Estimation of critical injection quantity for tunnel steel pipe reinforcement grouting using injection data partitioning and upper one-sided tolerance limits

Huikyeong Kim; Kyongnam Min; Jaewon Lee; Gukje Jo; Daeho Kim; Gab-young Chung; Changrim Choi; Hoki Ban

doi:10.9711/KTAJ.2026.28.4.321

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2026 Vol.28, Issue 4 Preview Page

Research Paper

Estimation of critical injection quantity for tunnel steel pipe reinforcement grouting using injection data partitioning and upper one-sided tolerance limits 주입 데이터 분할과 상측 단측 허용한계를 이용한 터널 강관보강 그라우팅 주입량 임계치 산정

31 July 2026. pp. 321-346

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Abstract

This study aims to establish an injection volume threshold (Q*) for grouted steel pipe reinforcement in tunnels, where quantitative management criteria for injection volume have not yet been clearly defined, by applying data partitioning together with an upper one-sided tolerance limit. Based on this threshold, the necessity of additional reinforcement in high-injection sections and the resulting improvement in stability were examined from the perspective of ground treatment extent. Using field data from a tunnel section where steel pipe reinforcement grouting—as an auxiliary tunnelling method—was applied, this study reviewed injection volume management criteria intended to prevent face loosening and collapse during excavation and to secure overall tunnel stability. Injectability was evaluated using flowmeter-based time (T)–pressure (P)–flow rate (Q) data, and section-to-section variation in injection volume was interpreted as reflecting differences in rock quality and joint development. Macroscopic injection volume patterns were first identified from the acquired T-P-Q data, after which the injection data were reorganized at 1 m intervals to obtain detailed locational information on sections exhibiting high-injection tendencies. An iterative search algorithm for data partitioning was then applied to the reorganized data to identify the normal injection population, and an upper one-sided tolerance limit was applied to that population to derive the injection volume threshold (Q*). The threshold (Q*) was defined as a statistical upper-bound management criterion for distinguishing high-injection sections from typical injection behavior. In addition, excessive groundwater inflow of up to 1,300 tonf/day occurred within the study section, which was evaluated as an anomalous case directly related to face stability. Accordingly, this study compared the spatial distribution of injection volume with face observation records to examine the potential spatial correspondence between high-injection sections and weak ground locations, and also confirmed the correspondence with excessive groundwater inflow and poor face conditions. Furthermore, the ground in high-injection sections identified by the threshold (Q*) was assumed to consist of weathered soil, and numerical analyses were performed using the surrounding ground treatment thickness as a variable to evaluate the improvement in stability associated with an expanded reinforcement extent. The results confirmed that, rather than directly determining the actual treatment area, the injection volume threshold (Q*) can serve to identify potential high-injection and weak ground sections, thereby contributing to a proactive response for subsequent tunnel faces.

Keywords

Steel pipe reinforcement grouting

Injectability

Probability distribution

Critical injection quantity

Tunnel face stability

본 연구는 터널 강관보강 그라우팅에서 주입량에 대한 정량적 관리기준이 명확하지 않은 상태에서 데이터 분할과 상측 단측 허용한계를 이용하여 주입량 임계치(Q*)를 산정하고, 이를 기반으로 고주입 관리구간의 보강 필요성과 안정성 개선 효과를 개량범위 관점에서 검토하고자 하였다. 본 연구는 터널 보조공법인 강관보강 그라우팅이 적용된 구간의 현장 자료를 바탕으로, 굴착 시 막장의 이완 및 붕락을 방지하고 터널 안정성을 확보하기 위한 주입량 관리기준을 검토하였다. 주입성 평가는 유량계 기반의 시간(T)-압력(P)-유량(Q) 데이터를 이용하여 수행하였으며, 구간별 주입량 차이는 암질 및 절리 발달 상태의 차이를 반영하는 것으로 해석하였다. 취득한 T-P-Q 데이터를 활용하여 거시적인 주입량 패턴을 우선 확인하고, 이후 주입량 자료를 1m 단위로 재구성하여 고주입 경향이 나타나는 세부 위치정보를 취득하였다. 재구성된 자료에 대해 데이터 분할을 위한 반복 탐색 알고리즘을 적용하여 일반 주입 모집단 구간을 식별하고, 상측 단측 허용한계를 적용하여 주입량 임계치(Q*)를 산정하였다. 주입량 임계치(Q*)는 일반적인 주입 거동과 구분되는 고주입 관리구간을 식별하기 위한 통계적 상한 관리기준으로 정의하였다. 또한 대상 구간에서는 최대 1,300 tonf/day 규모의 과다 지하수 유출이 발생하였으며, 이는 막장면 안정성과 직접적으로 관련되는 비정상 사례로 평가하였다. 이에 본 연구에서는 주입량 공간분포도와 막장면 관찰자료를 대조하여 고주입 관리구간과 취약 지반 위치 간의 공간적 대응 가능성을 검토하였으며, 과다 지하수 유출 및 불량 막장상태와의 대응성도 함께 확인하였다. 아울러 주입량 임계치(Q*)에 의해 식별된 고주입 관리구간의 지반을 풍화토 조건으로 설정하고, 터널 주변 개량두께를 변수로 한 수치해석을 수행하여 보강범위 확대에 따른 안정성 개선 효과를 검토하였다. 그 결과, 주입량 임계치(Q*)는 실제 개량면적을 직접 산정하는 값이라기보다 고주입 관리구간을 식별하고, 후행 막장에 대한 사전 대응에도 기여할 수 있음을 확인하였다.

키워드

강관보강그라우팅

주입성

확률분포

임계치

막장면 안정성

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Information

Publisher :Korean Tunneling and Underground Space Association
Publisher(Ko) :한국터널지하공간학회
Journal Title :Journal of Korean Tunnelling and Underground Space Association
Journal Title(Ko) :한국터널지하공간학회 논문집
Volume : 28
No :4
Pages :321-346
Received Date : 2026-06-26
Revised Date : 2026-07-09
Accepted Date : 2026-07-09
DOI :https://doi.org/10.9711/KTAJ.2026.28.4.321

Journal of Korean Tunnelling and Underground Space Association ISSN:2233-8292(Print) 2287-4747(Online) 한국터널지하공간학회 논문집

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