1 Introduction

The strength and resistance to plastic deformation of the soil-filling are significantly increased under compaction. The stability and safety of infrastructure like roads [1,2,3], airports [4,5,6,7,8], dams [9,10,11,12], and railways [13,14,15] rely on the roadbed or subgrade's ability to resist deformation. Therefore, the compaction quality of the filling needs to be strictly controlled to ensure the longevity and stability of these infrastructures and prevent potential consequences. Inadequate compaction of airport filling can lead to serious consequences such as road surface fractures, deformations, and uneven settlement. For example, uneven settlement on the runway of Lijiang Airport impacts safe operation, as shown in Fig. 1. In the meantime, improving the quality of road construction plays a crucial role in the development of a more sustainable and cost-effective urban infrastructure network in the transport sector.

Fig. 1
figure 1

Photo of uneven settlement happened on the Lijiang Airport runway

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Traditional compaction methods depend on active supervision during construction and random sampling tests after completion to evaluate the compaction quality of the filling, but they have obvious limitations, such as: (1) The conventional management approach is outdated. The human factor is a major influence on the manual supervision and management mode, which is prone to misjudgment of the number of compaction passes, and poor precision in controlling compaction quality can result in under-compaction, miss-compaction, and over-compaction in the construction area [16]. (2) The locations for routine sampling may not be representative due to there are only a limited number of random sampling locations on the site, which can hardly represent the compaction quality of the entire construction area. Moreover, sampling tests are more applicable for uniform samples. When the properties of fillings are distributed discretely, the distribution of the sampling test results do not follow a normal distribution, making it more challenging to use the results as the foundation for judging the compaction quality of the entire construction area [17]. (3) Inefficient and expensive. Some detection methods are destructive, which would damage the road’s surface. Others may require professional workers to operate with a long time span and are prone to delay the construction progress. Therefore, these inefficient, high-cost detection features do not match the criteria for massive mechanized construction [18]. (4) Post-inspection is not time-sensitive. The results of the quality assessment cannot be directly relayed to the construction staff on-site during the compaction process, because the compaction quality outcomes are often judged after the construction is finished. This leads to unavoidable over-compaction or under-compaction during the construction process, which can easily result in project delays due to the need for rework [11].

Researchers have suggested using digital compaction technologies to address the issues existing in conventional compaction techniques. The digital compaction method is to develop a digital construction management system by installing a positioning system on the roller, enabling real-time observation of the number of rolling passes and the roller' trajectories, eliminating the drawbacks of manual supervision and management [19, 20]. The digital compaction method has further developed into a continuous compaction control method with the advent of continuous compaction indicators, which entails mounting sensors on rollers to achieve compaction quality control through continuous detection of compaction quality and real-time monitoring of compaction parameters [21,22,23]. Compared with the number of rolling passes method, the continuous compaction control method can control the compaction process, that is achieving real-time control of the overall compaction quality and uniformity of the compaction surface. However, there are still many challenges that warrant further consideration. For instance, the evaluation of compaction quality still depends on human judgment, and the application of manual driving always results in control errors.

To solve the above-mentioned problems, some researchers have proposed an automatic rolling method based on unmanned technology [24,25,26,27]. The automatic rolling method allows the roller to operate according to pre-set instructions by modifying the roller, which mitigates the impact of human error and enables precise control of the roller. However, feedback control of the filling’s compaction quality still relies on human decisions, i.e., the compaction quality needs to be judged offline before the next step can be taken. With the development of sensor technology, automatic control technology, and artificial intelligence, the intelligent compaction method has become a new solution to achieve autonomous sensing, autonomous decision-making, and autonomous control by incorporating intelligent algorithms in the decision-making function [4, 16, 28,29,30]. The intelligent compaction method avoids unnecessary waste in the construction process and truly achieves energy-saving, environmentally friendly, green and efficient intelligent construction.

At present, the existing intelligent compaction methods are mainly for vibratory compaction, while our research on intelligent compaction of airport high fill is for impact compaction. Therefore, the research on three key issues of impact compaction in intelligent compaction is summarized, including compaction quality evaluation algorithm, dynamic optimized path planning and implementation of unmanned technology.

Indeed, advancements and achievements in intelligent compaction methods play a pivotal role in enhancing the management of compaction quality in earthwork. The research has shown that these potential directions include coupling problems of multiple indicators in intelligent evaluation algorithms, unmanned roller groups collaborative control problems, and intelligent decision-making and optimization problems of multi-vehicle compaction paths. To provide a comprehensive overview of the current compaction quality control methods, and to identify potential challenges and outline future research directions in this field, this paper reviews the literature on the methods of compaction, systematically narrates the current development of compaction quality control methods in the field of geotechnical engineering, and summarizes the work that has been done. The various compaction quality control methods and their corresponding issues are summarized in Sects. 2 to 5, and the main topics in contemporary intelligent compaction are discussed in Sect. 6, and the current research work and a vision for the future are summarized in Sect. 7.

2 Traditional compaction method

2.1 Compaction technology control method

The rolling passes control method and traces control method for rolling wheels are widely employed empirical compaction technology control methods at the moment.

2.1.1 Rolling passes control method

The control criteria for the number of rolling passes are determined by ensuring that the compaction achieved in the rolling test meets the required standards. However, strict requirements must be met when utilizing rolling passes to control the compaction quality. These include ensuring that the filling type, filling height, and underlying soil layer of the rolling section match those of the test section. Moreover, the roller's rolling parameters must be entirely consistent [31], as shown in Fig. 2.

Fig. 2
figure 2

Application conditions of rolling passes control method (recreated based on the concept of [31])

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However, the compaction passes control method is an outdated manual management approach, which is susceptible to human error and is prone to misjudgment of compaction passes. The poor precision of the compaction quality control in this method will result in under-compaction, miss-compaction, and over-compaction in the whole construction area.

2.1.2 Traces control method for rolling wheels

The traces control method for rolling wheels uses "no wheel trace" as the indicator of the completion of compaction, essentially controlling the degree of plastic deformation of the filler. However, this approach faces two significant issues. Firstly, whether the compaction state achieved "no wheel marks" is solely decided by the on-site construction staff making the decision relatively subjective. Moreover, this method is unable to evaluate the compaction quality quantitatively. Secondly, even if the plastic deformation of coarse-grained materials has stopped, the structure's mechanical properties may continue to change, leading to potential inaccuracies in quality assessment using the rolling wheel traces control method [31].

2.2 Sampling point detection control method

To ensure that no issue would occur during the construction process, on-site supervision is typically provided. The compaction quality of the earthwork is then verified at predetermined sampling points when construction is complete. The compaction indexes of traditional evaluation for fill materials of earthworks are generally density, strength, modulus, etc.

2.2.1 Physical indicator——density

There are two main reasons for using density as a compaction index. Firstly, the operation of the density test is simpler than the mechanical test; secondly, there is an underlying principle that the denser the filler, the stronger the resistance to deformation [31]. Indicators such as void ratio and relative density are utilized for non-cohesive soils, while the degree of compaction index is used for cohesive soils. The current methods for detecting density include the sand-cone method [32], cutting ring method [33], electromagnetic soil density gauge method [34], nuclear density gauge method [35], and non-nuclear density gauge method [36], etc. Figure 3 illustrates some of the testing equipment used.

Fig. 3
figure 3

Device for detecting density. a sand-cone cylinder. b cutting ring. c nuclear density gauge. d non-nuclear density gauge

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2.2.2 Mechanical indicators——strength and modulus

The compacted filler body serves to support both the upper structural load and vehicle load, making it crucial to have adequate deformation resistance. Mechanical indicators can be categorized into strength and modulus indicators. California bearing ratio (CBR) and impact test value (CIV) are examples of strength indicators. The dynamic cone penetrometer (DCP) method [37] and the Clegg impact soil test (CIST) method [38] are two techniques frequently used to measure strength. Modulus indicators include deformation modulus Ev2, rebound modulus E, dynamic modulus Evd, and foundation reaction coefficient K30, etc. The lightweight deflectometer gauge (LWD) method [39, 40], the soil stiffness gauge (SSG) method [41], and the plate load test (PLT) method [42] are some of the frequently employed techniques for determining modulus. Figure 4 displays some of the testing equipment used. The characteristics of the sampling point detection method are shown in Table 1.

Fig. 4
figure 4

Equipment for testing mechanical indicators of soil. a DCP. b CIST. c LWD. d SSG

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Table 1 Characteristics of sampling point detection method
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But the following issues with the sampling point detection method still need to be resolved: (1) If the distribution of fillings is uneven, the results of the compaction quality distribution will not follow a normal distribution, so the sampling test results are not necessarily representative and cannot accurately reflect the compaction state of the whole construction area; (2) Some detection methods are destructive and time-consuming, which seriously hinders the progress of the construction; (3) The results of the compaction quality inspection cannot be recorded in real-time, so the record may be falsified; (4) During the compaction process, the factors that need to be controlled include not only the degree of compaction but also the stability and uniformity of compaction. However, this requirement is not competent for traditional compaction sampling detection methods [31].

3 Digital rolling compaction method

To achieve process control for compaction, researchers have developed a digital construction management system that monitors compaction parameters and compaction conditions in real-time, known as the digital compaction method. The digital compaction method is divided into two categories based on different compaction quality control indicators: the rolling passes control method and the continuous compaction control method.

3.1 Rolling passes control method

The number of rolling passes is used as the control indicator of compaction quality, and the digital construction management system developed by introducing the navigation and positioning system can achieve real-time, continuous and automated monitoring of the construction quality of the filling project by monitoring the number of compaction passes and the compaction trajectory [43].

The current methods for calculating the number of rolling passes include the grid calculation method [44,45,46,47,48], the pixel point method [49], and the image analysis method [50], respectively.

The real-time monitoring system for compaction quality is generally divided into three parts: (1) Monitoring center. The monitoring center is the core of the system, mainly responsible for data processing, analysis, and other work of the system. Subsequently, all parties can communicate through the network and view construction quality information in real-time through the operating platform; (2) Database center. The database center is responsible for storing and managing all data in the system, ensuring the security and stability of data; (3) Navigation positioning and transmission terminal. Navigation and positioning are divided into reference stations and mobile stations. The reference station is fixed and installed in an open area near the construction area, while the mobile stations are installed on the road roller. These stations gather real-time positioning data and transmit it to the database center through network signals [45,46,47,48,49]. The common real-time monitoring scheme for compaction quality is shown in Fig. 5.

Fig. 5
figure 5

Digital compaction quality monitoring system. a Schematic diagram of real-time compaction quality monitoring for the core rock-fill dam (recreated based on the concept of [45, 46]). b Real-time monitoring scheme for impact compaction of airport high embankment (recreated based on the concept of [47])

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Strict requirements exist for controlling the number of rolling passes. It's necessary to compare several experimental sections before compaction, and the test conditions and rolling parameters of these sections should be consistent with the rolling section. However, ensuring these conditions during actual on-site construction can be challenging. Subsequently, the number of rolling passes needs to be constantly optimized due to the complexity of road bases or pavement materials used in construction sites. Therefore, the number of rolling passes is a macroscopic and empirical control method that cannot achieve fine control accuracy. To swiftly obtain information on the compaction quality of fillings, researchers have proposed continuous compaction indicators, and the continuous compaction method was born.

3.2 Continuous compaction control method

In 1975, the compaction meter co-developed by GEODYNAMIK and DYNAPAC in Sweden was applied to vibratory rollers, achieving the initial version of continuous compaction monitoring and control [51]. Then, the concept of continuous compaction control was formally presented in the early 1990s [52].

The continuous compaction control method involves evaluating the compaction conditions by monitoring the vertical vibration response signal for the vibrating wheel of the roller during the compaction process, and then the relevant compaction parameters and compaction conditions are visualized to guide the field compaction, which ultimately results in real-time monitoring and feedback control for the compaction quality of the whole construction area [53]. Figure 6 depicts the current continuous compaction monitoring system.

Fig. 6
figure 6

Continuous compaction control quality monitoring system (recreated based on the concept of [54) (AICV)

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Continuous compaction control research primarily focuses on two aspects: the investigation of continuous monitoring indicators and the development of compaction quality evaluation methods. The following section describes the existing continuous monitoring indicators and compaction quality evaluation methods.

3.2.1 Continuous monitoring indicators

At present, researchers have proposed a series of indicators for continuous monitoring of compaction quality, such as acceleration indicators, seismic wave velocity indicators, indicators based on roller-soil interaction, acoustic compaction amplitude indicators, and other indicators, which have been applied in scenarios like roads [1,2,3], airports [5, 6], dams [9,10,11, 56], and railroads [13], and so on.

Acceleration indicators can be classified into two categories: acceleration frequency domain indicators and acceleration time domain indicators. The earliest proposed acceleration frequency domain indicator was the compaction meter value (CMV) [57], which used the ratio of the second harmonic amplitude of vibration acceleration to the fundamental frequency amplitude. Subsequently, other frequency domain indicators had also been proposed, such as compaction value (CV) [11], compaction control value (CCV) [58], acceleration intelligent compaction value (AICV) [54], total harmonic distortion (THD) [59,60,61], resonant meter value (RMV) [62], oscillometer value (OMV) [63], turbulence factor (Ft) [64], etc. The time-domain indicators of acceleration include peak acceleration (ap) [56, 65,66,67], root mean square acceleration (arms) [56, 67], and peak acceleration factor (CF) [56, 68].

In addition to acceleration indicators, researchers have employed the seismic wave approach to assess the compaction quality of rockfill. Seismic wave indicators can be classified into three categories based on propagation mode: longitudinal wave velocity (P-wave) [69], transverse wave velocity (S-wave) [70, 71], and surface wave velocity (L-wave) [72]. Furthermore, indicators derived from roller-soil interaction have been utilized, such as machine drive powder (MDP) [73], dynamic elastic modulus (Evib) [74], material stiffness (Ks) [75], structural resistance (VCV) [76], and foundation reaction force (Fs) [77]. In addition, researchers have also proposed other indicators, such as acoustic compaction value (SCV) [10], ground-penetrating radar signal peak coefficient index [78], and energy indicators, such as Omega [79]、CEV [80]、DMV [81], etc. The specific details of above mentioned indicators are shown in Table 2.

Table 2 Classification of continuous monitoring indicators
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3.2.2 Evaluation methods for compaction quality

The compaction quality is influenced by a wide range of variables, including material parameters and compaction parameters. Numerous methods currently exist for establishing compaction quality models, including regression models [10, 11, 82, 83], neural network models [84,85,86,87], support vector machine models [88,89,90,91], fuzzy control models [86, 92], etc. Regression models can be further subdivided into linear regression models [2, 10, 11, 93, 94] and nonlinear regression models [56, 66, 67].

Currently, single-index compaction quality evaluation predominantly utilizes linear and non-linear regression methods. Zhu et al. [2] established a linear regression model between CMV and dry density of the sub-base, indicating a strong linear correlation. Zhang et al. [10] established a linear regression model between SCV and dry density of rockfill, which showed a strong linear correlation between them. Liu et al. [11] established a linear regression model between CV and compaction degree (dry density) of gravel mixed cohesive soil and rockfill material, and the results showed a strong linear relationship between CV indicator and compaction degree. Xu et al. [66] established a nonlinear regression model between the ap index of loess filling and the compaction degree of each layer of soil, with correlation coefficients greater than 0.92. Hua et al. [56] established linear regression models and hyperbolic regression models for ap, CMV, CF, and void ratio (relative dry density) of primary and secondary rockfill, respectively.

Given the low accuracy of models that rely solely on vibration signals without considering the properties of compaction materials, researchers have proposed multi-indicator compaction quality evaluation methods. These methods integrate the properties of compaction material parameters and vibration signals, as demonstrated in Table 3.

Table 3 Multi-indicators compaction quality evaluation methods
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4 Automated compaction method

With the advancement of unmanned driving technology, researchers have proposed an automatic compaction method to address the challenges caused by manual driving. This method is developed based on the continuous compaction control approach, which modifies the roller's control system to enable unmanned operation. The travel, reversing, and steering systems of the roller are all designed as automated elements that can be controlled using commands.

The first automatic control roller was used in asphalt pavement construction in Japan in the 1980s [97]. Following the swift progress of driverless technology in China, various universities sequentially developed unmanned vibratory roller systems, including Tsinghua University [98,99,100], Tianjin University [101, 102], Beihang University [103], Shanghai Jiao Tong University [104], Southeast University [105], Tongji University [106], and Chang'an University [107], et al. China Institute of Water Resources and Hydropower Research [108], China Academy of Railway Sciences Limited [109], and other companies have also conducted relevant research and engineering applications. Unmanned road rollers are shown in Fig. 7.

Fig. 7
figure 7

Unmanned rollers developed by various institutions [4, 7, 100, 108, 110]

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The National University of Defense Technology developed China's first unmanned roller, accomplishing basic functions like steering and parking [110]. Subsequent to these developments and evolving theories, a variety of unmanned rollers were successively introduced. China Water Resources and Hydropower 5th Engineering Bureau and Tongji University jointly developed an unmanned vibration roller modified by hydraulic steering [111]. Liu et al. [98, 99] from Tsinghua University developed a set of automatic driving systems of vibratory roller for hydraulic construction, in which the steering mechanism was modified by an electric steering wheel. Zhong et al. [101, 102] from Tianjin University has developed an unmanned vibration roller system, which also achieves automatic steering control by modifying the steering mechanical structure. Yu et al. [103] from Beihang University developed an automatic steering control mechanical structure called a robotic arm, which is used to control the steering wheel, brake, throttle, and gears. Luo et al. [104] from Shanghai Jiao Tong University designed an unmanned intelligent vibration roller and its system, using modified electric actuators. Huang et al. [112] designed an autonomous construction system for unmanned vibration rollers with PLC as the core controller. Currently, research on automatic compaction methods primarily focuses on the following areas:

  1. 1.

    Positioning technology

Currently, both Beidou and GPS positioning systems are commonly installed on unmanned vehicles, but they have inadequate anti-interference ability in complex situations. To cope with this, researchers have studied additional positioning techniques to improve accuracy in complex environments. With the help of laser emission devices, Gao et al. [105] created an unmanned roller system that successfully makes up for the drawbacks of conventional single positioning techniques. An unmanned rolling system that uses LiDAR range to assist in positioning in challenging situations devoid of positioning signals was created by Tsinghua University and Sichuan Chuanjiao Road and Bridge Corporation [113].

  1. 2.

    Path tracking

The path-tracking accuracy of unmanned rollers is directly related to the quality and efficiency of compaction, and the research on path-tracking control of unmanned rollers in China mainly includes the team of Xie from Tianjin University, Bian from Tongji University, and Liu from Tsinghua University. Bian et al. [106] studied a path-tracking control method based on a fuzzy control algorithm, which improved the performance of automatic rolling. The unmanned roller developed by Yao et al. [114] comes with anti-interference and heading estimation methods, which can achieve accurate trajectory tracking. Song et al. [115] proposed a path-tracking control framework for unmanned rollers to suppress composite disturbances. Fang et al. [116] considered the impact of roller vibration and designed a path-tracking control model to achieve the automatic rolling of unmanned rollers. Song et al. [7, 117] designed a path optimization method for headland turning to address the significant tracking errors that often experience at the turning point for unmanned impact rollers, effectively improving the turning tracking accuracy.

  1. 3.

    Obstacle identification

Identifying obstacles is crucial in the complex construction site environment where a roller may encounter moving or stationary obstructions. Chen et al. [108] created an unmanned roller system utilizing technologies such as LiDAR, shortwave radar, and satellite positioning, which are capable of performing tasks including obstacle recognition, path planning, path tracking, and obstacle avoidance. In order to identify filler and obstacles, Ye et al. [109] applied technologies like unmanned, continuous compaction detection, and image recognition to intelligent rollers. The obstacle avoidance functions of the autonomous rolling system created by Zhang et al. [100] have been effectively applied to the compaction quality control of rockfill materials for earth-rock dams.

  1. 4.

    Path planning

Path planning is an important research topic for unmanned rolling technology. Path planning is mainly divided into two types: static path planning and dynamic path planning. Zhang et al. [8] proposed an optimal dynamic path planning algorithm for the impact roller based on the rolling passes as the compaction quality control index. The automatic driving control system of impact rollers developed by Zhang et al. [118] has added the function of static path planning, achieving the cyclic multiple rolling of compaction machinery. Shi et al. [119] established a time–cost function for unmanned roller group operations based on the chaotic dragonfly method. With the principle of minimizing time cost, the task of fully covering the working face path was assigned to the roller groups, achieving efficient and collaborative compaction operations among all rollers. Shi et al. [120] further studied the collaborative control problem of multiple unmanned rollers, as well as the optimal compaction path planning problem and optimal compaction parameter determination problem of multiple unmanned rollers.

  1. 5.

    Collaborative control of multiple unmanned rollers

In large-scale construction tasks, a single roller is often insufficient, necessitating the deployment of multiple unmanned rollers on the construction site for cooperative compaction operations. Tsinghua University, in collaboration with XCMG Group and Sichuan Road and Bridge Group, developed a cooperative construction system for unmanned vibratory roller groups On May 27, 2020 [121]. On August 30 of the same year, the driverless construction machinery group developed by XCMG was applied for the first time in some sections of the Beijing-Xiongan Expressway, realizing the largest scale of unmanned cluster construction operation [122]. The unmanned roller fleet developed by Sany Heavy Industry Group has been used in numerous situations and locations around China in 2021, including the Yangxuan Expressway, Shanghai Dapo Viaduct, etc. [123], as shown in Fig. 8.

Fig. 8
figure 8

On-site Construction scene for unmanned roller fleets [122,123,124]. a Panzhihua-Dali Expressway. b Beijing-Xiongan Expressway. c Yangliu-Xuanwei Expressway. d The Viaduct in Shanghai

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The automatic rolling approach still has several drawbacks, such as the inability to independently tune compaction parameters and the fact that compaction quality control is still accomplished by manual off-line decision evaluation.

5 Intelligent compaction method

The intelligent compaction method, which is appropriate for more complicated construction situations, is characterized by an autonomous decision-making function and automatic compaction without human intervention. Figure 9 depicts the current intelligent compaction system. Zhang et al. [16] designed an intelligent compaction system composed of four key elements: an acoustic monitoring system, an intelligent decision system, an unmanned compaction system, and a real-time remote monitoring center, respectively. Among them, the intelligent decision-making system integrates artificial intelligence algorithms and operations research to dynamically optimize the compaction parameters of the compaction process from a global perspective, as shown in Fig. 9a. Botev and Azidhak [124] developed an intelligent compaction system for asphalt pavement construction, including sensors and external systems, a vehicle system, an operating system, and a decision system, as shown in Fig. 9b. An intelligent compaction system for roadbed pavement developed by Lin and Wang [125] is composed of a quality inspection system, an intelligent decision system, an unmanned compaction system, and a remote monitoring center. The intelligent decision system is based on a machine learning or artificial intelligence neural network model to predict the compaction construction parameters of the new compaction area by analyzing the existing compaction quality information, and the intelligent decision system is shown in Fig. 9c. Yao et al. [4, 126] developed an intelligent compaction quality monitoring system for airport high embankments based on technologies such as unmanned driving, virtual reality, the Internet of Things, and cloud computing. The upper monitoring platform can evaluate the compaction quality according to the monitored acceleration indicators, and determine the optimal path for the local area based on the compaction conditions. Following this, relevant compaction instructions are conveyed to the unmanned roller at the lower level to facilitate automatic compaction. Concurrently, the system utilizes virtual reality technology to synchronously display the on-site construction situation. The construction principle is shown in Fig. 9d.

Fig. 9
figure 9

Intelligent compaction principle block diagram. a Framework and structure of the intelligent rolling compaction system (recreated based on the concept [16]). b Functional model for autonomous compactor (recreated based on the concept [125]). c Schematic diagram of intelligent rolling structure (recreated based on the concept [126]). d Schematic graph of intelligent compaction (recreated based on the concept [127])

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The intelligent compaction methods mentioned above are based on optimal paths, unmanned driving, intelligent decision making and other technologies that avoid unnecessary waste in the construction process and achieve a truly energy-saving, environmentally friendly, green and efficient intelligent construction, which is also consistent with the theme of sustainable cities [127].

6 Key technologies for intelligent compaction

There is no excitation force in the compaction parameters of impact rollers due to the difference between the mechanical structure of impact rollers and vibratory rollers. Consequently, decision-making does not necessitate the dynamic optimization of vibration frequency and amplitude parameters. For intelligent impact rollers, the compaction path is the focus of decision-making and must be dynamically optimized from a global perspective, considering both compaction efficiency and quality. As a result, the compaction quality evaluation algorithm, dynamic optimal path planning, and unmanned implementation are the three key technologies for intelligent compaction research.

6.1 Compaction quality evaluation algorithm

The key issue in intelligent compaction is to evaluate the compaction quality in real-time, specifically, to establish the relationship between acceleration and dry density. Physical property indices (i.e. dry density value ρd or compaction degree K) are usually regarded as the compaction quality control indices for soil-filling, and the peak acceleration in continuous monitoring indicators is widely used. Therefore, the relationship between peak acceleration and dry density has been mainly studied. The current general method is to directly establish the relationship between peak acceleration and dry density, employing empirical formula based on limited field data. This approach has the following problems: (1) the relationship between peak acceleration and dry density is not so simple, and the expression of its function is uncertain. The function derived directly from human analysis may not accurately represent the true relationship and might only be applicable within a specific range. In some special cases, it may lead to invalid prediction in some cases. (2) The methods of formula fitting and parameter fitting lack reasonable scientific explanations and cannot reasonably reflect the development laws and trends of dry density change curves with complex coupling characteristics.

The relationship between peak acceleration and dry density is established from the perspective of the deformation mechanism. After detailed analysis, it reveals that the response of peak acceleration to dry density includes two different physical mechanisms. One is the response of peak acceleration to impact force, where the relationship between the force and the acceleration is by the kinematic law of objects. The other is the response of the void ratio of soil to the force, where the relationship between the force and void ratio of soil is by the constitutive law of soils. Firstly, the formula between peak acceleration and the impact was obtained based on the kinematic equation. Moreover, the deformation of soil is directly related to the stress on the soil. Therefore, the key to establishing the relationship between acceleration and dry density is to make clear the relationship between dry density (i.e. void ratio) and impact stress.

6.1.1 Relationship between impact stress and impact acceleration

Under the action of traction, the impact roller continuously keeps rolling forward until the wheels climb to the highest position, and then beats the ground and repeats, making the soil gradually become dense. For simplification of the analysis, the situation is modelled as a rammer impacting the soil, consisting of two stages, and excluding the rebound of the tamper after impact.

The first step is the free-falling process of the tamper where the tamper falls from the height h to the soil surface. The second step is the compaction process, where the tamper contacts the soil surface and moves downward with the soil until the speed decreases to 0.

When the displacement of the soil reaches the maximum, the peak value of impact stress on soil mass is expressed as

$$\sigma_{vm} = \frac{{m(g + a_{m} )}}{A}$$
(1)

where A is the bottom area of the rammer and am is the peak acceleration.

6.1.2 Relationship between impact stress and void ratio

The relationship between impact force and the void ratio is established through theoretical analysis. The rammer compacts the soil surface 'N' times until the post-impact dry density of the soil meets the predefined requirement, at which point the impact is ceased. The distribution of compaction points consisting of the peak impact stress and the corresponding void ratio is shown in Fig. 10. The curve connecting all the compaction points is termed the ‘compaction envelope’.where the solid black line represents the compaction envelope, the solid red line represents the K0 compression line(ACL), the solid cyan line represents the isotropic compression line of normally consolidated soil(NCL), and λ is the slope of the NCL and ACL in the e-ln(σv + ps) plane. When σv → ∞, ln(σv + ps) is approximately equal to lnσv. The solid blue line represents the compression curve for each impact, and the solid purple line represents the unloading curve, and the dashed black line represents the asymptote of the compaction envelope.

Fig. 10
figure 10

Sketch graph of compaction envelope for soil [127]

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It is found that the shape and variation pattern of the compaction envelope drawn in Fig. 10 is similar to the form of the isotropic compression line of the soil defined in the UH model [126], and therefore the equation of the compaction envelope is defined as follows

$$e = Z - \alpha \ln \left( {\frac{{\sigma_{vm} + C}}{1 + C}} \right)$$
(2)

where Z is the void ratio at 1 kPa for the compaction envelope, and the starting point of the compaction envelope is unique for the same kind of soil.

With the increase of impact times, the compaction envelope eventually tends to a straight line, which is defined as the asymptotic line of the compaction envelope, as shown in Fig. 10. The asymptotic line equation is defined as

$$e = J - \alpha \ln \sigma_{vm}$$
(3)

where J is the intercept of the asymptotic line, and α is the slope of the asymptotic line.

It is necessary to explain the difference between the compaction envelope, the compression curve for each impact, and the K0 compression curve. The compaction envelope is a special state curve, which describes the state of compactness of soil at each impact with a certain impact parameter. The compression curve for each impact is a process curve, which describes the process of soil hardening at each impact. When the peak value of impact stress is large enough, the compression line converges to the K0 compression curve.

6.1.3 Real-time calculation formulation for dry density

Combining the corresponding relationship between void ratio and dry density, the real-time calculation formulation for dry density was acquired by coupling the above two equations [126].

$$\rho_{d} = \frac{{G_{s} \rho_{w} }}{{J^{\prime} - \alpha \ln \left( {\frac{{a_{m} + g}}{B}} \right)}}$$
(4)

where J and α represent the soil parameters, ρd, and am are the dependent variable and the independent variable respectively.

6.2 Optimal path planning algorithm

Currently, the driving path of impact rollers in construction is determined subjectively by machine operators. This will inevitably lead to over-compaction or under-compaction in some parts of the construction area, making uneven compaction of the filling soil and possibly triggering uneven settlement of the construction site in the future. It is necessary to reasonably design the optimal rolling path of the rolling machinery to ensure that the compaction uniformity and compaction quality of the entire site meet the requirements.

6.2.1 Path design

Overlapping compaction method

According to the specifications requirements of compaction construction, the adjacent compaction range of wheels should have an overlap width of lo. The schematic of the linear path design is shown in Fig. 11. The trajectory of the construction machinery is designed according to the setting of the size of the wheel and the overlap, such as lines L1–L9. The first compaction in the far left area is completed after the impact compactor goes along the routes from L1 to L3.

Fig. 11
figure 11

Design of the linear path [4]

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Considering the turning of machinery, it is required to connect linear paths with circular arcs, as shown in Fig. 11, and the number of linear paths in the quadrilateral surface may be even or odd. In the first case, the machinery should go through L1 and turn to L8, which is in the middle of the surface. Along the direction marked in Fig. 11, L2, L9, L3, L10, L4, L11, L5, L12, L6, L13, L7, and L14 are passed successively. However, in the second case, the machinery turns back to L1 and goes through the extra path L15 after it passes through L14. No matter which case it is, the machinery can get back to the point where it starts. Then, during the compaction of the working surface, the machine uses the design radius rs and the finite angle α to delimit the search target location [4], as shown in Fig. 11.

Non-overlapping compaction method

The manner of the overlapping generates unequal compaction areas in the horizontal direction, which leads to uneven compaction throughout the site and affects the compaction quality. Therefore, the method of non-overlapping was proposed for compaction, as shown in Fig. 12. For the non-overlapping method of compaction, it is observed that there's a gap between two wheels from the parameters of the YP25. It is noted by the regulation that the non-overlapping method is reasonable and scientific as well as economically efficient.

Fig. 12
figure 12

Path generation [8]

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According to the turning radius and width of the construction machinery, the working surface ABCD is divided into two parts: turning areas ① and working areas ②, where the coordinates of points I, J, K, L, M, N, and numbers of the rolling band can be calculated by the coordinates of points A’, B’, C’, D’. Then the width of the rolling strip is calculated based on the construction technology of moving a wheelbase aside for impact rollers, and along the direction marked in Fig. 12, L1, L2, L3, L4, L5, L6, L7, and L8 are passed successively, and the path covering the entire working surface was generated [8].

6.2.2 Optimal path planning

Calculate the acceleration value of grids

The trajectory of the impact roller is approximately straight between the time t and t + 1 because of the high frequency of Beidou, as shown in Fig. 13. Firstly, the heading angle of the impact roller, and the coordinates of the points Pt and Pt+1 were obtained from the BeiDou positioning. Secondly, the acceleration data was bound by Beidou’s positioning data to obtain the acceleration vibration signal at the corresponding position. Then, the characteristic value of the signal, that is, the peak acceleration was extracted. Finally, the peak acceleration value was assigned to the attribute value at the grid P (i, j) under the wheel of the impact roller.

Fig. 13
figure 13

Calculate the acceleration value of the grid [8]

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It is known that the grids covered by the impact roller are fixed when the machine works along the straight route of the full coverage path. Let N define the number of grids, and api is the attribute value of the ith grid. The average peak acceleration is given by the expression:

$$\overline{a}_{p} = \frac{{\sum\limits_{i = 1}^{N} {a_{pi} } }}{N}$$
(5)

The planning of the optimal path

According to Eq. (5), the average acceleration peak of each strip in the construction area can be calculated respectively, and then the optimal path planning can be carried out, and the idea of the planning algorithm is as follows:

(1) When the impact roller passed the midline of the working surface(i.e., the line connecting the midpoint of AD and the midpoint of BC), the line segment Lleft or Lright remains the same.

(2) The average peak acceleration of each strip on both sides of the rolling strip was compared in turn to get the minimum \(\overline{a}_{p}\) and the corresponding path number.

(3) The closed path was generated using the non-overlapping compaction method, the optimal path is shown in Fig. 14.

Fig. 14
figure 14

Schematic diagram of the optimal path [8]

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(4) The above steps were repeated until the compaction quality meets the requirements of the working face.

6.3 Unmanned control for impact rollers

The optimal path offers a straightforward method to correct the compaction trajectory for machine operators. However, the compaction effect is still heavily dependent on the behavior of machine operators, who often do not strictly follow the designated path. Thus, unmanned control technology is first applied to the implementation of the optimal path. The path-tracking control of rolling machinery is divided into two parts: longitudinal motion control and lateral motion control, both of which adopt the PID control method.

(1) The longitudinal control for the roller is the roller’s speed control. The roller is generally driven at a constant speed set before the vehicle starts during normal operation, and the current vehicle speed is obtained based on the speed sensor installed at the wheels. Then, the speed control amount determined by the difference between the current speed and the set desired speed is converted into a corresponding control command to the speed controller, and then the vehicle adjusts its gear to achieve acceleration or deceleration in one cycle.

(2) The lateral control for the roller is controlling the lateral distance, which is the distance between the actual trajectory of the roller and the desired path. Firstly, the preview point on the planning path is determined based on the current position of the vehicle and the set preview distance. Then, the angle deviation \(\Delta \theta\) between the current heading angle of the roller and the target heading angle can be calculated from the position of the two points. Secondly, the desired steering angle of the roller is calculated by inputting the angular deviation into the upper PID controller. Thirdly, the angle deviation between the calculated desired steering angle and the actual angle detected by the sensor installed on the roller’s wheel is calculated and inputted to the lower PID controller. Finally, the corresponding electrical signal is output to the servo motor to control the rotation of the steering wheel, achieving the desired turning angle. The schematic of lateral control is shown in Fig. 15.

Fig. 15
figure 15

Schematic diagram of lateral tracking control for the roller [7]

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The principle of the lateral tracking control system is shown in Fig. 16, where the reference rolling trajectory is \(\xi_{r} = (x_{r} ,y_{r} ,\varphi_{r} )\), the actual trajectory of the roller is \(\xi = (x,y,\varphi )\), and the desired control amount of steering wheel turning angle is δd, while the actual turning angle of the actuator is δc. The lateral tracking control system is divided into five parts: (1) Planning path module. The planning path module mainly receives instructions from the upper controller, namely the rolling path of the working face; (2) Prescan analyzer. The prescan analyzer mainly provides appropriate preview points based on the set preview distance and current vehicle speed; (3) PID controller. The PID controller is mainly used to calculate the corresponding steering angle (δd) based on the current trajectory of the vehicle, the preview point, and the preview distance; (4) Actuator. The actuator achieves automatic steering control based on the current steering control command (δd) and the actual steering angle (δc); (5) Sensor module. The sensor module obtains the current front wheel angle (δc) and vehicle position of the vehicle (\(\xi\)).

Fig. 16
figure 16

Block diagram of lateral tracking control for the roller [7]

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A robot has been designed to replace the driver, as shown in Fig. 17a. Firstly, the corresponding coordinate points on the planning path were found in the system database based on the real-time position of the impact roller during the operation, and the preview point was set at a certain distance in front of the machine. Secondly, the heading and steering angle of the impact roller was calculated based on the position of the preview point and the current point of the roller, and then the command was sent to the motor driver of the robot arm, which would immediately execute the steering command. The actual effect of path tracking is shown in Fig. 17b.

Fig. 17
figure 17

Unmanned driving system and tracking effect. a Unmanned driving control system [4]. b Actual trajectory tracking effect [128]

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By utilizing advanced technological means and intelligent methods, the proposed intelligent compaction method improves construction efficiency, reduces resource consumption, and decreases the negative impacts on the environment, thus contributing to the construction of sustainable cities.

7 Conclusion

(1) Based on their distinct characteristics, the existing compaction quality control methods are divided into traditional compaction methods, digital compaction methods, automated compaction methods, and intelligent compaction methods. It can be found that the digital compaction method achieves real-time monitoring of compaction quality and feedback control of the compaction process. The automated compaction method eliminates the influence of manual driving, and the intelligent compaction method integrates autonomous decision-making functions. All these methods solved some problems existed in traditional compaction methods respectively, but quite a few challenges and limitations need further investigation.

(2) The proposed intelligent compaction method for airport high fill mainly includes three key technologies. Firstly, the compaction envelope concept was proposed, and then the real-time calculation equation of dry density was established based on the equation of motion and the compaction envelope asymptotic equation, which can truly reflect the dry density variation law with complex coupling characteristics for compacted soil. Secondly, the developed dynamic optimal path planning algorithm takes into account both compaction efficiency and compaction quality, achieving intelligent compaction process optimization control. Thirdly, the designed robotic arm has been successfully equipped with the impact roller so that it has achieved the automatic driving function.

(3) Intelligent compaction methods are the trend of future development, but they present numerous challenges when dealing with complex environments, such as the coupling problem of multiple indicators in intelligent evaluation algorithms, unmanned roller groups collaborative control problems, and intelligent decision-making and optimization problems of multi-vehicle compaction path, etc.