The quality of ground surface pregrouting (GSPG) is commonly qualitatively evaluated using single factor; however, the quality evaluation involves numerous facets, and a quantitative evaluation is rare. The aim of this study was to quantitatively evaluate the quality of a GSPG based on three aspects. The fuzzy analytic hierarchy process (FAHP) was adopted to obtain the final score and quality classification of the GSPG. Based on three aspects, namely, integrity, continuity, and sturdiness, a series of field tests was also conducted, qualitatively evaluating the quality of the GSPG preliminary, to obtain the required test data and verify the FAHP results. The results of the FAHP showed that the quality of the GSPG was 86.42, which could be classified as “Good”, whereas the field tests exhibited that the GSPG was effective, thereby verifying that the FAHP was reliable. In addition, the proposed method provided a detailed comprehension of the quality evaluation of GSPG and a frame of reference for analogous engineering.
Ground surface pregrouting (GSPG) is a technique in which a slurry containing several types of materials, such as cement, mortar, and some chemical polymers, is pumped into boreholes to improve the quality of rock mass and prevent water leakage [
The objective of GSPG is twofold: to improve the quality of the rock mass and prevent tunnel collapse during construction [
Generally, the targets of GSPG are the important parts of mountain tunnels, such as portal sections and shallow-buried sections. A poor quality of grouting may lead to geological disasters, such as collapse and water inrush. Hence, the quality evaluation of grouting is vital. This tends to be difficult owing to the complex geological conditions. Typically, the quality is evaluated indirectly using various tests. At present, the water pressure test is a common method [
Therefore, for multifactor evaluation, a quantitative method is required. The FAHP (fuzzy analytic hierarchy process), a mathematical method based on fuzzy theory, is used for the quantitative evaluation of an objective [
In this study, we have presented three facets: integrity, continuity, and sturdiness, to quantitatively evaluate the quality of a GSPG, using the FAHP. First, a series of field tests regarding the GSPG was performed in the Tongluoshan tunnel of southwest China, and five indices were tested. Then we qualitatively evaluated the quality of the GSPG. Finally, the FAHP was applied to quantitatively evaluate the quality using the five-test data, and the quality classification of the GSPG as well as the final score was obtained.
The analytic hierarchy process (AHP), a powerful and flexible multicriteria decision-making tool for complex problems where both qualitative and quantitative aspects need to be considered, was proposed by Saaty [
AHP model.
Nine-scaling method [
Values | Equal importance with regard to the two indices |
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1 | The two indices are equally important |
3 | The former is slightly more important than the latter |
5 | The former is more important than the latter |
7 | The former is much more important than the latter |
9 | The former is considerably more important than the latter |
2,4,6,8 | Intermediate values are used to reflect fuzzy inputs |
Reciprocal | The dominance of the second alternative is reflected compared with the first, |
Note: Table
The fuzzy method, which is based on the theory of fuzzy mathematics, was developed by Zadeh [
Range of evaluation results in the set
Element | Evaluation result (classification) | Range |
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Range of evaluation results in the set
Element | Evaluation result (classification) | Range |
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Membership function.
To illuminate the usage of the membership function clearly, we give an example where
By repeating the procedure stated above, all the membership vectors are calculated for all the indices calculated. Finally, by arranging these membership vectors, the membership matrix,
As stated above, the FAHP is comprised of three components. First, the evaluation target of a project is determined according to the research objective. Second, the AHP model is established. In the model, some essential factors, namely, criteria and indices, which strongly affect the evaluation target are selected, form a multilayer hierarchy model. The aim of this step is to obtain a weight matrix
Comprehensive evaluation process of the FAHP.
The Tongluoshan tunnel, which was control engineered on the Dianlin highway, is located in the Sichuan Province, China. It is 5197 m long and spans 12.7 m. The depth of the shallow-buried section near the Liaojia gully is merely 6–25 m (Figure
Profile of the grouting project.
Engineering geological profile of Liaojia gully
Profile of the GSPG zone and test zone
Log data in the test zone
A large inhomogeneity exists in the vertical and horizontal directions in terms of the stratum of the GSPG zone. Consequently, the arrangement of the grouting holes was in the form of a quincunx and the horizontal and vertical distances between two holes are 2 m (not all the holes are presented in Figure
Schematic of grouting and test holes arrangement in the test area (strike: 306°).
The grouting process was performed in three orders: primary, secondary, and tertiary grouting, represented by dark blue, orange, and green, respectively. The test data of the GSPG were obtained from five pairs of test holes (denoted by red). The holes before test were implemented to obtain the rock mass parameters before grouting, and the holes after test the parameters after grouting. The rock mass parameters before and after grouting were compared to qualitatively evaluate the quality of the GSPG.
The GSPG parameters are comprised of the grouting pressure, diffusion radius of the slurry, and grouting volume per borehole. In case of the grouting pressure, a high grouting pressure can make the slurry penetrate the stratum rapidly, and it is beneficial to precipitate the moisture of the slurry to accelerate its cementing process. However, an extremely high grouting pressure may split the rock mass, resulting in slurry loss [
More significantly, owing to a strongly weathered rock mass and highly developed groundwater, the slurry is easily diluted or even washed away, causing slurry loss. Moreover, the presence of numerous fissures in the rock mass in the test zone also facilitates slurry loss [
In general, to prevent the slurry from being highly diluted, relatively high concentrations are used in strongly weathered zones. If the groundwater is highly developed, the cement slurry needs a longer time to solidify, producing a worse effect of GSPG. Under this condition, adding some polymers to the slurry could decrease the slurry loss [
Given the complex geological conditions, however, the loss of the slurry tends to become difficult to measure before grouting. According to the engineering experience, the volume of the slurry should be more than the designed value to ensure the grouting quality.
First, the grouting volume per borehole is estimated preliminarily based on (
Second, the finishing standard of grouting is determined. It stipulates that the grouting flow is 20–35 L/min, with the grouting pressure reaching the final pressure and maintaining for 20–30 min [
Finally, in this GSPG, the grouting volume per borehole was estimated preliminarily using (
In practice, to render the GSPG more effective, we strictly followed the standard (the final grouting pressure exceeded the maximum designed value of 1.5 MPa, with the grouting flow being 20–35 L/min and the grouting pressure maintaining for 30 min) and add sodium silicate (water glass) to the slurry, with a concentrate of 35 Bé and a volume proportion of 3%–5%. The grouting volume per borehole in the test zone is as shown in Table
Grouting volume per borehole at the three sections.
Depth (m) | Number of boreholes | ||||
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1 | 2 | 3 | 4 | 5 | |
0–7 | 4.50 | 4.48 | 4.17 | 4.67 | 5.31 |
7–13 | 1.47 | 1.52 | 1.28 | 1.64 | 1.99 |
13–20 | 1.53 | 1.48 | 1.72 | 2.01 | 1.13 |
Total | 7.50 (0.9%) | 7.48 (0.7%) | 7.17 | 8.32 (12%) | 8.43 (13%) |
Please note that “(0.9%)”, “(0.7%)”, “(12%)”, and “(13%)” are the excess rates.
Owing to the complex geology conditions, the GSPG quality is required quantitative evaluation using the FAHP (Section
In general, the objective of a GSPG is twofold: to reduce the permeability rate and improve quality of the surrounding rock. Therefore, the tests can be performed based on the three aspects namely, the integrity, continuity, and sturdiness of the rock mass.
When a broken rock is cemented by the slurry, the integrity of the grouted rock mass improves. The integrity test is generally implemented by an ultrasonic method [
The integrity tests were implemented in both single boreholes (J1, J2, J3, J4, J5) (Figure
Schematic of the test of ultrasonic waves.
Single-borehole test
Double-borehole test
In the single-borehole tests, first, the ultrasonic data of the five boreholes are missing at a depth of 0–10 m (Figure
Sound velocity at different depths in the single-borehole tests.
J1
J2
J3
J4
J5
In the double-borehole tests, first, the ultrasonic data are missing at depths of 0–10 m before grouting (Figure
Sound velocity at different depths in the double-borehole tests.
J2-J1
J2-J3
J2-J5
Both the single-borehole and double-borehole teats reflect the improvement degree of the rock mass. The latter, however, is slightly higher than the former. This is partly because the ultrasonic wave is not sensitive to the fissures particularly those that are small. It tends to transmit in a complete rock rather than in the fissure-spreading, when it transmits in the stratum between two boreholes. In terms of the integrity, the two tests reveal that the GSPG is effective.
The continuity test generally entails an evaluation via the water pressure test [
Schematic of the water pressure test.
As for the continuity test, the key indices include four types (i.e., A, B, C, and D) of the
Five curve types of the water pressure test.
Curve types | Relationships between pressure and flow | Characteristics of curve types | Depictions |
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Type A | | Two curves (1-2-3 and 3-4-5) are straight lines originating at (0, 0) and are coincident | An excellent condition, where the seepage form is laminar flow. Fissures do not change throughout the test. |
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Type B | | Two curves (1-2-3 and 3-4-5) converge to the | An acceptable condition, where the seepage form is turbulent flow. Fissures do not change throughout the test. |
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Type C | | Two curves converge (1-2-3 and 3-4-5) to the | An acceptable condition where the fissure form changes and the permeability of the rock mass increases as the test pressure increases, but the change is temporary and reversible. As the pressure decreases, the fissures return to the original form, showing a behavior of elastic expansion. |
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Type D | | Curve 1-2-3 converges to the | A bad condition, where the fissure form changes and the permeability of rock increases as the pressure increases. This change is permanent and irreversible. The flow is significantly increased and cannot be restored to its original form, indicating fissures are split. |
Permeability rate and curve types obtained from the five pairs of the test holes.
Depth (m) | Before or after grouting | Number of boreholes | ||||
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1 | 2 | 3 | 4 | 5 | ||
0–7 | Before | 53.97/D | 50.91/D | 65.61/D | 62.13/D | 53.78/B |
After | 4.90/A | 5.12/A | 4.69/B | 4.67/B | 4.72/A | |
7–13 | Before | 47.12/D | 45.50/D | 42.00/D | 41.18/D | 46.21/C |
After | 4.31/A | 4.26/B | 4.81/C | 5.18/D | 4.33/A | |
13–20 | Before | 34.42/C | 30.36/D | 36.16/D | 41.10/D | 36.19/A |
After | 3.44/A | 3.69/A | 3.21/A | 3.96/B | 3.15/A |
Note: the unit of the permeability rate is Lu.
As shown in Figure
As shown in Table
Proportion of each curve types before and after grouting.
Before grouting
After grouting
After grouting, the permeability rate is 4.30 Lu (very low) on average, which decreases by approximately 90%. Then the proportion of type A and B increases to 60% and 27%, respectively, whereas that of type D is reduced to 6%. These results indicate that a considerable number of fissures are filled, and most of them would not be split when grouting. Therefore, in terms of the continuity, the GSPG is effective.
In the sturdiness test, the unconfined compressive strength of the rock samples [
Increase rate of the unconfined compressive strength of the rock samples before and after grouting.
Number of rock samples | Before grouting (MPa) | After grouting (MPa) | Increase rate of unconfined compressive strength of the rock samples (%) |
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P1-1 | 10.5 | 12.3 | 17.1 |
J1-2 | 13.5 | 15.3 | 13.3 |
P2-1 | 19.2 | 21.2 | 10.4 |
J2-2 | 21.7 | 23.4 | 7.8 |
P3-1 | 15.3 | 17.1 | 11.8 |
J3-2 | 14.1 | 16.3 | 15.6 |
P4-1 | 13.2 | 15.6 | 18.2 |
J4-2 | 18.3 | 20.6 | 12.6 |
P5-1 | 17.1 | 19.4 | 13.5 |
J5-2 | 18.7 | 20.3 | 8.6 |
These tests can only be utilized to qualitatively evaluate the quality of a GSPG, with the results being effective or ineffective. Hence, an FAHP based on the three facets was performed to quantitatively evaluate the quality, obtaining the quality classification (as well as the final score) of the GSPG.
AHP model for the GSPG.
Evaluation results of the target and their scores.
Elements | Evaluation results | Scores |
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| Excellent | >90 |
| Good | 80–90 |
| Moderate | 60–79 |
| Bad | <60 |
Definitions of the evaluation results for each index.
Index | Symbol | Range of each evaluation result | Test data | |||
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Excellent | Good | Moderate | Bad | |||
Increase rate of sound velocity in single-borehole test (%) | | >15 | 10–15 | 5–10 | <5 | 16 |
Increase rate of sound velocity in double-borehole test (%) | | >15 | 10–15 | 5–10 | <5 | 7 |
Curve types of water pressure test | | A | B | C | D | A: 60%, B:27%, C: 7%, D: 7% |
Decrease rate of permeability rate (%) | | >80 | 60–80 | 40–60 | <40 | 90 |
Increase rate of the unconfined compressive strength of rock samples (%) | | >15 | 10–15 | 5–10 | <5 | 13 |
Calculation of the four index memberships.
Increase rate of sound velocity in single-borehole test
Increase rate of sound velocity in double-borehole test
Decrease rate of permeability rate
Increase rate of the unconfined compressive strength
The FAHP was performed to quantitatively evaluate the quality of GSPG in this study. To qualitatively evaluate the quality of the GSPG and obtain the required data in the FAHP, a series of field tests were also implemented.
The integrity test results showed that the sound velocity in the single-borehole tests and the double-borehole tests increased by 16% and 7%, respectively. The continuity test results showed that the curve types were primarily type A, accounting for a total of 60% after grouting, with the permeability rate decreased by approximately 90%. Concurrently, the sturdiness test result showed that the unconfined compressive strength of the rock samples increased by approximately 13%. These results indicated that the fissures were effectively filled and that the rock performance was improved by the GSPG, thereby suggesting that the GSPG was effective.
Based on the three aspects and five indices, the FAHP was conducted to quantitatively evaluate the quality of the GSPG. The results showed that the final score of the GSPG was 86.42, which could be classified as “Good”. Moreover, the results from the FAHP were consistent with that from the field tests; thus, verifying that the FAHP was reliable and that it could be applied to the quality evaluation of the GSPG. With the qualitative and quantitative evaluations being conducted comprehensively, this quality evaluation of the GSPG provided a frame of reference for analogous engineering.
The test data used to support the findings of this study are available from the corresponding author [Hua Xu] upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This study is financially supported by the National Key Research and Development Program of China (2016YFB1200401) and the Western Construction Project of the Ministry of Transport (Grant no. 2015318J29040). This support is gratefully acknowledged.