmental improvements.
In order to further improve the accuracy of the quantitative methods, more factors can be considered in the future, such as the water content of stratum and the additives added in the sludge, and more categories can be considered according to the actual situation. Author contribution Rui Chen designed the paper framework and wrote the manuscript. Lanxin Li maintained research data and wrote the manuscript. Kai Yang conducted a research and investigation process. Fumin Ren contributed to funding acquisition. Chenggang Xi, Yang Lin, and Hai Zheng provided technical and editorial assistance.
Funding This work was supported by the National Key Research and Development Program, "Precise management control in construction and demolition waste and engineering demonstration" [grant number 2018YFC0706000].
Data availability The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations
Ethics approval and consent to participate Not applicable.

Consent for publication Not applicable.
Competing interests The authors declare no competing interests.