Carbon FootprintsCFCarbon Footprints2831-932XOAE Publishing Inc.10.20517/cf.2026.62Original ArticleA novel allocation method and critical transport distance for industrial by-products in concretePanLei12WangYuanfeng2FuYufang1ZhangBoqun2GuoXiaohui3ShiChengcheng4LiuYinshan5WangLiping2XueShaoqin2ChangXinlei2LiuXiaodong21Research & Innovation Center, Research Institute of Highway Ministry of Transport, Beijing 100088, China.2School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China.3China Petroleum International Pipeline Co., Ltd., Beijing 102200, China.4School of Management, Tianjin University of Commerce, Tianjin 300134, China.5Institutes of Science and Development, Chinese Academy of Sciences, Beijing 100190, China.Correspondence to: Yuanfeng Wang, School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China. E-mail: cyfwang@bjtu.edu.cn
Received: 26 May 2026 | First Decision: 22 Jul 2026 | Revised: 2 Aug 2026 | Accepted: 17 Aug 2026 | Published: 23 Sep 2026
Academic Editors: Weina Meng, Kathleen B. Aviso | Copy Editor: Shu-Yuan Duan | Production Editor: Shu-Yuan Duan
Cement production accounts for about 8% of global CO2 emissions, making it the largest industrial source in the construction material chain. Replacing cement with industrial by-products (IBPs) in concrete is a core pathway to reducing carbon footprint, but a scientifically sound allocation method is essential for accurately quantifying the carbon reduction contribution of IBPs. At present, the mainstream allocation methods in this field suffer from significant spatial and temporal fluctuations and low accounting stability, which seriously interfere with the accurate assessment of the carbon footprint and carbon emission reduction benefits of concrete incorporating IBPs. This study established an innovative production cost-based economic allocation principle for IBPs carbon footprints, which takes the manufacturing costs of primary industrial products and associated IBPs as the allocation core and considers their operational linkages within the industrial chain. Meanwhile, based on 929 groups of fly ash (FAH) concrete mix proportion data, a life cycle assessment approach was employed to systematically evaluate the carbon footprint characteristics of FAH concrete and quantify its critical transport distances (CTD). The findings indicate that the environmental impacts allocation principle and concrete mix design dominate the carbon footprint reduction potential and CTD of FAH. Low-carbon transportation equipment can significantly expand FAH’s CTD by reducing transport-related carbon footprint, which provides a scientific basis for the rational planning of large-scale promotion and efficient utilization of FAH. The proposed method offers a transferable methodological framework and may be adapted for carbon footprint accounting and carbon emission reduction contribution evaluation of other IBPs.
Industrial by-products (IBPs) are non-primary outputs generated during industrial processes, with substantial production volumes. For instance, China alone produces approximately 600 million tons of fly ash (FAH) annually[1]. Improper management of these IBPs can lead to land occupation, soil and water contamination, air pollution, as well as resource depletion and energy inefficiency. However, through resource utilization, these IBPs can be transformed into high-value building materials, which not only eliminate environmental pollution but also reduce the carbon footprint over the whole life cycle of building materials, lower enterprise production costs, create economic value, and boost industrial technological innovation[2-5]. More importantly, the resource utilization of IBPs is a key path to reducing the carbon footprint of construction engineering, a core strategy for achieving circular economy and low-carbon development, and a critical support for advancing global sustainable development goals and building a resource-efficient, low-carbon, and environment-friendly society.
Concrete, the most widely used construction material globally, is highly energy-intensive and carries a huge carbon footprint throughout its production chain, with cement manufacturing being the dominant emission source[6-8]. According to research, producing one ton of cement emits approximately 0.85 ~ 0.92 tCO2eq[9], with the cement sector contributing about 8% of total human-caused carbon emissions[10,11]. This oversized carbon footprint has become a major bottleneck restricting the sustainable development of the concrete industry. Using pozzolanic IBPs as supplementary cementitious materials (SCMs)[12-14] to partially replace cement is the most technically mature and economically feasible strategy to reduce the concrete carbon footprint and achieve substantial carbon reduction[15-18].
Multiple studies confirm that clinker substitution with SCMs reduces the carbon footprint of concrete by over 30%[19]. Singh and Prasad[20] reported that 65% FAH replacement reduces concrete carbon footprint by 54%. Orozco et al.[21] noted that 10%/15%/20% FAH replacement yields concrete carbon footprint reductions of 8.5% ~ 9.4%/8.5% ~ 20.7%/2.4% ~ 19.2%. Jiang et al.[22] pointed out that compared with ordinary concrete, a well-designed FAH concrete mix proportion can reduce its carbon footprint by up to 60.3%. Liao et al.[23] presented that when cement was completely replaced by FAH, the carbon footprint of FAH concrete was 7.9% ~ 21.2% lower than that of ordinary concrete. Li et al.[24] found that for alkali-activated slag-FAH concrete, when the strength grade is C30, the carbon footprint was reduced by 77.3% ~ 80.7%; when the strength grade is C50, the carbon footprint was reduced by 76.9% ~ 81.3%. Orozco et al.[25] verified that 25%/50% FAH replacement lowers the carbon footprint by 22% ~ 30.6%/44% ~ 51.4%. These data fully demonstrate that FAH concrete makes an outstanding contribution to carbon footprint reduction in the decarbonization of building materials.
Long-distance transportation can generate additional carbon emissions[26], which may gradually offset the carbon emission reduction benefits brought by FAH replacement. High-volume FAH mixes may even have a higher full-cycle carbon footprint than conventional concrete. This highlights that transport-related carbon footprint is a key factor restricting the carbon emission reduction contribution of SCMs. Jamora et al.[27] calculated that the critical transportation distance of FAH was 2841 km, beyond which the carbon footprint advantage of FAH concrete would disappear. O’Brien et al.[28] reported FAH’s CTD (11,000km ~ 54,000 km), influenced by carbon footprint differences among transport modes. Bajpai et al.[29] found a CTD of 3219.27 km, beyond which the carbon footprint of FAH concrete exceeds that of conventional concrete.
The EU Waste Directive of 2008 stipulates certain conditions that materials must meet in order to be regarded as IBPs rather than waste[30]. Chen et al.[31] studied according to this directive and showed that FAH meets all the conditions for being an IBP and thus should not be regarded as waste. Therefore, when FAH is used as a cement substitute, its full-chain carbon footprint must be rigorously quantified, and its carbon emission reduction contribution must be accurately evaluated.
The life cycle assessment (LCA) results of green concrete carbon footprint strongly depend on the environmental impacts allocation principles of the modeled SCMs[32]. Currently, three primary methods are widely used: mass-based, economic, and no allocation[31]. Hafez et al.[33] reviewed 59 green concrete LCA papers and found that only 14 addressed allocation, with 8 using economic and 6 combining mass/economic approaches. Hossain et al.[15] reviewed LCA studies on concrete production using SCMs to replace cement over a decade and found that approximately 78% of the studies chose “no allocation”, and approximately 37% chose the economic allocation principle. They emphasized the limitations of economic allocation due to temporal and spatial price volatility. Common allocation approaches can be found in Reference[15].
Even under the same allocation principle, carbon footprint calculation results vary greatly among researchers. For example, Chen et al.[31] presented that when the mass/economic allocation principles are selected, the environmental impacts allocation coefficients of FAH are 12.4% and 1%, respectively, and the carbon footprint per unit mass of FAH is approximately 495% and 41% of that of ordinary Portland cement, respectively. Zhang[34] provided the localized environmental impacts allocation coefficients of FAH in China. When the mass/economic allocation principles are selected, the environmental impacts allocation coefficients of FAH are 21.5% and 1%, respectively, and the carbon footprint per unit mass of FAH is approximately 174% and 8.1% of that of cement. Hossain et al.[15] obtained FAH allocation coefficients of 12.41% (mass allocation principle) and 2.18% (economic allocation principle), and the carbon footprint per unit mass of FAH is approximately 412% and 91% of that of cement. They further found that, relative to the economic allocation principle, applying the system-expansion-based allocation principle reduces the carbon footprint of SCM concrete by approximately 10% to 28%. This indicates that mass allocation methods result in considerably higher environmental impacts for concrete containing SCMs. Nevertheless, traditional economic allocation coefficients exhibit considerable temporal and spatial variability[31,35-37], resulting in unstable carbon footprint accounting and unreliable evaluation of carbon emission reduction benefits.
The divergent results reported in the literature reveal a critical contradiction in current allocation practices: the choice of allocation principle profoundly affects the assessed carbon footprint of SCMs, yet no consensus exists on which principle is most appropriate. The mass-based allocation, while physically transparent, tends to substantially overestimate the environmental burden of IBPs, thereby underestimating their carbon reduction contribution and discouraging their beneficial use. Conversely, the no-allocation approach, though maximizing the apparent benefit of IBPs, ignores the fact that IBPs are an integral output of the production system, thus failing to reflect their true environmental footprint. The traditional economic allocation, which attempts to balance these extremes by incorporating market values, introduces significant temporal and spatial volatility, leading to unstable and non-comparable results across different studies and regions. The deficiency of research lies in the lack of an allocation method that can simultaneously achieve theoretical rationality, result stability, and practical applicability. While system expansion has been proposed as an alternative, its application requires clear identification of substituted product systems, which is often complex and data-intensive[35-37].
Against this backdrop, the present study aims to fill this lack by proposing a novel allocation principle based on production costs - a parameter that is both economically meaningful and intrinsically stable. This method not only retains the economic rationale of value-based allocation but also overcomes the volatility inherent in market-price-based approaches. Using life cycle assessment, the present study analyzed the carbon footprint characteristics of FAH concrete and the CTD of FAH under different allocation principles, and clarified the carbon emission reduction contribution of FAH under multiple scenarios. The research results provide a theoretical foundation for accurate carbon footprint assessment and scientific carbon emission reduction potential evaluation of FAH resource utilization, and offer a methodologically transferable framework that, with appropriate adjustments, may be applicable to other IBP types for formulating targeted low-carbon development policies in the construction industry.
METHODS AND DATATraditional allocation principles
The environmental impacts (core: carbon footprint) of IBPs from production to final use can be expressed by:
where Ii refers to the carbon footprint of IBPs i; Cj represents the carbon footprint allocation coefficient of the jth allocation method; Itei and Isei denote the total production impact, and the secondary processing impact, respectively; Ti stands for the carbon footprint generated when IBPs are transported to the place of use, which is not included when calculating the carbon footprint factor of IBPs.
Mass allocation principle
The no-allocation principle (C0) treats waste as valueless, exempting it from primary production carbon footprint. However, valuable IBPs need to share part of this burden. Mass-based allocation (Cm) distributes carbon footprint proportionally to mass, as given in[31]:
where Cm represents mass allocation coefficient; mmain-product and mby-product refer to the mass of industrial main product and IBPs, respectively.
As indicated in the introduction, the carbon footprint of IBPs derived from mass allocation is significantly overestimated, which underestimates the carbon emission reduction contribution of IBPs and is unfavorable for their promotion. Therefore, this principle was excluded from subsequent analysis.
Economic allocation principle
To better allocate the environmental impacts of IBPs, Chen et al.[31] proposed the traditional economic allocation principle (Ce), which allocates carbon footprint via market prices, as given in:
where Ce stands for the carbon footprint allocation coefficient of IBPs based on the economic allocation principle; e × m represents production revenue.
Using Equation (3), the FAH’s carbon footprint allocation coefficient was 5.31%. The production volume, production cost, cost composition, and data sources used for calculation all come from the literature[38]. This coefficient is then applied to the total production impact via Equation (1), yielding the carbon footprint factor of 303.81 kgCO2eq/t for FAH under the traditional economic allocation principle.
New economic allocation principle
The production cost of a product encompasses all production expenses incurred by an enterprise during the production process. It represents the capital outlay that the enterprise advances in anticipation of generating revenue. The production cost of the product is composed of three components: direct materials, direct labor, and manufacturing overhead. Direct materials refer to the raw materials that form the physical substance of the product, along with the primary and auxiliary materials that facilitate product formation. Direct labor denotes the employee compensation of workers engaged in product manufacturing. Manufacturing overhead consists of various indirect costs incurred by the enterprise’s production department for product manufacturing and service provision, including the consumption of machine supplies, the salaries of workshop management personnel, depreciation expenses, office expenses, and utility bills such as water and electricity charges.
Based on the production cost of products, a new economic allocation principle was proposed, as expressed by
where Cc is the carbon footprint allocation coefficient of IBPs based on the new economic allocation principle; c × m refers to total production cost.
The proposed method adopts production cost as an alternative economic basis for allocating environmental burdens to industrial IBPs. Its theoretical rationality rests on three aspects. First, in a multi-product system, the main product and the IBP are generated jointly within the same production process. Production cost-encompassing direct materials, direct labor, and manufacturing overhead-directly measures the resources actually invested by the enterprise to obtain each output. Compared with market prices, which are significantly influenced by supply-demand dynamics and policy interventions, production cost more genuinely reflects the “resource contribution” of the IBPs within the production system, thereby providing a more reasonable basis for determining its share of the environmental burden.
Second, the production-cost principle is intrinsically aligned with the “industrial-chain linkage” nature of IBPs. As clarified by the EU Waste Framework Directive, IBPs are an organic part of the production process. When IBPs are valorized, their environmental burden allocation should reflect their inherent connection with the main product. Using production cost rather than market value can accurately characterize this intrinsic industrial-chain relationship.
Third, the method is well compatible with the ISO 14044 framework. When system expansion or process subdivision is infeasible, ISO 14044 permits allocation based on parameters such as economic value. Our method is an improved variant of traditional economic allocation, replacing volatile market prices with more stable production costs as the allocation basis.
Using Equation (4), the FAH’s carbon footprint allocation coefficient was 1.94%. The production volume, production cost, cost composition, and data sources used for calculation all come from the literature[38]. This coefficient is then applied to the total production impact via Equation (1), yielding the carbon footprint factor of 115.11 kgCO2eq/t for FAH under the new economic allocation principle. Cao et al.[39] have demonstrated that the volatility of the producer price index is significantly lower than that of the commodity price index. Therefore, the FAH allocation coefficient obtained by the new economic allocation principle has less volatility and better stability.
LCA method
ISO standards define four LCA phases: goal definition, inventory analysis, impact assessment, and interpretation[40,41]. Two functional units are adopted to capture different perspectives of carbon footprint performance: FU1 (kgCO2eq/m3) represents the volumetric carbon footprint per cubic meter of concrete, while FU2 (carbon footprint intensity,kgCO2eq/MPa/m3) normalizes the carbon footprint by compressive strength to account for the trade-off between environmental impact and mechanical performance. FU2 is given in[34]
The system boundary, as illustrated in Figure 1, encompasses all processes from raw material extraction to the concrete plant gate, following the “cradle-to-gate” approach.
System boundary of FAH concrete. FAH: Fly ash.
The carbon footprint factors of the production process used for calculating the carbon footprint of FAH concrete were derived from literature[42-46], among which the carbon emission factor of Class 8b trucks is 0.104341 kgCO2eq/(t·km). The transport distances for materials and energy at various stages were set [Table 1].
Distance of material and energy transport at each stage
Transport stages
Materials or energy
Mode
Distance
Transport I/km
Cement raw materials to cement plant
Class 8b truck
40
Gypsum to cement plant
Class 8b truck
40
Sand to fine aggregate plant
Class 8b truck
10
Rock to coarse aggregate plant
Class 8b truck
5
Transport II/km
Cement to concrete plant
Class 8b truck
176
Fine aggregate to concrete plant
Class 8b truck
176
Coarse aggregate to concrete plant
Class 8b truck
176
Transport III/km
Crude oil to energy processing plants
Pipeline
637
Coal to coal-fired power plant
Class 8b truck
176
Diesel, gasoline to the petrol station
Oil tank truck
176
Diesel, gasoline to the product oil transfer center
Pipeline
637
Electricity to the construction site
Line loss rate：4.84%
Data collection
A dataset of 1256 concrete mix designs was compiled, consisting of 929 groups of FAH concrete (with FAH content > 0) and 327 groups of ordinary concrete (with FAH content = 0) as controls, categorized by 28-day compressive strength and FAH content [Table 2][30,47-64], providing a large dataset for accurate carbon footprint calculation and carbon reduction contribution evaluation[47-64]. The mix proportion data of all 1,256 concrete samples were grouped according to the compressive strength grade, as shown in Table 3. The data were screened according to the following criteria: (1) complete records of 28-day compressive strength and all mix proportion components (cement, FAH, water, aggregates, and admixtures); (2) clearly reported mix designs without missing critical parameters; and (3) test results obtained under standard curing conditions. No additional preprocessing such as data imputation or transformation was applied.
Groups with strengths and dosage ranges
Compressive strength(MPa)
Range
[30,40)
[40,50)
[50,60)
[60,70)
[70,80)
≥ 80
Number
449
311
178
144
88
86
Ratio (%)
35.75
24.76
14.17
11.46
7.01
6.85
FAH content(%)
Range
0
(0 ~ 10]
(10 ~ 20]
(20 ~ 30]
(30 ~ 40]
(40 ~ 50]
(50 ~ 60]
＞ 60
Number
327
94
248
229
160
107
65
26
Ratio (%)
26.04
7.48
19.75
18.23
12.74
8.52
5.18
2.07
FAH: Fly ash.
Groups with strength classes
Class
C30
C35
C40
C45
C50
C55
C60
＞ C60
Number
225
224
186
125
96
82
99
219
Ratio (%)
17.91
17.83
14.81
9.95
7.64
6.53
7.88
17.44
RESULTS AND ANALYSISCarbon footprintRapid estimation model
Under the C0 allocation principle, Figure 2 illustrates the relationships between the compressive strength and the carbon footprint as well as carbon footprint intensity. For functional unit FU1, the carbon footprint increases with higher compressive strength, whereas for FU2, carbon footprint intensity decreases. Furthermore, the dispersion of carbon footprint intensity under FU2 is lower than that of carbon footprint under FU1.
Carbon footprint and carbon footprint intensity. (A) Carbon footprint (FU1) versus compressive strength; (B) Carbon footprint intensity (FU2) versus compressive strength.
Given the low variability of carbon footprint intensity, an allometric function was used for fitting, resulting in:
$$ C_{i}=114.74 f_{c, 28}^{-0.068} \\ $$
The carbon footprint per unit strength can be calculated using Equation (6) and the compressive strength, allowing rapid per-volume carbon footprint estimation and markedly improving efficiency.
Figure 3 illustrates the carbon footprint and carbon footprint intensity of FAH concrete under the Ce and Cc allocation principles. Regardless of the principle, the carbon footprint increases with strength under FU1, while carbon footprint intensity decreases under FU2, with lower dispersion than FU1. The fitting formulas for carbon footprint intensity under each principle are listed in Table 4.
Carbon footprint and carbon footprint intensity. (A) Carbon footprint and carbon footprint intensity under the Ce allocation principle; (B) Carbon footprint and carbon footprint intensity under the Cc allocation principle.
Carbon footprint intensity fitting formulas under different allocation principles
Allocation principle
Equation
R2
Ce
$$ C_{i}=146.55 f_{c, 28}^{-0.712} $$
0.8291
Cc
$$ C_{i}=126.34 f_{c, 28}^{-0.065} $$
0.7705
Carbon footprint characteristics
Based on the 929 sets of FAH concrete mix proportion data, carbon footprints were calculated under different allocation principles, and the corresponding statistical parameters were derived. These parameters include the maximum value ($$ C_{\mathrm{FU}_{1}, \text { max }} $$), minimum value ($$ C_{\mathrm{FU}_{1}, \text { min }} $$), median value ($$ \bar{C}_{\mathrm{FU}_{1}} $$), mean value ($$ \mu_{\mathrm{FU}_{1}} $$), standard deviation ($$ \sigma_{\mathrm{FU}_{1}} $$), and variation coefficient ($$ \delta_{\mathrm{FU}_{1}} $$) of the carbon footprint. Table 5 presents the calculation results.
Statistical parameters of carbon footprint
Allocation principle
Parameter
C30
C35
C40
C45
C50
C55
C60
> C60
C0
$$ C_{\mathrm{FU}_{1}, \text { max }} $$
480.46
522.02
514.32
578.72
619.40
528.99
567.58
610.38
$$ C_{\mathrm{FU}_{1}, \text { min }} $$
245.90
287.86
226.45
310.26
243.51
310.26
311.44
334.31
$$ \bar{C}_{\mathrm{FU}_{1}} $$
368.76
380.33
388.56
397.23
416.65
433.96
462.12
487.88
$$ \mu_{C_{F U_{1}}} $$
366.87
381.61
395.20
408.00
429.40
432.76
460.11
485.10
$$ \sigma_{C_{F U_{1}}} $$
44.22
48.76
50.09
52.36
67.01
48.99
52.99
45.49
$$ \delta_{C_{F U_{1}}} $$
12.05%
12.78%
12.67%
12.83%
15.61%
11.32%
11.52%
9.38%
Ce
$$ C_{\mathrm{FU}_{1}, \text { max }} $$
521.20
597.02
576.66
633.40
666.38
612.54
567.58
610.38
$$ C_{\mathrm{FU}_{1}, \text { min }} $$
265.35
318.94
246.99
376.30
267.42
400.01
407.14
417.82
$$ \bar{C}_{\mathrm{FU}_{1}} $$
397.60
413.34
424.18
431.19
443.39
464.84
486.07
512.15
$$ \mu_{C_{F U_{1}}} $$
401.58
415.62
427.61
443.39
457.66
467.07
488.45
513.03
$$ \sigma_{C_{F U_{1}}} $$
36.78
37.33
41.43
46.92
59.02
34.19
33.90
30.98
$$ \delta_{C_{F U_{1}}} $$
9.16%
8.98%
9.69%
10.58%
12.90%
7.32%
6.94%
6.04%
Cc
$$ C_{\mathrm{FU}_{1}, \text { max }} $$
495.90
542.03
530.85
599.44
629.58
560.64
567.58
610.38
$$ C_{\mathrm{FU}_{1}, \text { min }} $$
253.27
299.64
234.23
344.52
252.57
346.52
347.70
381.52
$$ \bar{C}_{\mathrm{FU}_{1}} $$
380.63
394.12
399.89
411.66
427.55
444.97
469.95
499.56
$$ \mu_{C_{F U_{1}}} $$
380.02
394.50
407.48
421.41
440.11
445.76
470.85
495.68
$$ \sigma_{C_{F U_{1}}} $$
39.43
42.69
45.40
48.79
62.72
41.47
44.90
38.71
$$ \delta_{C_{F U_{1}}} $$
10.38%
10.82%
11.14%
11.58%
14.25%
9.30%
9.54%
7.81%
Table 5 shows that, under any allocation principle, the mean and median carbon footprint of FAH concrete increase with strength grade. In contrast, the standard deviation and coefficient of variation exhibit notable variability across grades, with the highest values for C50. This variability also reflects the variation in carbon footprint caused by differing mix proportions within the same strength grade.
A violin plot is a statistical chart that combines the features of a box plot and a kernel density plot. It uses the box plot concept to display various percentiles of the data, while the kernel density plot is used to show the “contour” effect of the data distribution. The kernel density plot is usually displayed on both sides of the box plot, forming a shape similar to a violin. The larger the “contour”, the more the data is concentrated in that area, and vice versa, indicating fewer data points in that area. Figure 4 illustrates the distribution of carbon footprint across different strength grades and allocation principles, clearly showing that the median carbon footprint increases with compressive strength grade, and the probability density peaks near the median.
Carbon footprint distribution characteristics under different allocation principles. (A) Violin plot of carbon footprint distribution under the C0 allocation principle; (B) Violin plot of carbon footprint distribution under the Ce allocation principle; (C) Violin plot of carbon footprint distribution under the Cc allocation principle. The green shaded regions represent the kernel density estimation contours, which indicate the probability density distribution of the carbon footprint data, the wider the green area, the more concentrated the data points at that value. IQR: Interquartile range.
Meanwhile, there is an “overlap” in the carbon footprint of different strength grades of FAH concrete, which is mainly attributable to two reasons. Firstly, since FAH is used as an SCM to replace cement, the amount of cement used is reduced, thereby reducing the carbon footprint. For example, when the strength grade of FAH concrete is C50 or even higher, owing to the different FAH contents, its carbon footprint may be lower than that of C30 concrete. Secondly, since the mix proportion determines the amounts of materials used, a good mix proportion can consume fewer materials while meeting the compressive strength requirements, thus reducing the carbon footprint. However, if the mix proportion is not optimal, the use of FAH may not reduce the carbon footprint. In some instances, the carbon footprint exceeds that of ordinary concrete with the same or even higher strength grades. This highlights the importance of mix proportion optimization. In addition, the properties of raw materials, construction procedures during the concrete production process, and the testing process can also increase the variability of carbon footprint of FAH concrete[30,34].
Critical transport distance
O’Brien et al.[28] noted that the transport distance of FAH greatly affects the environmental load of FAH concrete: longer distances gradually offset the environmental benefits of incorporating FAH. Therefore, analyzing the FAH’s CTD is necessary. The CTD was calculated using the average carbon footprint of conventional concrete (0% FAH, i.e., the 327 control groups) at various strength grades as a reference. The critical transportation distance of FAH is shown in Equation (7), where the FAH content is greater than 0 (this study has 929 sets of data).
$$ L_{\text {limit }}(i, j)=\frac{C_{F U_{1} \-0 \%}-\Delta C_{F U_{1} \-C_{i}-F A H \%}}{2 \times E F_{T_j} \times m_{F A H} / 1000} $$
where Llimit(i,j) is the CTD for a given scenario; $$ C_{F U_{1}-0 \%} $$ is the reference carbon footprint at 0% FAH content; $$ \Delta C_{F U_{1} \-C_{i}-F A H \%} $$ represents the carbon footprint of concrete with different FAH dosages based on the principle of allocating the environmental impact of FAH, excluding all transportation stages of FAH; $$ E F_{T_j} $$ and mFAH are the carbon footprint factor for a transport mode [kgCO2eq/(t·km)] and the mass of FAH (kg). To account for environmental impacts from empty driving, the transport distance is doubled[65].
The influence of mix proportion uncertainty on the CTD
Using Equation (7), the CTD of FAH was calculated for different strength grades of FAH concrete under various allocation principles. Figure 5 presents the CTD values for C30, C40, C50, and C60. In all strength grades, negative CTD values appear, particularly for lower grades such as C30 and C40, indicating that FAH application results in a higher carbon footprint than that of the reference scenario. This phenomenon primarily results from sub-optimal mix proportions, which cause higher material consumption and consequently offset the carbon reduction potential of FAH.
Critical transport distance of FAH. (A) CTD distribution for C30; (B) CTD distribution for C40; (C) CTD distribution for C50; (D)CTD distribution for C60. FAH: Fly ash; CTD: critical transport distance.
At lower FAH content levels, the CTD exhibits a wider distribution range, primarily due to uncertainties in mix proportion design. When an optimal FAH concrete mix proportion is achieved, the significant reduction in material usage leads to a substantially lower carbon footprint compared to the reference value. In calculating FAH’s CTD using Equation (7), both the carbon emission reduction from material savings and FAH’s inherent carbon emission reduction capability are considered as FAH’s contribution. In this case, the mass of FAH is relatively small, which increases the CTD.
When cement is replaced by an equal mass of FAH without compromising concrete strength, the CTD of FAH increases as the FAH dosage rises. However, this is not the case in practice. High FAH content reduces the compressive strength of concrete[66]. When additional cement or admixtures are needed to achieve the same strength grade, the carbon reduction advantage of FAH is reduced. Moreover, given the relatively large mass of FAH in this case, the CTD for FAH decreases. Furthermore, when a substantial amount of FAH is utilized, although the CTD would not become negative, there can be instances where the CTD is quite small. Most FAH comes from power plants, so it is often transported over long distances to concrete processing plants. A very short CTD causes FAH concrete’s carbon footprint to surpass the reference value, making it difficult to meet carbon emission reduction goals. This also fully underscores that optimizing the mixing ratio is the key to carbon reduction, and even an indispensable step.
The CTD values for FAH concrete of various strength grades across all mix proportion schemes were averaged to obtain a statistically meaningful CTD for FAH, as illustrated in Figure 6. As shown in Figure 6, for all strength grades of FAH concrete, increasing the carbon footprint allocation coefficient raises the carbon footprint coefficient of FAH and reduces its CTD. Under the allocation principles of C0, Cc, and Ce, when the strength grade of FAH concrete is C50, the CTD for FAH is the largest, measuring 1,992 km, 1,646 km, and 1,079 km, respectively. Next, for C35, the CTD values are 1811 km, 1,465 km, and 899 km, respectively. For C30, the values are the smallest, at 1,171 km, 825 km, and 259 km. Based on these, the unweighted average CTD across all strength grades under the C0, Cc, and Ce allocation principles are 1,538 km, 1,166 km, and 599 km, respectively, with a maximum difference of 939 km. This fully demonstrates the significance of the environmental impact allocation principle.
FAH’s CTD in statistical sense. FAH: Fly ash; CTD: critical transport distance.
The influence of uncertainty of transport vehicles on the CTD
In addition to concrete mix proportions and FAH content, transport modes also significantly influence the CTD of FAH. Table 6 lists the carbon emission factors for various transport modes[67]. In this table, various transport modes are denoted as Ti.
Transport mode carbon emission factors [kgCO2eq/(t·km)]
Transport modes
factor
Transport modes
factor
Light petrol truck transport (load 2 t): T1
0.334
Medium-sized gasoline truck transport (load 8 t): T2
0.115
Heavy petrol truck transport (10 t load): T3
0.104
Heavy gasoline truck transport (load 18 t): T4
0.104
Light diesel truck transport (load 2 t): T5
0.286
Medium-sized diesel truck transport (load 8 t): T6
0.179
Heavy diesel truck transport (load 10 t): T7
0.162
Heavy diesel truck transport (load 18 t): T8
0.129
Heavy diesel truck transport (load 30 t): T9
0.078
Heavy diesel truck transport (load 46 t): T10
0.057
Electric locomotive transport: T11
0.010
Diesel locomotive transport: T12
0.011
Rail transport (average for the Chinese market): T13
0.010
Liquid cargo ship transport (deadweight 2,000 t): T14
0.019
Dry bulk carrier transport (deadweight 2,500 t): T15
0.015
Container ship transport (deadweight 200TEU): T16
0.012
When calculating the CTD of FAH using different transport modes, since the load capacities of T1 and T5 are only 2t, which are not suitable for the transport of building materials, T1 and T5 are excluded. Since the carbon emission factors of T3 and T4, as well as T11 and T13 are the same, only one of each pair is selected for calculation. The CTD values for different transport modes are then averaged across all strength grades of FAH concrete, resulting in the CTD of FAH under the C0, Cc, and Ce allocation principles. The specific values are shown in Table 7 and Figure 7.
CTD of FAH under different transport modes. FAH: Fly ash; CTD: critical transport distance.
CTD of FAH under different transport modes (km)
Transport modes
C0
Ce
Cc
T2
2,227
867
1,688
T3
2,462
959
1,866
T6
1,431
557
1,084
T7
1,581
616
1,198
T8
1,985
773
1,504
T9
3,283
1,279
2,488
T10
4,493
1,750
3,405
T12
23,281
9,066
17,643
T13
30,292
11,007
22,707
T14
13,479
5,249
10,214
T15
17,073
6,648
12,938
T16
21,341
8,310
16,173
Maximum difference
28,861
10,450
21,623
The CTD values in this table are overall averages over all compressive strength grades for each transport mode, whereas Figure 6 presents compressive strength grade-specific averages for the Class 8b truck only. Hence, the T3 value in Table 7 differs from the corresponding values shown in Figure 6. CTD: Critical transport distance.
As indicated in Table 7, based on the allocation principles for C0, Cc, and Ce, the maximum variations in the CTD of FAH across different transport modes reach 28,861 km, 21,623 km, and 10,450 km, respectively. Evidently, distinct transport modes significantly influence the CTD of FAH. Under the C0, Cc, and Ce allocation principles, the CTD of FAH is highest for transport mode T13, at 30,292 km, 22,707 km, and 11,007 km, respectively, and lowest for mode T6, at 1,431 km, 1,084 km, and 557 km, respectively.
As illustrated in Figure 7, the CTD of FAH for transport modes to the right of the red dashed line (T12 to T16) is substantially higher than for those to the left, which are gasoline or diesel trucks with varying load capacities. This suggests that while road transport offers advantages in convenience and flexibility, it proves to be the least effective mode for carbon reduction. For both gasoline and diesel trucks, the carbon footprint factor decreases as load capacity rises, leading to a corresponding increase in the CTD of FAH. Therefore, when road transport is necessary, trucks with higher load capacities should be used wherever road conditions permit.
When applying the C0 allocation principle to road transport, the T10 mode yields the longest CTD for FAH at 4,493 km, while the T6 mode presents the shortest at 1,431 km-with the former being 3.14 times the latter. Under the Ccand Ce allocation principles, the CTD for FAH under the T10 mode measures 3,405 km and 1,750 km, respectively. For the T6 mode, these values are 1,084 km and 557 km, respectively. Notably, rail transport (encompassing railway, diesel locomotive, and electric locomotive transport in this study) outperforms waterway transport in carbon reduction. Consequently, the recommended hierarchy for transport mode selection prioritizes rail, followed by waterway, and then road transport. Rational mode selection and transport structure optimization play a pivotal role in achieving carbon reduction goals, such as multimodal transportation[26].
Uncertainty in transport distance parameters
It should be noted that the material transport distances used in this study are fixed empirical values derived from typical supply chain configurations in the Chinese context [Table 1]. In practice, these distances may vary considerably depending on the geographical location of raw material sources, concrete plants, and construction sites. Such variations introduce additional uncertainty into the calculated CTD of FAH. While a comprehensive probabilistic analysis of distance parameters is beyond the scope of this study, the potential influence of transport distance uncertainty on CTD results should not be overlooked. Future research will employ Monte Carlo simulation or other uncertainty quantification techniques to systematically assess the sensitivity of CTD outcomes to variations in transport distance parameters.
Rationality and applicability of different allocation principles
The various allocation principles considered or proposed in this study each have their own theoretical applicability and limitations (See Table 8). The no-allocation principle, while simple and maximizing the apparent emission-reduction benefit of IBPs, ignores the fact that IBPs are an integral output of the production system - inconsistent with the paradigm shift from “waste” to “resource” in circular economy thinking. The mass-allocation principle, although physically clear, severely overestimates the environmental burden of IBPs, as shown in the introduction and previous studies (e.g., the carbon footprint per unit mass of FAH can exceed 400% of that of cement), which discourages IBP utilization. The traditional economic allocation reflects economic value differences, but its allocation coefficient depends heavily on fluctuating market prices (with notable temporal and spatial variability), leading to unstable and less comparable outcomes. The production-cost method proposed here captures the real resource consumption of IBPs within the production system while avoiding uncertainties caused by market price volatility; thus, it achieves a better balance between rationality and stability in allocation results.
Systematic comparison of different allocation approaches
Allocation principle
Basis
Key advantage
Main limitation
No allocation (C0)
By-product bears no burden from the primary production process
Simplifies and maximizes the apparent emission-reduction benefit of IBPs
Ignores the fact that IBPs are an integral output of the production system; underestimates their true environmental burden
Mass allocation (Cm)
Mass ratio of main product to by-product
Physically clear and data-accessible
Severely overestimates the environmental burden of IBPs, discouraging their beneficial use
Traditional economic allocation (Ce)
Market prices of main product and by-product
Reflects differences in economic value
Market prices vary greatly over time and space due to supply-demand and policy shifts, leading to unstable results
System expansion
Avoided burden from substituted products
Captures system-level environmental benefits
Requires clear identification of the substituted product system; modelling can be complex
Proposed method (Cc)
Production costs of main product and by-product
Reflects real resource input, stable, and explicitly linked to the industrial chain
Production-cost data may involve confidential business information
IBP: Industrial by-product.
Implications of allocation-method selection on policy and engineering practice
The results clearly demonstrate that the choice of allocation principle fundamentally affects the assessed emission-reduction contribution of IBPs. Taking the CTD as an example: under the traditional economic principle, the average CTD of FAH is only 599 km, whereas under our proposed method it reaches 1,166 km, and under no allocation it is 1,538 km. Such order-of-magnitude differences imply that using the traditional economic principle may severely underestimate the long-distance transport potential of FAH, thereby restricting its supply to wider regions and affecting the layout of low-carbon building-material industries. Therefore, a more rational and stable allocation method is a prerequisite for accurately assessing the carbon-reduction benefits of IBPs and for formulating sound regional resource-utilization policies.
CONCLUSIONS
This paper proposed a novel economic allocation principle for the environmental impacts of IBPs, based on the production costs of both the main product and the IBPs. Using life cycle assessment, it analyzed the carbon footprint characteristics of FAH concrete and FAH’s CTD under different allocation principles and mix proportions. The influence of transport vehicles on CTD was further examined.
(1) A new economic allocation principle for the environmental impacts of IBPs was proposed, offering better stability than the traditional economic allocation principle. The proposed method, with appropriate case-specific adjustments, has the potential to be extended to other IBPs such as blast furnace slag and silica fume;
(2) Mix proportions significantly affect the carbon footprint and carbon footprint intensity of FAH concrete. As compressive strength increases, the carbon footprint rises while carbon footprint intensity declines, with the latter showing lower variability. Based on this carbon footprint intensity, a prediction model for the carbon footprint of FAH concrete was established;
(3) The allocation principle greatly affects the CTD of IBPs. For the Class 8b truck, the C0 and Ce principles yield the maximum (1,538 km) and minimum (599 km) distances for FAH, respectively, a difference of up to 939 km.
(4) Under the C0, Cc, and Ce allocation principles, rail transport (average for the Chinese market) yields the largest CTD for FAH, at 30,292 km, 22,707 km, and 11,007 km, respectively, whereas medium-sized diesel trucks (8 t load) give the smallest, at 1,431 km, 1,084 km, and 557 km;
(5) The quality of mix proportion and different transport modes can seriously affect the CTD of FAH. Regarding different transport modes, the priority selection principle is rail transport first, followed by waterway transport, and then road transport.
Based on this study, future research could focus on the following areas: (1) analyzing how different production processes of industrial main and by-products affect their carbon footprint allocation coefficients; (2) examining the influence of various development scenarios on the carbon footprint allocation coefficients of industrial by-products under the proposed principle; (3) assessing how uncertainties in cement and concrete production affect the critical transport distance of fly ash; and (4) investigating the impact of multimodal transport (road, rail, waterway) on the carbon reduction potential of fly ash concrete and its critical transport distance as infrastructure advances; (5) In addition, given the use of fixed empirical transport distances in this study, future work should incorporate probabilistic uncertainty analysis of distance parameters to further enhance the robustness of CTD assessments.
The data and materials are available from the corresponding author upon reasonable request.
AI and AI-assisted tools statement
AI-assisted tools (Doubao-Seed 2.1 Pro, released on 2026-06-23) were used in the preparation of this manuscript solely for the creation of Figure 1, graphical abstract, and English grammar proofreading. The schematic diagram in Figure 1 and Graphic Abstract were drafted with the assistance of AI-based drawing tools to enhance visual clarity and presentation. No AI tools were used for data analysis, data interpretation, or the writing of the manuscript. All authors take full responsibility for the accuracy, integrity, and final content of the manuscript.
Financial support and sponsorship
This work was sponsored by the “Joint Scientific Research Project Funding by the National Natural Science Foundation of China and the Macao Science and Technology Development Fund (52361165660)”, “National Key Research and Development Program of the 14th Five-Year Plan (2024YFC3808002)” and “Fundamental Research Special Fund for Central Public Welfare Research Institutes (2025-9047)”.
Conflicts of interest
Guo, X. is affiliated with China Petroleum International Pipeline Co., Ltd., while the other authors have declared that they have no conflicts of interest.
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