Analysis of the Temporal and Spatial Evolution Behavior of Earth Pressure in the Shield Chamber and the Ground Settlement Behavior During Shield Tunneling in Water-Rich Sand Layers

Abstract

Earth Pressure Balance (EPB) shield machines have been widely used in subway construction due to their versatility and safety. During the shield tunneling process, the earth pressure in the shield machine chamber is crucial for controlling ground settlement and ensuring the safety of surrounding buildings. However, current research on the temporal and spatial evolution of earth pressure in water-rich sand layers and its relationship with ground settlement is relatively insufficient. This study focuses on the shield tunneling project between Liuzhou East Road and Puzhou Road on Nanjing Metro Line 11. First, laboratory and on-site tests were conducted to optimize the slump properties of the sediment. Then, based on Terzaghi’s theory and statistical methods, the temporal and spatial evolution trends of the earth pressure in the shield chamber under water-rich sand conditions were explored. Finally, by adjusting earth pressure control parameters on-site and monitoring ground settlement, the impact of earth pressure changes on ground settlement was analyzed. Results showed a linear correlation between the actual earth pressure and shield burial depth. For water-rich sand with medium permeability, the theoretical earth pressure was calculated using Terzaghi’s water-soil combined method in shallow sections, and the average of combined and separated methods in deep sections. The decay envelope showed an exponential downward trend, with rapid decay initially and slower decay later. As earth pressure control values increased, pre-consolidation settlement increased, instantaneous settlement decreased, pre-consolidation settlement rate slightly increased, and instantaneous settlement rate decreased. When excavation pressure was below theoretical pressure, higher instantaneous settlement rates could threaten surface structures. This research offers vital theoretical and data references for shield tunneling in water-rich sand layers and supports related EPB shield machine theory studies.

1. Introduction

As urbanization advances, the demand for convenient and efficient metro transportation increases. Shield tunneling machines are commonly used in metro projects, and their types are chosen based on geological and hydrological conditions. The Earth Pressure Balance (EPB) shield machine, which is suitable for low-permeability soils like clay, silt, and sand, is widely used because of its safety and effectiveness in preventing ground settlement through precise earth pressure control. It stabilizes the tunnel face by adjusting the pressure in the shield chamber and is particularly useful in urban areas [1,2,3]. For soft soils or loose sand layers, EPB machines require high sealing and stable cutter torque to prevent collapse and maintain formation stability by adjusting the earth pressure [4]. Therefore, stabilizing and accurately adjusting the earth pressure in the shield chamber and controlling ground settlement are crucial for ensuring the safety and quality of shield tunneling.

Water-rich sand layers, which are saturated with weak particle bonding and high permeability, pose significant risks for shield tunneling. To address this issue, researchers have conducted extensive studies. Peng et al. [5] analyzed the rapid flow erosion in water-rich sand layers during metro construction in Guangdong, China, tracking the process and revealing its mechanism. Mei et al. [6] studied the impact of shield tunneling parameters on ground settlement in Xi’an Metro, China, suggesting suitable ranges for parameters like torque, speed, earth pressure, and slurry volume. Yao et al. [7] developed a risk assessment framework for shield tunneling in water-rich sand layers using cloud models, AHP, and entropy weight methods based on Chengdu Metro data. Li et al. [8] created a 3D model considering fluid-solid coupling for water-rich strata in Tianjin Metro, simulating construction impacts on settlement and deformation. These studies mainly focus on improving construction safety but lack in-depth research on controlling earth pressure.

Researchers have conducted theoretical studies on earth pressure balance. Fan et al. [9] modified the passive limit earth pressure coefficient based on Coulomb’s theory, proposing an effective method for calculating displacement-dependent passive earth pressure in cohesionless soils, validated by experimental data. Fang et al. [10] used limit equilibrium theory with soil-water characteristic curves and Mohr-Coulomb criterion to predict vertical distribution of loose earth pressure in unsaturated soils. Shi et al. [11] solved consolidation equations under linear unloading using Terzaghi’s theory and effective stress principle, confirming consistency between theoretical and measured results. These earth pressure calculation theories are widely used in engineering. In shield tunneling, Hou et al. [12] analyzed water-soil pressure distribution, construction parameters, and face stability in large-diameter EPB tunneling. Lin et al. [13] calculated additional soil stress and consolidation settlement, finding that tunneling speed and downtime significantly affect ground settlement. Zhu et al. [14] studied thrust changes and derived a calculation formula. Cao et al. [15] discussed optimal earth pressure control methods. The problem of earth pressure balance is essentially a dynamic process in which the stress on the soil is closely related to its temporal evolution. However, existing studies mostly focus on specific time nodes or the impact of a single time factor, lacking a coupled analysis of time effects across multiple stages. The spatial distribution of earth pressure does not exist in isolation; there is a spatial coupling effect between the earth pressure states in different regions. Nevertheless, current research is mostly confined to the analysis of a single spatial objectand lacks a systematic exploration of spatial relevance across the entire domain. The coupled interaction between time and space constitutes the core difficulty in the problem of earth pressure balance, and existing studies have not yet developed an effective analytical framework. The safe and efficient construction of earth pressure balance shields highly depends on the precise control of the temporal and spatial evolution of earth pressure.

Changes in earth pressure can affect the ground surface characteristics. Researchers have extensively studied the relationship between earth pressure and ground settlement. Based on shield tunneling parameters, Zhang et al. [16] used a soft computing model to create a ground settlement prediction model for EPB tunnels. Hu et al. [17] studied the response of sandy soils with different water contents during EPB tunneling through scale model tests and numerical simulations, finding that water content significantly impacts settlement profiles and magnitudes. Ling et al. [18] developed a finite element model for ground settlement caused by EPB tunneling, validated by field tests. Kohestani et al. [19] used a random forest model to predict maximum ground settlement during EPB tunneling, considering geological and shield parameters. Hashimoto et al. [20] analyzed monitoring data from shield tunneling in soft clay, stiff clay, and sandy soils, offering relevant construction suggestions. Golpasand et al. [21] assessed ground settlement from excavation of Tehran Metro’s East-West Line 7 (EWL7) and Abuzar Tunnel, examining the lateral earth pressure coefficient’s impact. Despite these studies, further research is required on the sensitivity of ground settlement to changes in earth pressure in water-rich sand layers.

Shield tunneling occurs deep underground, making it difficult to adjust parameters in real time based on surface changes. In the current construction process, an empirical method combined with minor adjustments is usually adopted to reduce the impact of shield tunneling on the ground surface. However, given the many complex conditions during shield tunneling (such as changes in burial depth and equipment shutdowns) traditional empirical methods may lead to construction risks. Therefore, it is urgent to determine the temporal and spatial evolution behavior of earth pressure in the shield chamber based on reasonable theories and clarify the impact of earth pressure changes on ground settlement in water-rich sand layers to help improve the safety of shield tunneling.

This study uses shield tunneling data from the Liuzhou East Road to Puzhou Road section of Nanjing Metro Line 11. First, laboratory and on-site sediment improvement tests were conducted to optimize the sediment properties. Then, based on Terzaghi’s theory and probabilistic statistical methods, the temporal and spatial evolution trends of earth pressure in the shield chamber under water-rich sand conditions were explored. Finally, by adjusting the earth pressure control parameters on-site and using surface settlement monitoring data, the sensitivity of the impact of earth pressure changes on ground settlement in water-rich sand layers was analyzed. The findings will enhance shield tunneling safety and quality.

2. Research Highlights and Strategies

• Combined with field and laboratory tests, sediment improvement in water-rich sand layers was optimized.
• The theoretical earth pressure for EPB tunneling in water-rich sand layers at different burial depths was calculated using Terzaghi’s theory.
• The decay pattern of earth pressure during shield tunneling was analyzed using probability and statistics.
• Based on field tests, the impact of earth pressure changes on the ground in water-rich sand layers was investigated.

The research strategy is shown in Figure 1.

3. Engineering Case Study, Experimental Process, and Theoretical Model

3.1. Introduction to the Engineering Case Study

Engineering Background

The data in this paper were obtained from the shield tunneling of the Liuzhou East Road to Puzhou Road section of Nanjing Metro Line 11, as shown in Figure 2. This section, about 1100 m long, is near the Dunliang River, adjacent to residential districts, parking areas, and bus terminals, and passes under existing metro lines and box culverts, presenting high technical difficulty and quality requirements.

The shield tunneling section mainly passes through sandy silt and silty sand layers with a thin layer of plain fill on the surface and a high groundwater level. The geological conditions of the shield tunneling section are shown in Figure 3. The water-rich sand layer, which has medium strength, low-to-medium compressibility, and medium permeability, is the main stratum penetrated by the shield. The basic geological parameters are listed in

Table 1. Geological conditions of water-rich sand layers.

Parameter	Unit	Value
Permeability coefficient	cm/s	4 × 10−2
Cohesion	kPa	2.1
Internal friction angle	°	33.6
Coefficient of earth pressure at rest	-	0.37
Silt content	%	11.6

.

Two EPB shield machines were used for the section, launched from Puzhou Road Station, and received at Liuzhou East Road Station. Assembled to about 85 m in length, the shield tunneling machine mainly consists of a cutter head, shield, thrust system, screw conveyor, belt conveyor, and segment-erection system, as shown in Figure 4. The main performance parameters of the EPB shield machine used in this project are presented in

Table 2. Main performance parameters of the EPB shield tunneling machine.

Parameter	Unit	Value
Shield length	m	≈9.1
Overall length	m	≈85
Total weight	t	≈550
Structural form	-	Spoke type
Excavation diameter	mm	6860
Open rate	%	46
Speed range	rpm	0~3.5
Rated torque	kN·m	7131
Front shield diameter	mm	6830
Middle shield diameter	mm	6820
Tail shield diameter	mm	6810
Tail shield gap	mm	30
Maximum thrust	kN	48,552
Maximum driving speed	mm/min	100

.

3.2. Experimental Process

3.2.1. On-Site Sediment Improvement Test

To stabilize the soil at the excavation face during shield tunneling, sediment improvement is required based on the stratum properties. Water, foam, bentonite, etc., are injected through reserved pipes on the cutterhead and mixed with soil by the rotating cutterhead. This improves the bearing capacity and flowability of the soil. The foam generation and injection system and the bentonite tank of the shield machine are shown in Figure 5a,b. In this study, combined with the actual project, on-site tests were conducted on the injection volumes of materials and the slump of improved sediments. The tested sediments were taken from the end of the belt conveyor’s sediment vehicle and tested in the tunnel immediately, as shown in Figure 5c. The slump test procedure followed the relevant requirements of the Chinese standard ‘Standard for quality control of concrete’ (GB 50164-2011) [22].

The foaming agent was the SF-02 type produced by Shenyang Xinshanmeng Building Materials Co., Ltd. (Shenyang, China), with the basic technical indicators listed in

Table 3. Main technical indicators of the foaming agent.

Parameter		Unit	Value
Appearance		-	Transparent or pale yellow liquid
pH value		-	7.1
Density (25 °C)		g/cm3	1.03
Foam Support Force (15 min, 25 °C)		mN/m	39.5
Half-life	15 °C	min	30
	20 °C		18

. The sodium-based bentonite has the basic technical indicators listed in

Table 4. Main technical indicators of bentonite.

Parameter	Unit	Value
Methylene blue absorption	g/100 g	33
Colloid index	mL/15 g	400
Swelling ratio	mL/g	20
pH value	-	8.0~9.5
Fineness (200 mesh)	-	95

. The sediment parameters for the shield tunneling section are listed in Table 1. In the actual project, the volume ratio of the foaming agent to the foam solution was 6.6%, and the mass ratio of bentonite to water was 38.9%.

3.2.2. Sediment Improvement Lab Test

In order to quantitatively analyze the effects of water, foam, bentonite, and other materials on sediment properties and provide a key theoretical reference for future related projects, this study conducted laboratory sediment tests in combination with on-site sediment improvement trials. The materials used in the laboratory were identical to those used on-site, and the soil was collected from the same depth as the soil layer near the shield tunneling area. Based on the on-site equipment, the foam expansion ratio for the laboratory tests was set at 18, and the bentonite flow time was set at 43 s. The proportions of each material were determined in combination with the on-site research conclusions. A horizontal concrete mixer was used for sediment mixing, followed by a slump test. The testing process is shown in Figure 6.

During shield tunneling, when the machine stops, the improved sediment at the tunnel face cannot be discharged until a while later. Therefore, this study analyzed the slump values of the mixed soil 30 min post-mixing, and 60 min post-mixing.

Five parallel groups were set up in the experiment to minimize random errors caused by equipment and operation.

3.2.3. Shield Tunneling Earth Pressure Control Test

To analyze the impact of earth pressure changes on ground settlement, this study conducted on-site earth pressure control tests in sections with minimal burial depth change and a safe distance from important structures based on shield tunneling site conditions. The test section, located in the middle of a bus station and parking lot (see Figure 1), corresponds to ring numbers 530 to 630 and is marked in grey in Figure 7.

The test section was in a gentle downhill excavation phase, with a shield burial depth ranging from 21.71 m to 22.44 m. Therefore, there was little change in the actual earth pressure controlled on-site and the theoretical earth pressure in this section. For safety, based on the normal excavation earth pressure, four test groups were set up on-site: −0.2 bar, +0.2 bar, +0.4 bar, and +0.6 bar, each excavating 25 rings.

Ground surface settlement monitoring uses manual methods with measurement points along the centerline of the shield tunneling section. A Trimble DiNi03 level is used to measure settlement changes in the area and nearby points. The monitoring frequency is once per day, covering 50 rings before and after the shield cutterhead’s position. Monitoring points are 10 cm-long nails driven into the ground, and monitoring lasts for at least 15 days after the shield cutterhead passes.

3.3. Theoretical Model

The earth pressure balance shield tunneling process involves the constant establishment of soil pressure balance at the tunnel face. Different earth pressures in the chamber lead to different soil pressure balance relationships. An active soil pressure balance is usually required to prevent face collapse. Currently, Terzaghi’s theory is commonly used to establish this balance, which includes separate and combined water-soil calculations. For metro tunnels with different burial depths, the water-soil combined Terzaghi’s theoretical earth pressure is calculated using Equation (1). In the case of water-soil separate calculation, the soil’s unit weight $\lambda$ uses the buoyant unit weight ${\lambda }^{\prime }$, and the water pressure is calculated separately, as shown in Equation (2).

$$\left\{\begin{array}{ll}{\sigma }_x=k\gamma (h+R)& (h<2D)\\ {\sigma }_x={\displaystyle \frac{\lambda b-c}{\tan \phi }}\left[1-e^{-k\tan \phi ({\displaystyle \frac{h+R}{b}})}\right]& \hspace{1em}(h<2D)\end{array}\right.$$

(1)

$${\sigma }_w=q{\gamma }_w(h_w+R)$$

(2)

where, ${\sigma }_x$ is the theoretical earth pressure in the shield chamber (MPa); $k$ is the lateral earth pressure coefficient of the soil layer; $\lambda$ is the average bulk density of the overlying soil; $h$ is the tunnel burial depth (m); $R$ is the tunnel diameter (m); $c$ is the soil cohesion (MPa); $\phi$ is the soil’s internal friction angle (°); and $b$ is the semi-span of the natural arch, $b=R+R\tan (45°-\phi /2)$.

4. Research Results

4.1. Sediment Improvement Research Results

4.1.1. On-Site Test Research Results

Based on the shield tunneling site conditions and with safety assured, various sediment improvement ratios were evaluated. Considering the sediment discharge and the mechanical status of the shield machine, the dosages of the foaming agent and bentonite were determined, as shown in Figure 8. For the water-rich sand layer, with a 6860 mm excavation diameter and 1.5 m excavation depth, the suggested dosages are 0.12–0.14 m³ of foaming agent and 4–5 m³ of bentonite, controlling the slump value at 10–25.

Under these sediment improvement parameters, the EPB shield machine can maintain good excavation performance. In the Nanjing Metro Line 11 project, the measured average cutterhead torque was 1945.5 kN·m, average total thrust force was 21,239.6 kN, average screw conveyor pressure was 29.1 bar, and average screw conveyor torque was 4.3 kN·m. The spoil discharge at the screw conveyor tail was good, with no lumping or surging observed.

4.1.2. Laboratory Test Results

To analyze the sediment improvement in EPB shield tunneling through water-rich sand layers and provide a theoretical reference for future projects, this study set up three experimental groups based on on-site tests:

Group 1: Undisturbed soil.

Group 2: Undisturbed soil + 10% bentonite.

Group 3: Undisturbed soil + 5% foam.

Group 4: Undisturbed soil + 10% bentonite + 5% foam.

The results, shown in Figure 9, indicate that unimproved water-rich sand sediments have a low slump of 7–10, with minimal changes over time. The addition of bentonite and foam significantly increased the slump, particularly for Group 3 (foam only), which had the highest slump and better flowability. However, its slump increases over time, potentially causing a surge in the shield restart. Thus, foam-only improvement is not recommended. Group 4 (bentonite + foam) exhibited a higher slump than Group 2 (bentonite only), with better flowability and less time sensitivity. The combination of bentonite and foam improves flowability and ensures stability over extended periods.

4.2. Temporal and Spatial Evolution Behavior of Earth Pressure in the Shield Chamber

4.2.1. Spatial Evolution Behavior of Earth Pressure in the Shield Chamber

Metro lines are typically designed with a gradient to facilitate drainage and construction. Thus, the spatial position of the EPB shield machine changes within a three-dimensional space during construction. As indicated by Equation (1), the primary factor influencing the earth pressure in the shield chamber is the tunnel burial depth. For the first phase of Nanjing Metro Line 11, the burial depth of the Liuzhou East Road to Puzhou Road section first increased and then decreased, reaching a maximum of 25.35 m. To reflect the actual earth pressure parameters controlled during shield tunneling, excavation data were extracted and processed using MATLAB Version r2024b.

During the shield tunneling construction process, in order to quickly determine the initial shield chamber pressure value based on the shield burial depth, engineering and technical personnel usually simplify the assumption that the earth pressure increases linearly with the increase in depth under the condition of a single soil layer. Under the condition of water-rich sand layers, this paper conducts a linear fitting on the relationship between earth pressure and depth in order to provide key experience references for relevant technical personnel. As excavation progressed, the actual earth pressure correlated linearly with the burial depth, as shown in Figure 10. Linear fitting results suggest that in water-rich sand layers, when using a shield tunneling machine with a large opening rate, the earth pressure can be preliminarily estimated based on the fitting results. This finding provides crucial actual earth pressure control values for EPB shield tunneling in water-rich-sand layers.

To explore the theoretical calculation values of earth pressure in the shield chamber, this study applied Terzaghi’s earth pressure calculation theory to compute earth pressure at different depths, considering both water-soil separate and combined calculations. The results shown in Figure 11 indicate significant fluctuations in the earth pressure values at the transition between shallow and deep burial depths. Moreover, the water-soil separate calculation yields higher earth pressure values than the combined calculation. The water-soil separation method is suitable for geological conditions with high permeability, while the combined method is appropriate for low-permeability conditions. As shown in Table 1, the geological conditions of this project are water-rich sand layers with a permeability coefficient of 4 × 10⁻². Therefore, the average values of the water-soil separate and combined calculations were computed, revealing a high degree of consistency with the actual project. To analyze the deviation between the calculated and measured data, this paper calculates the Root Mean Square Error (RMSE). The RMSE of Terzaghi (combined) is 0.510, the RMSE of Terzaghi (separate) is 0.304, the RMSE of the average value is 0.287, and the RMSE when using separate calculations for shallow burial and average value for deep burial is 0.281. To reduce earth pressure fluctuations at the shallow and deep burial transitions during Terzaghi’s theoretical calculation for water-rich fine sand layers with medium permeability, this study recommends using the water-soil combined calculation for theoretical earth pressure in shallow burial stages and the average of separate and combined calculations for deep burial stages.

4.2.2. Temporal Evolution Behavior of Earth Pressure in the Shield Chamber

(1)

Earth pressure variation behavior

During non-excavation phases, such as segment erection and material preparation, the shield machine stops excavating, the screw conveyor is closed, and earth pressure in the chamber is maintained. However, due to soil disturbance near the tunnel face and lack of sediment improvement, earth pressure decay may occur over time. To explore the temporal evolution trend of earth pressure under stop-restart conditions, this study extracted shield machine data during stoppage and restart using MATLAB. Figure 12 and Figure 13 show that during stop-restart periods, earth pressure decays to varying degrees, with differences in decay rate and duration at different locations.

It is commonly believed that earth pressure fluctuations are influenced by multiple factors, including site conditions and mechanical status. To quantify the changes in earth pressure, this study conducted a statistical analysis using actual project data, and the results are shown in Figure 14, Figure 15 and Figure 16. Figure 14 indicates that the median earth pressure decay is 0.3 bar, the mean is 0.35 bar, and the overall variation range is stable with few abnormal values. This suggests that when the EPB shield machine is not excavating, the earth pressure in the chamber decreases to some extent but remains generally stable. Additionally, the duration of earth pressure decay was investigated, reflecting the duration of the non-excavation state. As shown in Figure 15, the median decay duration for the project is 30 min, and the mean is 41.8 min. Longer durations may be due to equipment maintenance, adjustment, or other factors causing prolonged non-excavation. Figure 16 shows the average earth pressure decay rate during the stop-restart periods. Results show that, except for individual large fluctuations due to equipment errors, the average earth pressure decay rate is 0.02 bar/min in the project, with a median of 0.01 bar/min, indicating a slow decay trend. This implies that in earth pressure balance shield tunneling, a reliable face support can be maintained for a certain time in non-excavation states to stabilize the soil.

(2)

Earth pressure attenuation behavior

Due to the combined effect of various factors, such as the transportation stage of materials required for shield tunneling construction, connection stage of equipment water pipes, and maintenance stage of blades, the non-excavation state of the EPB shield machine often lasts for a relatively long period. At this point, the soil pressure in the earth chamber is often in a state of slow decline. From the perspective of maintaining soil pressure balance, excessively low soil pressure leads to surface settlement. Analyzing the time-dependent decay trend of earth pressure in the chamber during such periods can ensure construction quality and safety. Therefore, this study separately analyzed the earth pressure-time data during prolonged non-excavation periods using actual project data. Since spatial position changes can affect earth pressure, the data was normalized. Results, shown in Figure 17, indicate that the colored line segments represent the extracted earth pressure decay feature curves, which decrease in a stepwise manner due to sensor precision limitations. Moreover, these curves were within a similar range and showed a similar decay trend. Based on existing data, an envelope curve was drawn using probability statistics, as shown in Figure 17, with a fast decay rate in the first half and a slower rate in the second half. The method for drawing the envelope curve is as follows: first, many different values are taken for the parameters of the fitting curve, and these curves are drawn. Then, the intersection points and envelope situation between the fitting curves and the actual data are quantified, and the envelope range is calculated. Finally, the fitting curve with the largest envelope range and the best consistency in the trend is selected as the envelope curve. Fitting analysis in ORIGIN shows that the earth pressure decay curve during non-excavation periods generally follows an exponential decay trend. Combined with the fitting results, this study provides crucial theoretical and data references for earth pressure control of EPB shield machines in non-excavation states in water-rich sand layers.

4.3. Analysis of Ground Settlement Patterns Under Earth Pressure Control Conditions

(1)

Ground settlement behavior

When shield tunneling advances, surrounding soil is disturbed, causing ground settlement. Before the shield machine’s cutterhead reaches the excavation face, soil near the monitoring point may be disturbed, causing some pre-settlement. When the shield machine passes the monitoring point, the balance between the earth pressure in the shield chamber and the soil at the face is disrupted, leading to an instantaneous settlement. When the shield tail clears the monitoring point, consolidation settlement occurs later under the combined effects of secondary grouting, grout shrinkage, and soil creep. The ground settlement curve for shield tunneling in the water-rich sand layer of this project is shown in Figure 18.

To clarify the impact of earth pressure changes on ground settlement in water-rich sand layers, this study conducted on-site experiments during shield tunneling. While maintaining stable grouting, the earth pressure control values in the shield chamber were changed. As per the findings in Section 4.2, the theoretical and actual earth pressure control values for the test section ranged between 2.2 and 2.3 bar. Consequently, the earth pressure in this section was set to 2.0–2.1, 2.4–2.5, 2.6–2.7, and 2.8–2.9 bar. The changes in pre-settlement and instantaneous settlement under different earth pressures, including their values and rates, were analyzed, and the results are presented in Figure 19a,b, respectively.

As shown in Figure 19a, with an increase in earth pressure control, the pre-consolidation settlement increases while instantaneous settlement decreases. Pre-consolidation settlement increases with higher pressure because exceeding the pre-consolidation pressure triggers a sharp increase in soil compressibility and disrupts the stable soil structure. When the earth pressure at the tunnel face is less than the soil pressure from the soil’s self-weight, active sliding and greater instantaneous settlement occur. A smaller soil pressure also means less disturbance to the unexcavated soil, resulting in a smaller pre-consolidation settlement. Moreover, when the earth pressure is within the theoretical range, the sum of the pre-consolidation and instantaneous settlements is smaller, reducing the impact on the ground surface. From Figure 19b, as the earth pressure control increases, the pre-consolidation settlement rate slightly increases while the instantaneous settlement rate decreases. Excavation with earth pressure below the theoretical value leads to a higher instantaneous settlement rate, potentially destabilizing surface structures. It should be noted that due to the greater surface settlement at lower earth pressures, the on-site test was conducted in an area without surface structures, thereby avoiding adverse effects.

(2)

Stability of ground settlement

To analyze surface settlement after the shield leaves the monitoring point, the Augmented Dickey-Fuller (ADF) test was used to assess the stability of the consolidation settlement data and evaluate risks. The ADF test is used to determine whether a sequence has a unit root: if the sequence is stationary, there is no unit root; otherwise, there is a unit root. Therefore, the hypothesis of the ADF test is that there is a unit root. If the obtained significance test statistic is less than the three confidence levels (10%, 5%, 1%), it means that we have (90%, 95%, 99%) confidence to reject the null hypothesis. In this paper, the difference is solved by Python (Version 3.10) based on the ‘stm.adfuller’ function in the Statsmodels library.

Table 5. ADF test results for late consolidation settlement data.

Soil Pressure Control Value (Bar)	ADF	p
2.0~2.1	−2.89	0.047
2.2~2.3	−3.42	0.011
2.4~2.5	−3.78	0.003
2.6~2.7	−3.60	0.006
2.8~2.9	−3.15	0.023

presents the ADF test results. At a 0.05 significance level, the later consolidation data under various earth pressures were stable, indicating a stable surface settlement after the shield departed from the monitoring point. Thus, the soil remained stable with minimal settlement risk post-shield passage during construction.

5. Conclusions

In this study, based on the shield tunneling data from the Liuzhou East Road to Puzhou Road section of Nanjing Metro Line 11 and the construction characteristics of the shield machine, probability, statistics, and other methods were used to obtain the temporal and spatial evolution trends of earth pressure in the shield chamber under water-rich sand conditions. The results provide important theoretical and data references for EPB shield tunneling in water-rich sand layers and are helpful for research on earth pressure decay theory.

(1)

The actual earth pressure is linearly correlated with the shield burial depth. When using a shield machine with a large opening rate in water-rich sand layers, the relationship between actual earth pressure y (bar) and burial depth x (m) is: y = 0.0973x + 0.0909.

(2)

Terzaghi-based earth pressure calculations show significant fluctuations at the shallow-to-deep burial transition. The water-soil separate calculation yields a higher earth pressure than the combined calculation. For medium-permeability water-rich fine sand layers, the water-soil combined calculation is used for shallow burials, and the average of both methods is used for deep burials.

(3)

During shield stop-restart periods, earth pressure in the chamber decays to varying degrees, with differences in decay rate and duration at different locations. In non-excavation states, reliable tunnel face support can be maintained for a certain period to stabilize the soil.

(4)

The earth pressure decay envelope, based on decay patterns, shows an exponential downward trend, with rapid decay initially and slower decay later. This envelope is crucial for controlling the stability of the shield chamber during non-excavation periods.

(5)

As the earth pressure control value increases, the pre-consolidation settlement increases while the instantaneous settlement decreases. The pre-consolidation settlement rate increases slightly, and the instantaneous settlement rate decreases. When excavation pressure is below the theoretical value, the instantaneous settlement rate is high, potentially destabilizing surface structures.

(6)

In subsequent studies, based on the accurate analysis results of the earth pressure balance in water-rich sand layers presented in this paper, the influence of the additional stress from surrounding buildings on the earth pressure balance can be further considered within an appropriate and safe range.