Surface Subsidence Engineering: Theory and Practice

By CSIRO PUBLISHING

Underground coal mining disturbs both the overburden strata and the immediate floor strata. The subject of surface subsidence deals with the issues associated with the movement of overburden strata, which are the layers from the seam to the surface, where structures and water resources important to human activities are located.

Surface Subsidence Engineering provides comprehensive coverage of the major issues associated with surface subsidence. The chapters are written by experts on surface subsidence in the three leading coal producing and consuming countries in the world: Australia, China and the United States. They discuss general features and terminologies, subsidence prediction, subsidence measurement techniques, subsidence impact on water bodies, subsidence damage, mitigation and control, and subsidence on abandoned coal mines. In addition, the final chapter addresses some of the unique features of surface subsidence found in Australian coal mines. The book provides information on coal seams ranging from flat to gently inclined to steep to ultra-steep seams.

Written for mining engineers, geotechnical engineers and students of mining engineering, this book covers both theories and practices of surface subsidence. Unlike previous publications, it also deals with the subsidence impact on surface and groundwater bodies, crucial resources that are often neglected by subsidence researchers.

• Language: English
• Publisher: CSIRO PUBLISHING
• Release date: Sep 1, 2020
• ISBN: 9781486312566

Book preview

SURFACE

SUBSIDENCE

ENGINEERING

THEORY AND PRACTICE

EDITOR: SYD S. PENG

Copyright The Authors 2020. All rights reserved.

Except as permitted by applicable copyright laws, no part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, duplicating or otherwise, without the prior permission of the copyright owner. Contact CSIRO Publishing for all permission requests.

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Contents

Preface

List of contributors

1General features of surface movement basin

Wenbing Guo and James Barbato

1.1 Introduction

1.2 Formation of the surface movement basin

1.3 Characteristics of the surface movement basin

1.4 Surface movement and deformation characteristics of the major cross-section of the movement basin

1.5 Surface movement and deformation characteristics of the whole basin after mining

1.6 Relationship between surface subsidence and geological and mining conditions

2Prediction of surface subsidence

Huayang Dai, Syd S. Peng and Zach Agioutantis

2.1 Introduction

2.2 Typical curve method

2.3 Profile function method

2.4 Probability integration method

2.5 Surface subsidence prediction for special conditions

2.6 Prediction of dynamic subsidence and residual subsidence

2.7 Subsidence prediction software

3Measurement of surface subsidence and surface structures

Wenbing Guo

3.1 Introduction

3.2 Design of survey points

3.3 Setup of the survey points

3.4 Measurements of surface movement

3.5 Other surveying methods

3.6 Subsidence data analysis

3.7 Measurement of surface structure damage

4Subsidence impact on water systems

Deepak P. Adhikary, Qingdong Qu, Andy H. Wilkins, Brett A. Poulsen, Hua Guo and Yanchun Xu

4.1 Introduction and overview

4.2 Water systems in coal mining regions

4.3 Overburden disturbance by underground mining

4.4 Estimating hydrogeological zones and understanding mine groundwater dynamics

4.5 Assessment of mining impact on groundwater and surface water systems

4.6 Prevention of mine water inrush: Chinese guidelines

5Surface subsidence damage, mitigation and control

Syd S. Peng and Junying Zhang

5.1 US experience

5.2 China experience

6Subsidence over abandoned mines: US experience

Richard E. Gray

6.1 Introduction

6.2 Development history of US coalfields

6.3 Coal production and reserves

6.4 Underground mining impacts

6.5 Methods of underground mining

6.6 Room and pillar mining

6.7 Stope mining in steeply dipping seams

6.8 Subsidence with active mining

6.9 Total extraction

6.10 Total extraction subsidence experience

6.11 Multiple seam mining

6.12 Coal pillar and mine floor strength

6.13 Subsidence over abandoned mines

6.14 Evaluating the potential for subsidence

6.15 Evaluation of existing conditions: situations with a low risk of subsidence

6.16 Mine stabilisation

Colour plates

7Surface subsidence: Australian experience

Ken Mills and James Barbato

7.1 Introduction

7.2 Background

7.3 Brief history of underground mining

7.4 Understanding of subsidence behaviour in Australia

7.5 Mechanics of subsidence behaviour

7.6 Measurement of surface subsidence

7.7 Subsidence prediction methodologies

7.8 Subsidence effects

7.9 Horizontal movement

7.10 Components of horizontal movement

7.11 Prediction of horizontal movement

7.12 Strain

7.13 Surface subsidence impacts

Index

Preface

Underground coal mining disturbs not only the overburden strata, but also the immediate floor strata. The former is much more significant because it involves strata from the seam level all the way to the surface, where structures and water resources important to human activities are located. The issues associated with the movement of overburden strata due to underground coal mining together comprise the subject of surface subsidence.

This book covers all major subjects associated with surface subsidence. The chapters were written by top experts on surface subsidence in three leading coal producing and consuming countries in the world, including Australia, China and the US. The subjects include general features and terminologies (Chapter 1), subsidence prediction (Chapter 2), subsidence measurement techniques (Chapter 3), subsidence impact on water bodies (Chapter 4), subsidence damages, mitigation and control (Chapter 5), and subsidence on abandoned coal mines (Chapter 6). Chapter 7 addresses some of the unique features of surface movement found in Australian coal mines. The coal seams studied cover the whole range from flat to gently inclined, steep and ultra-steep seams. The book also deals with subsidence impact on surface and groundwater bodies that are the source of life on Earth, a topic that is often neglected by subsidence researchers.

Surface Subsidence Engineering: Theory and Practice is unique in that it covers both theories and practices, combining the research experience of top experts in three countries in three continents - this has never been done before on the subject of surface subsidence. Obviously, with such a broad range of mining, geological and cultural backgrounds, there are similarities and differences in approach among the chapters.

Syd S. Peng

Morgantown, WV

USA

October 2019

List of contributors

Deepak Adhikary

CSIRO, Mineral Resources, Brisbane, Qld, Australia

Zacharias Agioutantis

University of Kentucky, Lexington, KY, USA

James Barbato

Mine Subsidence Engineering Consultants, Sydney, NSW, Australia

Huayang Dai

China University of Mining and Technology, Beijing, China

Dick Gray

DiGioia, Gray & Associates LLC, Pittsburgh, PA, USA

Hua Guo

CSIRO, Mineral Resources, Brisbane, Qld, Australia

Wenbing Guo

Henan Polytechnic University, Jiaozuo, Henan, China

Ken Mills

SCT, Wollongong, NSW, Australia

Syd S. Peng

West Virginia University, Morgantown, WV, USA; Henan Polytechnic University, Jiaozuo, Henan, China; and China University of Mining and Technology, Xuzhou, China

Brett Poulsen

CSIRO, Mineral Resources, Brisbane, Qld, Australia

Qingdong Qu

CSIRO, Mineral Resources, Brisbane, Qld, Australia

Andy Wilkins

CSIRO, Mineral Resources, Brisbane, Qld, Australia

Yanchuan Xu

China University of Mining and Technology, Beijing, China

Junying Zhang

China Coal Research Institute, Beijing, China

1General features of surface movement basin

Wenbing Guo and James Barbato

1.1 INTRODUCTION

After coal mining, the immediate roof strata above the gob move and bend downward under the action of dead weight stress and the gravity of overlying strata (Peng 1992; Yuang et al. 2010). When the stress exceeds the strength of the rock layer, the immediate roof breaks, and falls successively. The main roof moves and bends along the normal direction to the bedding plane in the forms of beam or plate, resulting in fracture and separation. As the face advances, the range of strata affected by mining expands continuously. When the mining area is large enough, the strata movement reaches the surface. It forms a subsidence basin on the surface that is much larger than the gob area (Fig. 1.1).

Fig. 1.1. Overburden strata and surface movement due to longwall coal mining.

Surface subsidence caused by underground coal mining is a very complicated process in time and space. The movement of the surface point goes through a whole process from movement initiation to violent movement and finally to a stop. Since the characteristics of surface subsidence after the face has stopped (final subsidence) differ from those when the face is moving (dynamic subsidence), both must be investigated (Guo 2019; Peng 2017).

1.2 FORMATION OF THE SURFACE MOVEMENT BASIN

1.2.1 Types of surface movement

1.2.1.1 Surface movement basin

During underground longwall mining, when the gob reaches a certain size, overburden strata movement reaches the surface and forms a low area of limited size above the gob. This area is much larger than the mined-out area and is known as the surface subsidence basin, or more exactly the surface movement basin (Plate 1). When the coal seam is horizontal and the gob is rectangular in shape, the movement basin is approximately elliptical immediately above the gob. The formation of a surface subsidence basin changes the original form of the surface, causes the elevation and horizontal position of the surface to change, and has an impact on surface structures such as houses, roads, rivers, railways, the ecological environment and so on (Zhang et al. 2003).

1.2.1.2 Cracks, compression heave and steps

In the outer margin area of a surface movement basin, cracks may occur on the surface. The depth and width of cracks are related to the presence and thickness of the surface alluvium layers. Cracks are generated when the plasticity of the alluvium layers is high and the surface tensile deformation exceeds 6–10 mm/m. Generally, the surface cracks are not connected with the underground longwall gob, and may disappear at some depth. When mining intensity is high, cracks or steps may appear on the surface (Fig. 1.2).

Fig. 1.2. Types of surface damage caused by longwall mining.

1.2.1.3 Collapse pit, potholes/sinkholes

Collapse pits often appear in steep coal seams, but occur more easily in special geological and mining conditions. When the mining depth is very small and the mining height is very large, the failure height of overburden is not consistent. This is due to different mining heights resulting in funnel-shaped collapse pits on the surface.

Cracks, steps or sinkholes on the surface can be very harmful to surface structures. Therefore, when mining under buildings, railways or water bodies, large cracks, steps and collapse pits should be avoided as much as possible (Yu and Zhang 2010).

1.2.2 Development of surface subsidence basin

The surface movement basin is formed gradually as the face advances. Generally, when the face moves forward from the setup room for a distance equal to or exceeding 1/4–1/2 of mining depth, mining influence will reach the surface and cause surface subsidence. As the face continues to advance, the gob area increases, the area of influence on surface expands, surface subsidence increases and the surface subsidence basin expands. When the gob size reaches a certain level, the maximum subsidence value will no longer increase and a flat bottom subsidence basin will be formed (Fig. 1.3). When the face stops advancing, surface movement will not stop immediately but will continue for a period of time; subsidence velocity for each surface point does not increase, instead it decreases gradually until stabilised, forming the final surface movement basin. At this time, the basin is also known as the static or final movement basin.

Fig. 1.3. Processes of forming surface movement basin. 1,2,3,4 = different positions of face advance; s1, s2, s3, s4 = surface movement basins formed when the face is at the corresponding positions of 1, 2, 3 and 4, respectively; s04 = final surface static movement basin; h0 = mining depth.

1.2.3 Types of surface subsidence basin

Surface movement basins are generally divided into three types – subcritical, critical and supercritical – according to the influence area of mining on the surface.

The concept of critical mining or full gob size that produces maximum possible surface subsidence must be introduced first, because it is related to the definition of the three types of surface subsidence basin. In critical mining, the gob dimensions (critical gob size) are equal to 1.22–1.4 times the mining depth in both the seam strike (panel length or longitudinal) and seam dip (faceline or transverse) directions. If the gob does not satisfy the dimension in one or both directions, it is subcritical mining. If the gob exceeds the required dimension in both directions, it is supercritical mining. When the gob size is equal to or larger than 1.2–1.4 times the mining depth, it is called the full subsidence or full gob size.

1.2.3.1 Subcritical subsidence basin

When the size of the gob is smaller than the critical mining size under the geological and mining conditions, the subsidence value at any point on the surface does not reach the maximum possible value. The surface movement basin thus produced is called a subcritical subsidence basin, and it is a funnel shape (Fig. 1.4). When the face reaches the critical mining size in one direction (strike or dip) and fails to reach the critical mining size in the other direction, it is also considered subcritical mining. At this time, the surface movement basin is a trough shape (Fig. 1.5).

Fig. 1.4. Funnel-shaped subcritical subsidence basin.

Fig. 1.5. Trough-shaped subsidence basin.

1.2.3.2 Critical subsidence basin

When the subsidence of only one point in the surface movement basin reaches the maximum possible value under the geological and mining conditions, it is called full or critical mining. The basin is shaped like a bowl with pointed bottom (Fig. 1.6). Field measurement shows that when the length and width of the gob reach or exceed (1.2–1.4) h0 (h0 is the average mining depth), the surface movement reaches full mining in both directions, as stated earlier.

Fig. 1.6. Critical subsidence basin.

Another convenient criterion for critical mining is the allocation of angle of full subsidence, ѱ. On the major cross-section of the subsidence basin, the angle between the horizontal line at gob edge and the line connecting point ‘o’ on the surface before mining to the gob boundary (Fig. 1.6) is the angle of full subsidence. Point ‘o’ is the point projected by the point of maximum possible subsidence on the subsidence profile. For critical mining, there is only one point that reaches the maximum possible subsidence value on the subsidence profile (Fig. 1.6). Note that for flat seams, the lines (dotted lines in Fig. 1.6) forming the angles of full subsidence at the opposite side of gob edge intersect exactly at the surface before mining (point ‘o’ in Fig. 1.6). For subcritical mining, they intersect below the surface before mining, while for supercritical mining they intersect above the surface before mining. For supercritical mining, there is a flat bottom at the centre of the basin. Therefore, the edges of the flat bottom on both sides are projected onto the surface before mining (o1 and o2 in Fig. 1.7) to define the angle of full subsidence or vice versa. For inclined seams, the angles of full subsidence on the downdip and updip sides as well as along the strike direction are denoted ѱ1, ѱ2 and ѱ3, respectively.

Fig. 1.7. Supercritical subsidence basin.

1.2.3.3 Supercritical subsidence basin

When the gob size continues to expand after full mining is reached, the influenced area of the surface expands correspondingly but the maximum subsidence value of the surface no longer increases. The flat bottom will appear in the surface movement basin. When the subsidence value of multiple points on the surface reaches the maximum possible value, the mining is called supercritical mining. At this time, the surface movement basin is called a supercritical mining subsidence basin, and is shaped like a washbasin (Fig. 1.7).

1.3 CHARACTERISTICS OF THE SURFACE MOVEMENT BASIN

1.3.1 Three areas of the surface subsidence basin (transverse to panel)

The in situ measured results show that the area of the surface movement basin is much larger than the corresponding gob. The shape of a surface movement basin depends on the gob shape and the inclination of the coal seam. The relative position of the basin and gob depends on the inclination of the coal seam. In the movement basin, the movement and deformation at different locations are not the same. When the surface above the gob is flat, the gob has reached supercritical mining and no large geological structure is within the influenced area of mining, the final (static) surface movement basin can be divided into three zones (Fig. 1.8).

Fig. 1.8. The three zones of a surface movement basin.

1.3.1.1 Centre zone (neutral area)

The centre zone of the surface movement basin is located in the centre part of the basin (Fig. 1.8). Within this area, surface subsidence is uniform, surface subsidence value reaches the maximum possible value under the geological and mining conditions, other displacement and deformation values are close to zero and there are no obvious cracks.

1.3.1.2 Inner marginal zone (compressed area)

The inner marginal area of the surface movement basin is generally located between the boundary of the gob and that of the centre zone (Fig. 1.8). In this area, the surface subsidence varies and the ground moves towards the centre of the basin, forming a concave profile and producing compressive deformation. Generally, no cracks appear in this zone.

1.3.1.3 Outer marginal zone (tensile area)

The outer marginal zone of the surface movement basin is located between the gob boundary and the basin boundary (Fig. 1.8). In this zone, surface subsidence is not uniform and ground movement is towards the centre of the basin, forming a convex profile and producing tensile deformation. When the tensile deformation exceeds a certain value, surface tensile cracks will appear.

1.3.2 Boundaries of the surface subsidence basin

According to the influence of surface movement and deformation on structures and surface, there are three boundaries in the surface movement basin.

Figure 1.9 shows the three boundaries in the surface movement basin due to underground longwall mining. On the major cross-section of the basin, AB is the outermost boundary, A′B′ is the dangerous boundary and A″B″ is the cracks boundary.

Fig. 1.9. Three boundaries of the surface movement basin.

1.3.2.1 Outermost boundary

The outermost boundary of a surface movement basin is theoretically defined by the basin boundary where the surface movement and deformation are zero. In field measurement, the point with 10 mm subsidence is generally taken as the boundary point due to survey errors. Therefore, the outer boundary is actually the contour line formed by the points with 10 mm subsidence (Fig. 1.9A,B,C,D).

1.3.2.2 Dangerous boundary

The dangerous boundary (Fig. 1.9A′,B′,C′,D′) is defined as the boundary of critical deformation value, which means the building within the boundary will be damaged. The critical deformation values commonly used in China are tilt (t) = 3 mm/m, horizontal strain (e) = 2 mm/m and curvature (k) = 0.2 mm/m². The dangerous boundary is determined by the outermost position of these three critical deformation values.

1.3.2.3 Cracks boundary

The cracks boundary (Fig. 1.9A″,B″,C″,D″) is defined by the line where the outmost cracks of a surface movement basin will occur.

1.3.3 Angle parameters of the surface subsidence basin

The boundaries of a surface movement basin are usually determined by angular parameters (Peng 2006, 2008). The angular parameters describing the boundaries on the major cross-section of a surface movement basin are mainly angle of draw (δ0), angle of critical deformation (δ), angle of outmost crack (δ") and angle of alluvium critical deformation (φ) (Fig. 1.10).

Fig. 1.10. Angle parameters in surface subsidence profile along the faceline direction.

1.3.3.1 Angle of draw

When the mined-out gob has reached the critical size (or nearly so) on the major cross-section, the acute angle between the line connecting the edge of the movement basin with 10 mm subsidence and the gob edge, and the horizontal line at the gob edge, is the angle of draw. When there is an alluvium layer, the line connecting basin boundary and gob edge consists of two parts. In the alluvium layer, the angle of critical deformation, , for alluvium is used to draw the line BC (Fig. 1.11) at point B on the contact plane between the underlying bedrock and alluvium layer. The acute angle between the line connecting the intersection point B and the gob edge, and the horizontal line at the gob edge, is called the boundary angle. On different cross-sections, the angles of draw can be classified into strike angle of draw, down-dip angle of draw and updip angle of draw, denoted by δ0, β0 and γ0, respectively.

Fig. 1.11. Angle of critical deformation for alluvium layer.

1.3.3.2 Angle of critical deformation

Critical deformation is the amount of deformation that failure of a surface structure initiates. Different structures have different threshold values or critical deformation that causes a structure to start to fail.

When the mined-out gob has reached the critical size (or nearly so), the acute angle between the line connecting the point of critical deformation on the major cross-section of the basin and the gob edge, and the horizontal line at the gob edge, is the angle of critical deformation. Depending on direction, the angles of critical deformation can be classified into strike angle of critical deformation, downdip and updip angles of critical deformations, denoted by δ, β and γ, respectively.

1.3.3.3 Angle of outmost crack

When the mined-out gob has reached the critical size (or nearly so) on the major cross-section, the acute angle between the line connecting the outmost surface crack and the gob edge, and the horizontal line at the gob edge, is the angle of outmost crack. Depending on direction, the angles of outmost crack can be classified into strike angle of outmost crack, downdip and updip angles of outmost cracks, denoted by δ, β and γ" respectively.

1.3.3.4 Angle of alluvium critical deformation

As shown in Fig. 1.11, the acute angle between the line connecting points B and C and the horizontal line at the gob edge is called the angle of critical deformation for alluvium, φ. B is the intersection point of the line from the gob boundary drawn at an angle equal to the angle of critical deformation for the overlying rock strata, to the interface between the overlying bedrock and the alluvium. C is the surface point with 10 mm subsidence. The angle of critical deformation for alluvium is not related to the dip angle of coal seam; rather, it is mainly related to the properties of the alluvium.

1.3.3.5 Angle of maximum subsidence

Unlike the horizontal coal seams, the maximum subsidence point of the surface is not directly above the centre of the gob after mining in inclined and gently inclined coal seams. In those seams, on the major cross-section of the surface movement basin, the angle between the line connecting the centre point of the gob and the point of maximum subsidence on the subsidence profile projected on the surface before mining, and the horizontal line at the gob edge on the downdip side, is the angle of maximum subsidence, θ (Fig. 1.12a). The field-measured data show that the angle of maximum subsidence is related to the lithology of overlying rock and coal seam inclination. In inclined or gently inclined coal seams, θ decreases with increases in coal seam inclination. Generally, it can be expressed by:

Fig. 1.12. Definition of angle of maximum subsidence.

where Cr = a coefficient related to rock lithology; and α = the dip angle of coal seam.

1.4 SURFACE MOVEMENT AND DEFORMATION CHARACTERISTICS OF THE MAJOR CROSS-SECTION OF THE MOVEMENT BASIN

1.4.1 Surface movement and deformation parameters

The effects of surface subsidence can be described by various parameters. These parameters are often measured using survey points firmly installed on the surface (Guo 2013a, b). The subsidence effects are therefore described by the absolute and relative movements of these fixed points on the surface. Methods of measurement for surface movements are described in Section 3.4 of this book.

Surface movement due to underground longwall mining includes both vertical and horizontal components. Subsidence usually refers to vertical displacement. The term subsidence referred to in this book is the vertical component unless specifically described as the horizontal component or a combination of the two components.

The absolute displacements of the surface are described in an xyz Cartesian coordinate system. The x- and y-axes are orthogonal and in the horizontal plane. They can be oriented east–west and north–south or parallel and perpendicular to the centreline of the underground longwall panel. The z-axis is in the vertical direction. The moving trajectory of a surface point depends on the relationship between the surface point and the relative position of the face in time and space. As shown in Fig. 1.13, the movement vector of a point can be resolved into vertical and horizontal components. The vertical component is called subsidence and the horizontal component is called horizontal displacement.

Fig. 1.13. Symbols and terminology used for movement of a surface point.

There are several surface movement and deformation parameters including vertical displacement, horizontal displacement, slope or tilt, curvature, horizontal strain, twist and shear strain. Generally, on the major cross-section of a movement basin, the movement and deformation of each point are measured by setting up survey points. Figure 1.14 shows several survey points on the major cross-section of the surface movement basin. Before and after the surface movement, the elevation and distance from a reference point(s) or coordinates of each point are measured, and the movement and deformation of each point can be obtained through calculation.

Fig. 1.14. Movement and deformation analysis of each station on the surface.

1.4.1.1 Vertical displacement

The vertical displacement is the vertical component of the surface movement vector. Vertical displacement (Sn) represents the change in level/elevation of a fixed point on the surface. This parameter is also referred to as vertical subsidence or simply as subsidence. Vertical displacement is a scalar quantity and can be expressed in units of millimetres (mm), metres (m), inches ("), or feet (').

The value of vertical displacement at a fixed point on the surface is equal to the initial elevation (hn0) minus the final elevation (hnm), as defined in Eqn 1.2 and illustrated in Fig. 1.15.

Fig. 1.15. Cross-section illustrating vertical displacement at a fixed point on the surface.

Vertical displacement develops directly above the underground mining area. It is greater above the areas of repeated extraction and lesser above chain and remnant pillars. This component extends outside of the mining area and its magnitude reduces to very small values at distances of approximately half the depth of cover from the limit of repeated extraction.

The profile of vertical displacement can be measured using a traditional ground monitoring line comprising a line of uniformly spaced survey points. An example of a typical profile across a series of subcritical panels is illustrated in Fig. 1.16.

Fig. 1.16. Typical profile of vertical displacement across a series of subcritical panels.

The maximum vertical displacement (Smax) is the greatest measured value along the monitoring line.

Absolute vertical displacement itself generally does not result in impacts on surface features. The potential for impact occurs due to differential vertical displacements (i.e. surface tilt and surface curvature) or differential horizontal displacements. However, vertical displacement can affect flooding and ponding on the surface.

1.4.1.2 Surface slope or tilt

Surface slope (T) represents the gradient (i.e. first derivative) of a vertical displacement profile. This parameter is also referred to as tilt or change in grade, as it represents the change in slope of the natural surface.

Surface slope is a vector quantity and it can be expressed as a magnitude (T) and direction in plan (θ’). Alternatively, this parameter can be expressed as two orthogonal components in plan (Tx and Ty). The orthogonal components represent the gradients of the subsidence basin along their respective axes.

The magnitude of surface slope can be expressed in units of millimetres per metre (mm/m), a ratio (dimensionless), percentage (%) or feet per 100 ft. The orientation can be expressed as an angle (°) from true north or relative to the underground panel axes.

The component of surface slope along a traditional ground monitoring line can be determined by taking the difference in vertical displacement between two adjacent survey points (S1 and S2) and dividing it by the initial horizontal distance (di) between them, as defined in Eqn 1.3 and illustrated in Fig. 1.17.

Fig. 1.17. Cross-section illustrating surface slope between two fixed points on the surface.

The surface slope measured using traditional ground monitoring lines represent the gradient of the surface subsidence basin along the line. The surface slope across or oblique to the monitoring line cannot be directly measured using a single line of survey points.

The surface slope in two orthogonal directions (Tx and Ty) can be measured using a square grid of survey points. The magnitudes of these two components are defined in Eqn 1.4 and illustrated in Fig. 1.18. These components are based at Point 1 as shown in the figure.

Fig. 1.18. Orthogonal components of surface slope between a grid of fixed points on the surface.

These components can be resolved to provide the maximum surface slope or the surface slope in any direction. The maximum surface slope in any direction (T) and its orientation (θ) are defined as:

An example of a typical profile of surface slope across a series of subcritical panels is illustrated in Fig. 1.19. The surface slope is based on the vertical displacement profile illustrated in Fig. 1.16 and has been derived using Eqn 1.3. This figure represents the component of surface slope along the monitoring line.

Fig. 1.19. Typical profile of surface slope across a series of subcritical panels.

The maximum surface slope (Tmax) and the minimum surface slope (Tmin) are the greatest (most positive) and least (most negative) values along the monitoring line, respectively. Positive values of surface slope represent increasing vertical displacement and negative values represent decreasing vertical displacement, when an absolute (positive) value of vertical displacement is adopted.

Surface slope can cause serviceability impacts on building structures, including door swings, drainage issues in gutters and wet areas. It