Research on fine collection and interpretation methods of discontinuities on high-steep rock slopes based on UAV multi-angle nap-of-the-object photogrammetry

Abstract

The rapid and accurate acquisition of discontinuity parameters of rock masses is of paramount significance for the stability assessment of rock slopes. However, the complex and hazardous terrain of high-steep rock slopes poses challenges to conventional survey methods. Given this, this study proposes the unmanned aerial vehicle (UAV) multi-angle nap-of-the-object photogrammetry technology. This method can comprehensively consider the terrain development characteristics of high-steep rock slopes and the orientation characteristics of dominant discontinuity sets. With trained pilots, high-quality image acquisition with millimeter resolution can be achieved. This method effectively overcomes issues like texture distortion, shadow obstruction, and low resolution commonly found in conventional UAV 3D models. Subsequently, a novel non-contact method is presented for obtaining discontinuity parameters, including orientation, trace length, spacing, aperture, and roughness, based on the 3D real-scene model of the slope. The feasibility and reliability of this method are verified by collecting 1728 discontinuities along the 1300-m length of a rock slope at a construction site on a railway in southeastern Tibet. A comparison with manually measured results indicates average differences of 2° for dip and dip direction; 1.3 cm and 9 mm for trace length and aperture, respectively; and 1.89 for JRC. The study also reveals that the effective resolution of the 3D model is approximately 1 to 2 times the theoretical resolution of a UAV image, providing crucial guidance for obtaining high-quality images on high-steep rock slopes. The method proposed in this study holds significant practical value in the stability assessment and disaster prevention of rock slopes.

Full text

Vol.:(0123456789)
Bulletin of Engineering Geology and the Environment (2024) 83:142
https://doi.org/10.1007/s10064-024-03646-5
ORIGINAL PAPER
Research onfine collection andinterpretation methods
ofdiscontinuities onhigh‑steep rock slopes based onUAV multi‑angle
nap‑of‑the‑object photogrammetry
ShengyuanSong1· MingyuZhao1· WenZhang1· FengyanWang2· JianpingChen1· YongchaoLi1
Received: 18 July 2023 / Accepted: 18 March 2024
© The Author(s) 2024
Abstract
The rapid and accurate acquisition of discontinuity parameters of rock masses is of paramount significance for the stabil-
ity assessment of rock slopes. However, the complex and hazardous terrain of high-steep rock slopes poses challenges to
conventional survey methods. Given this, this study proposes the unmanned aerial vehicle (UAV) multi-angle nap-of-the-
object photogrammetry technology. This method can comprehensively consider the terrain development characteristics of
high-steep rock slopes and the orientation characteristics of dominant discontinuity sets. With trained pilots, high-quality
image acquisition with millimeter resolution can be achieved. This method effectively overcomes issues like texture distor-
tion, shadow obstruction, and low resolution commonly found in conventional UAV 3D models. Subsequently, a novel non-
contact method is presented for obtaining discontinuity parameters, including orientation, trace length, spacing, aperture,
and roughness, based on the 3D real-scene model of the slope. The feasibility and reliability of this method are verified by
collecting 1728 discontinuities along the 1300-m length of a rock slope at a construction site on a railway in southeastern
Tibet. A comparison with manually measured results indicates average differences of 2° for dip and dip direction; 1.3 cm
and 9 mm for trace length and aperture, respectively; and 1.89 for JRC. The study also reveals that the effective resolution
of the 3D model is approximately 1 to 2 times the theoretical resolution of a UAV image, providing crucial guidance for
obtaining high-quality images on high-steep rock slopes. The method proposed in this study holds significant practical value
in the stability assessment and disaster prevention of rock slopes.
Keywords High-steep rock slope· Discontinuity· Parameter interpretation· UAV oblique photogrammetry·
UAV multi-angle nap-of-the-object photogrammetry
Introduction
Various geological hazards pose a serious threat to people’s
lives, property safety, the economy, and the sustainable
development of a region (Fanos 2019; Gan etal. 2022). Par-
ticularly, in recent years, there has been a significant increase
in engineering projects in southwest China (Wang etal.
2020b; Bao and Li 2020; Shi etal. 2023). Given such chal-
lenging engineering conditions, there is a need for disaster
investigation methods that are better suited to the rugged
terrain of steep slopes (Zhan etal. 2019; Xing etal. 2021;
Li etal. 2022). Especially for large-scale, high-steep rock
slope engineering in complex terrains, there is a demand for
more efficient, accurate, and secure methods for acquiring
rock mass structure information (Eshiet and Sheng 2017;
Cui etal. 2022; Yan etal. 2022). This is crucial as these
discontinuities control the deformation and mechanical char-
acteristics of the rock mass (Azarafza etal. 2017; Bostanci
etal. 2018; Zhan etal. 2021).
The most widely used method in engineering practice for
investigating discontinuities is manual contact-based meth-
ods (Song and Lee 2001; Lyman 2003), such as the scan-
line method (Priest and Hudson 1981; Park and West 2002)
and window sampling method (Mauldon 1998; Eccles and
Redford 1999). The International Society of Rock Mechan-
ics has released a series of methods for manually obtaining
* Jianping Chen
chenjp@jlu.edu.cn
1 College ofConstruction Engineering, Jilin University,
Changchun130026, China
2 College ofGeo-Exploration Science andTechnology, Jilin
University, Changchun130026, China

Bulletin of Engineering Geology and the Environment (2024) 83:142 142 Page 2 of 21
geometric and mechanical parameters of discontinuities
(ISRM 1978). Unfortunately, these methods often have lim-
ited access to survey areas, low efficiency, and high work
intensity and are highly susceptible to the influence of ter-
rain. To mitigate the impact of complex terrain conditions
on the acquisition of discontinuity information, numerous
scholars have conducted studies using ground-based 3D laser
scanning (Fanos 2019; Chen etal. 2021a) and close-range
photogrammetry techniques (Bonilla-Sierra etal. 2015; Xu
etal. 2020; Song etal. 2022). Relying on the advantages of
non-contact and telemetry, this method has made certain
progress in obtaining and characterizing the discontinuity
information of small-scale rock slopes. For example, the
automatic recognition and parameter interpretation algo-
rithms of discontinuities based on 3D laser point clouds have
become more mature (Wichmann etal. 2019; Wang etal.
2023). However, this method makes it very difficult to select
scanning or photography sites when facing high-steep rock
slopes with steep terrain and complex slope shapes (Gigli
and Casagli 2011; Menegoni etal. 2019). Moreover, the
steep slope forces an increase in the elevation angle of the
camera, leading to increased image distortion, reducing data
accuracy (Westoby etal. 2012; Riquelme etal. 2014). There-
fore, a new method is urgently needed for the non-contact
acquisition and interpretation of discontinuity information
on high-steep rock slopes. In contrast, multi-rotor UAVs,
with robust attitude control and maneuverability, can capture
high-resolution digital images or point clouds of such slopes,
overcoming terrain restrictions. They serve as a powerful
tool for obtaining information on the rock mass structure in
complex terrains.
At present, the development of UAV photogrammetry
technology and real-scene 3D reconstruction technology
has made it more convenient to use 3D real-scene mod-
els for geological surveys (Zhou etal. 2021; Zhang etal.
2023). However, existing studies are not perfect in using
3D real-scene models of high-steep rock slopes to obtain
fine parameters of discontinuities (Salvini etal. 2020; Chen
etal. 2021b; Kong etal. 2021). In terms of image acquisi-
tion, multi-lens oblique photogrammetry effectively over-
comes the shortcomings of single-lens vertical photography
in obtaining lateral information of ground objects (Zhang
etal. 2020; Deng etal. 2021). However, in high mountain
and canyon areas, the huge terrain height difference results
in uneven ground resolution of the image. Although the
development of terrain-following flight technology has to
some extent improved this issue (Lee etal. 2022; Ren etal.
2022), the spatial orientation of the lens during the pho-
tography process has not changed with changes in terrain.
Consequently, problems such as texture distortion, shadow
occlusion, and low resolution of slope 3D models still exist.
The emergence of UAV fixed angle nap-of-the-object pho-
togrammetry technology has made it possible to obtain fine
parameters of ground objects (He 2019). Unfortunately, this
method cannot adapt to the constantly changing morphology
of high-steep rock slopes, and it does not consider the orien-
tation characteristics of dominant discontinuity sets. In terms
of using slope 3D real-scene models to identify discontinui-
ties, the main focus is on identifying planar outcrops, and the
recognition of linear outcrops remains a thorny issue (Kong
etal. 2021). In terms of obtaining discontinuity parameters,
the main focus is on obtaining orientation and trace length,
with limited attention given to other geometric parameters,
especially studies on obtaining fine parameters such as aper-
ture (Salvini etal. 2017; Bar etal. 2021; Chen etal. 2021b).
Although some scholars have proposed methods for obtain-
ing single parameters such as discontinuity spacing and
roughness, their integration and automation with methods
for obtaining other parameters are insufficient (Wichmann
etal. 2019; Salvini etal. 2020). Therefore, an integrated
method for identifying and interpreting key parameters of
rock mass discontinuities is still needed. Furthermore, in the
process of identifying and interpreting discontinuities using
3D real-scene models of high-steep rock slopes, the resolu-
tion of the 3D model plays a crucial role in determining
the discernible scale of these discontinuities. Unfortunately,
there is currently limited study on the relationship between
UAV photography methods, UAV image resolution, and 3D
model resolution. Clarifying this issue is of great signifi-
cance for guiding the use of UAVs to obtain slope images
and carry out fine recognition of discontinuities. In sum-
mary, despite the contributions of previous studies, there still
exist significant challenges in achieving high-quality UAV
image acquisition and fine interpretation of key parameters
of discontinuities for complex structured high-steep slopes.
This study focuses on a construction site in the southeast-
ern Tibetan Plateau, elucidating the quantitative relation-
ship between UAV image resolution and the resolution of
the rock slope’s 3D real-scene model. A high-quality UAV
image acquisition method is proposed, suitable for the chal-
lenging terrain of high-steep rock slopes, which is the UAV
multi-angle nap-of-the-object photogrammetry technique.
Based on this, interpretation methods for key parameters
such as discontinuity orientation, trace length, spacing,
roughness, and aperture are proposed. The reliability of
these methods is validated through comparison with on-site
manual measurements. This study provides crucial technical
support for the fine acquisition of discontinuity parameters
on high-steep rock slopes in challenging terrain conditions.
Study area
The study area is located in the southeastern region of
Tibet, within Chada village, Luolong County, Changdu
City (Fig.1). A railway under construction passes through

Bulletin of Engineering Geology and the Environment (2024) 83:142 Page 3 of 21 142
the study area, connecting Chengdu and Lhasa. The study
area has typical mountain-canyon geomorphology, with the
river valley forming a “U” shape. The slopes on both sides
are steep, with a relatively flat bottom in the river valley.
The elevations of the mountain tops on the left and right
slopes are 4700 m a.s.l. and 4500 m a.s.l., respectively, with
a vertical difference exceeding 500 m and an average slope
greater than 60°.
The Dongcuoqu River travels across the valley floor
with a flow direction of 30° NE and a water level altitude of
about 3696 m a.s.l., as shown in Fig.2. The exposed strata
in the research area mainly include the Cenozoic Paleogene
Zongbaiqun Formation (E2Z), the Mesozoic Cretaceous
Duoni Formation (K1d), and the Paleozoic Permian Laigu
Formation (C2P1l). The Zongbaiqun Formation is mainly
composed of sandstone and mudstone; the Duoni Formation
is mainly composed of slate, metamorphic sandstone, and
coal seams; and the Laigu Formation is mainly composed
of slate and metamorphic sandstone. In addition, locally vis-
ible intrusive rocks are cretaceous monzogranite (ηγK) and
Jurassic granodiorite (γδJ) in the study area (Lai etal. 2021)
(Fig.2). Quaternary avalanche accumulation, alluvium, and
moraine are widely spread across valley’s slope bodies and
accumulation fans. In addition, in terms of the geological
structure, there is a SE-NW trending reverse fault (Xinben
fault) developed in the southeastern part of the study area
(Fig.2). The width of the fault zone is about 10~25 m, and
no signs of its activity are found in the Quaternary strata.
To sum up, the study area is characterized by a high-steep
rock slope with large elevation differences and a large area
of exposed rock surfaces. Under the influence of complex
tectonics, weathering, freeze-thaw, and other factors, the
rock mass structure of the studied slopes is broken and can
easily lead to geological phenomena such as rockfall, land-
slides, and rock avalanches.
Potential geological disasters will pose a huge threat to
the construction and safe operation of railways in the study
area. Therefore, it is necessary to quickly obtain discontinu-
ity information and evaluate the stability of complex high-
steep rock slopes. Given the high-steep terrain environment,
conventional survey methods are difficult to carry out, and
there is an urgent need for a non-contact rock mass struc-
ture information collection method that can fully consider
the complex terrain conditions of high-steep rock slopes. In
this study, a slope area downstream of the right bank with
an elevation of 3650~4500 m and a general orientation of
about 70° is chosen as the study bank to test the feasibility of
the proposed multi-angle nap-of-the-object photogrammetry
technology for finely obtaining discontinuity information of
high-steep rock slopes. This method will be described in
detail in the following sections.
Methodology
UAV multi‑angle nap‑of‑the‑object
photogrammetry technology
The UAV multi-angle nap-of-the-object photogrammetry
technology mainly includes four key steps, as shown in
Fig.3 (Zhao etal. 2023).
Fig. 1 Location of the study area and general engineering geology along the Sichuan-Tibet railway. a The location of the Sichuan-Tibet Railway
in China. b The location of the study area and the main faults and earthquake distribution along the Railway

Bulletin of Engineering Geology and the Environment (2024) 83:142 142 Page 4 of 21
Step 1: site survey
During the site survey stage, investigators need to roughly
determine the scope to be photographed. At the same
time, according to the on-site terrain conditions, deter-
mine the site for the take-off and landing of the UAV.
In addition, it is also necessary to investigate the overall
strike of the slope and the number of dominant discon-
tinuity sets, etc. When designing oblique photography
routes, adjusting the direction of the route to be parallel
to the slope strike will be beneficial for saving electricity
and improving efficiency. In the design stage of multi-
angle nap-of-the-object photography routes, it is neces-
sary to adjust the direction and angle of photography
based on the orientation of the dominant discontinuity
sets.
Step 2: low‑resolution 3D terrain acquisition
This stage focuses on the acquisition of low-resolution
3D terrain using UAV oblique photography supported by
terrain-following flight technology. By quickly obtaining
UAV images of the study area and establishing a 3D real
scene model, basic data is provided for the next detailed
investigation of the terrain development characteristics and
discontinuity orientation characteristics of high-steep slopes.
Therefore, the resolution requirement for UAV images is
relatively low, typically in the range of a few centimeters
to a few tens of centimeters, which is sufficient to meet the
needs. The implementation steps are consistent with conven-
tional UAV aerial survey procedures. This involves defin-
ing the task area, planning flight routes, and configuring
flight parameters such as altitude, speed, and image overlap,
among other aspects. After conducting on-site image acqui-
sition operations, the reconstruction of the 3D terrain of the
study area can be initiated.
Step 3: multi‑angle route design
The multi-angle photography route design is based on
the low-resolution 3D real-scene terrain data obtained in
the second step and is implemented using DJI Terra soft-
ware. By carefully browsing the 3D real-scene model of
the study area, the undulating shape of the slope and the
position and shape of the raised block are investigated. At
the same time, the position of the anti-dip discontinuity
on the slope should also be determined. If the scale of the
slope is particularly large, the task area can be divided
according to characteristic lines such as ridge lines or val-
ley lines. For each task area, a multi-angle photography
Fig. 2 The geological and tec-
tonic setting of the study area

Bulletin of Engineering Geology and the Environment (2024) 83:142 Page 5 of 21 142
task is designed separately. Route design requires macro-
level consideration, encompassing both horizontal and
vertical aspects.
First, measure the width and height of the slope in the
task area. Along the strike of the slope, it is an S-shaped
design route from bottom to top (Fig.4a). The number of
routes to be designed in the horizontal direction (x) can be
calculated according to Eq. (1). To ensure that the UAV
images have sufficient overlap, its flight speed in the hori-
zontal and vertical directions (Vh, Vp) needs to be calculated
according to Eqs. (2) and (3).
(1)
x
=
fH −aDC
h
aDC
p
(1−p)+1(rounds toward positive infinity
)
where a is the sensor pixel dimension, f is the focal length of
the camera lens, h is the frontal overlap, p is the side overlap,
t is the time interval for the UAV to take pictures, H is the
slope height, Ch is the number of pixels on the long side of
the sensor, Cp is the number of pixels on the short side of the
sensor, and D means the photography distance.
In addition, for the complex blocks that are raised on the
slope and the positions of anti-dip discontinuities, it is also
necessary to design a wrap-around multi-angle photogra-
phy route centered on them. The specific photography angle
(2)
v
h=
aDC
h
(1−h)
tf
(3)
v
p=
aDC
p
(1−p)
tf
Fig. 3 UAV multi-angle nap-
of-the-object photogrammetry
workflow

Bulletin of Engineering Geology and the Environment (2024) 83:142 142 Page 6 of 21
design is illustrated in Fig.4b. When designing photography
angles, it is not only necessary to shoot vertically with the
discontinuity, but also from angles such as top, bottom, left,
and right to reduce the possibility of blind spots in photogra-
phy. Finally, there is the setting of the photography distance.
As shown in Eq. (4), the photography distance and the pixel
size of the sensor will directly affect the ground resolution of
the UAV image. Therefore, both parameters need to be taken
into account when designing the photography distance.
where f refers to the focal length of the lens, D means the
photography distance, a denotes the pixel size of the sensor,
and GSD defines the image’s ground sampling distance.
The two UAVs used in this study for multi-angle nap-of-
the-object images are 0.0026 mm and 0.0044 mm in a pixel
size of the sensor respectively (Table1), so to obtain mil-
limeter-scale UAV images, the photography distance should
be less than 36 m or 80 m. Thanks to the 3D model of the
slope obtained in the previous step, in the multi-angle route
design stage, the flight route and the position of the UAV
when shooting can be accurately determined.
Step 4: on‑site acquisition andimage quality
enhancement
Upload the multi-angle route task to the aircraft to perform
the shooting task. When the shape of the raised blocks or
other positions on the slope is highly complex and there is
(4)
f∕D=a∕GSD
significant difficulty or risk in automatic flight, manual pho-
tography supplementation on-site becomes necessary. The
operator controls the UAV to approach the location to be
photographed and manually adjusts the position and shooting
angle of the UAV using the real-time monitoring screen on the
ground remote control. Then, the real-time obstacle avoidance
function of the UAV is essential to determine the photography
distance. Assuming a preset photography distance of 50 m, set
the forward-looking obstacle avoidance distance of the aircraft
to 50 m on the remote control, and then, guide the UAV to
fly horizontally to the photography point. When the remote
control issues a distance alarm signal, indicating that the UAV
has reached the preset distance. During manual photography,
it is advisable to maintain a moderate flying speed, gener-
ally within 5 m/s. At this pace, capturing a photo every 1~2 s
can meet the overlapping requirements of the images. After
obtaining the image, it is necessary to optimize the image with
significant differences in color or brightness within the image
to further improve its recognizability. Use the UAV manager
developed by FeiMa or Photoshop software to establish an
optimization effect template and perform batch uniform light-
ing and color processing of images, avoiding local overexpo-
sure or underexposure within the image to achieve a unified
and coordinated color.
Identifying andinterpreting discontinuities ina3D
model ofhigh‑steep rock slope
This section details the basic principles of identifying
discontinuities on 3D models and the basic principles of
Fig. 4 UAV multi-angle nap-of-the-object photogrammetry frame-
work. a Nap-of-the-object photography considering the overall terrain
development characteristics of the slope. b Multi-angle nap-of-the-
object photography considering discontinuity orientation characteris-
tics and local complex terrain

Bulletin of Engineering Geology and the Environment (2024) 83:142 Page 7 of 21 142
measuring feature points on discontinuities. At the same
time, a series of algorithms based on discontinuity fea-
ture points to solve the orientation, trace length, spacing,
aperture, and JRC are proposed. In this study, the EPS 3D
Mapping System (http:// www. sunwa ysurv ey. com. cn/ page8?
produ ct_ id= 138, last access: October 2, 2023) is used as a
tool to obtain the discontinuity feature points. Meanwhile, to
realize the batching and automation of the above-mentioned
parameter calculation, the authors have developed the rock
discontinuity parameter calculation and analysis system
(RPA). The workflow for identifying discontinuities on a
3D model and solving for key parameters is shown in Fig.5.
Under natural conditions, the outcrop forms of rock mass
discontinuities are complicated and diverse and can be
roughly classified into four types (Zhao etal. 2024): planar
outcrop, stepped outcrop, linear outcrop, and mixed outcrop
(Fig.6). Different technical procedures should be used to get
the parameters for discontinuities of different outcrop types,
and the particular approaches are as follows.
Trace length interpretation
The essence of trace length measurement is to measure
the distance between two points in space. Generally, when
measuring the trace length on the slope 3D model, it is not
necessary to consider the sampling window, and all visible
discontinuities on the 3D model should be measured. There-
fore, the trace length is defined by the longest length of a
discontinuity in any direction. Assuming that the endpoint
coordinates of a trace line for a discontinuity are P1(x1, y1, z1)
and P2(x2, y2, z2), the trace length d can be expressed as
On a slope 3D model, the trace length can be interpreted
for different types of outcrops. The following is a description
of the feature point selection and measurement principles:
(1) For planar outcrops (Fig.6a), measure the two feature
points with the longest distance within the disconti-
nuity’s exposure range directly on the 3D model, and
calculate the trace length using Eq. (5).
(2) For mixed outcrops (Fig.6b), measure two endpoints
within the linear extension range and one endpoint far-
thest from the planar extension. Calculate three trace
lengths between these feature points, with the longest
one determining the trace length of the discontinuity.
(3) Calculate the trace length for stepped and linear out-
crops (Fig.6c, d) by selecting the two farthest end-
points on the 3D model and using Eq. (5).
(5)
d
=
√(
x
2
−x
1)
2
+
(
y
2
−y
1)
2
+
(
z
2
−z
1)
2
Table 1 UAV hardware parameters and image acquisition
UAV FeiMa D200 DJI Phantom 4 RTK DJI Matrice 300 RTK
Equipment photo
Sensor size (mm2) 23.5×15.6 13.2×8.8 35.9×24
Sensor pixels 6000×4000 5472×3648 8192×5460
Pixel dimension (mm) 0.0039 0.0026 0.0044
Focal length (mm) 25/35
93
5
Positioning Accuracy
(Vertical / Horizontal)
2cm+1ppm / 1cm+1ppm 1.5cm+1ppm / 1cm+1ppm 1.5cm+1ppm / 1cm+1ppm
Photography distance (m) 191 90 70
Frontal overlap 80% 85% 85%
Side overlap 60% 70% 70%
Sorties 334
Photos 4705 2075 2435
Time spent on photography (mins) 85 100 84
Theoretical GSD (cm) 3.0 2.6 0.9
Actual GSD (cm) 1.5~20 1.4~12 0.5~4.6

Bulletin of Engineering Geology and the Environment (2024) 83:142 142 Page 8 of 21
It should be noted that determining the longest trace line
directly from planar and mixed outcrops might be challeng-
ing at times. Therefore, additional potential trace line end-
points must be measured, and the maximum trace length
should be determined through comparison.
Orientation interpretation
The essence of dip and dip direction measurement is to meas-
ure the spatial orientation of a discontinuity. To solve the dis-
continuity dip and dip direction, the coordinates of three or
more feature points on the discontinuity are measured on the
slope 3D model, the plane of the discontinuity is fitted, and
the plane normal vector is calculated.
Assuming that n feature points are measured on a discon-
tinuity, the equation of the discontinuity can be expressed as
z = Ax + By + C, and its normal vector (positive in the upward
direction) is t = (−A, −B, 1). A, B, and C can be obtained
according to the least-squares method:
(6)
⎡
⎢
⎢
⎣
A
B
C
⎤
⎥
⎥
⎦
=
⎛
⎜
⎜
⎜
⎜
⎝
⎡
⎢
⎢
⎢
⎣
x1y11
x2y21
⋮⋮⋮
xnyn1
⎤
⎥
⎥
⎥
⎦
T⎡
⎢
⎢
⎢
⎣
x1y11
x2y21
⋮⋮⋮
xnyn1
⎤
⎥
⎥
⎥
⎦
⎞
⎟
⎟
⎟
⎟
⎠
−1
⎡
⎢
⎢
⎢
⎣
x1y11
x2y21
⋮⋮⋮
xnyn1
⎤
⎥
⎥
⎥
⎦
T⎡
⎢
⎢
⎢
⎣
z1
z2
⋮
zn
⎤
⎥
⎥
⎥
⎦
Then, from the normal vector, the dip direction β and dip
α can be obtained:
when A = 0
when A ≠ 0
Selection principles for feature points of discontinuities
in different outcrop types are as follows:
(1) For planar outcrops (Fig.6a), feature points should be
located at sites where the dip direction of the disconti-
nuity changes, often at the inflection points along the
edge of the discontinuity. The enclosed polygon area
formed by these feature points should be maximized.
When three feature points are used, the inner angle
(7)
⎧
⎪
⎪
⎨
⎪
⎪
⎩
𝛼=∣ arctan(B)∣
𝛽=
⎧
⎪
⎨
⎪
⎩
𝜋∕2, B<0
3𝜋∕2, B>
0
∀,B=0
(8)







𝛼=∣ arctan

A2+B2

∣
𝛽=




arctan (B∕A),A<0, B≤0
arctan (B∕A)+2𝜋,A<0, B>
0
arctan (B∕A)+𝜋,A>0
Fig. 5 Discontinuity identifica-
tion and parameter fine interpre-
tation workflow

Bulletin of Engineering Geology and the Environment (2024) 83:142 Page 9 of 21 142
of the enclosed triangle should range between 30 and
150°.
(2) For mixed outcrops (Fig.6b), if the planar outcrop sec-
tion has numerous change points in the dip direction, it
is considered the planar outcrop for feature point meas-
urement; otherwise, it is considered the stepped outcrop
for feature point measurement.
(3) The feature points for the stepped outcrop (Fig.6c) are
the sites where the dip direction changes (the inflec-
tion point of the ladder). When there are three feature
points, the inner angle of the enclosed triangle should
be no more than 150° and no less than 30°.
(4) For linear outcrops (Fig.6d), undulations are prevalent
on discontinuities, often of a minor scale. To accom-
modate linear outcrops, feature points at the “peaks”
and “troughs” of the undulations in the direction of the
undulations must be measured. Due to the small scale
of undulations, even slight errors in feature point meas-
urements can result in significant interpretation errors.
Accurately interpreting discontinuities that exhibit a
near-planar mirror state is often challenging.
Spacing interpretation
The distance in the normal direction between two adjacent
discontinuities within the same set is commonly defined as the
spacing (Riquelme etal. 2014; Farmakis etal. 2020). When
interpreting the spacing using high-resolution 3D real-scene
models of high-steep rock slopes, two scenarios can be con-
sidered: (1) For situations where it is visually apparent that
the discontinuities are parallel and exhibit relatively orderly
outcrops, the spacing can be directly measured on the 3D
model using the “two-point method” (Eq. (5)). (2) For the
majority of irregularly exposed discontinuities, the spacing
can be determined by solving for the distance between them
based on the interpreted 3D discontinuities. Treating the dis-
continuities as disks in space, with trace length representing
the diameter and the midpoint of the trace as the center, the
Fig. 6 a–d The outcrop types of
rock mass discontinuities and
the selection of feature points

Bulletin of Engineering Geology and the Environment (2024) 83:142 142 Page 10 of 21
spatial orientation of the disk is determined based on the dip
direction and dip angle. Multiple measurement lines are uni-
formly arranged along the average orientation direction of the
dominant discontinuity set. The distance between two adjacent
disks intersecting with a measurement line represents a spac-
ing value (Eq. (9)). The average of all these spacing values is
calculated as the final spacing for that set of discontinuities.
This method accounts for the true 3D state of the discontinui-
ties, yielding results that better reflect actual conditions.
where P0(x0, y0, z0) represents a point on the survey line,
n(a, b, c) is the directional vector of the dominant set of dis-
continuities, C(xc, yc, zc) is the center of the disk, r is the
radius, and t is the parameter in the equation of the straight
line.
The selection of discontinuity feature points is based
on the principle introduced in the “Orientation interpreta-
tion” section.
JRC interpretation
In existing methods for obtaining JRC, the morphology
information of discontinuities is mostly collected in a
contact (Stimpson 1982; Aydan etal. 1996) or non-con-
tact way (Kulatilake etal. 2006; Belem etal. 2007), and
then, the JRC values are solved based on corresponding
algorithms. However, most of these methods are easily
limited by the equipment and on-site terrain environ-
ment, making it difficult to conduct investigations on
high-steep rock slopes. Based on this, this study pro-
poses a non-contact method for obtaining the surface
morphology of discontinuities based on a 3D real-scene
model of high-steep rock slopes. Considering the wide-
spread applicability of Barton’s straight edge method
(Barton and Choubey 1977) in practical engineering,
this study adopts this method to calculate the JRC (Eq.
(10)).
where Ry denotes the greatest undulation of the discontinu-
ity, Ln is the length of the discontinuity sampling, and L0
denotes the length of the laboratory size of the discontinuity
(10 cm).
Considering the size effect, the JRC for discontinuities
with a length greater than 10 cm is calculated using Eq. (11)
(Bandis etal. 1981), where JRCn represents the joint rough-
ness coefficient with a sampling length Ln and JRC0 is the
joint roughness coefficient under laboratory size.
(9)
(
x
0
+at −x
c)2
+
(
y
0
+bt −y
c)2
+
(
z
0
+ct −z
c)2
=r
2
(10)
JRC
=
[
450 +50 lg
(
10Ln
L
0)]Ry
L
0
The specific method for obtaining the morphology of dis-
continuities is as follows:
(1) For planar outcrops (Fig.7a), a measuring reference
line is drawn along the dip direction of the discon-
tinuity, acting as a straight ruler reference. Survey
lines can be established in any required direction. The
fluctuation feature points of the discontinuity are then
measured along the reference line at predetermined
intervals. Generally, intervals equal to approximately
1% of the total measuring length suffice to provide
a comprehensive impression of roughness. Consider-
ing the scale effect of the JRC solution, it is believed
that more ideal results can be obtained with a sam-
pling length ranging between 0.1 and 1 m, as validated
through extensive practice.
(2) The inflection points of the linear outcrop (Fig.7b) can
be directly measured on its surface, and the fluctuation
contour of the surface is described. All inflection points
within the sample range should be measured to accurately
represent the true fluctuation shape of the discontinuity.
(3) For the stepped outcrop, one of the stepped surfaces
is chosen as the interpretation surface. The inflection
points of the surface’s fluctuation change are measured
using the same method as for the linear outcrop.
(4) The mixed outcrop is often treated as a linear outcrop
for measurement. When the length of the linear outcrop
section is short (less than 10 cm), it is considered a
planar outcrop for measurement.
Under ideal conditions, feature points measured
according to the above principles are all placed on the
plane of the fracture profile; however, the natural rock
mass profile is not an ideal plane. Therefore, the least-
squares method is applied to fit the fracture profile based
on the contour curve’s feature points, and all points were
projected onto the plane. The universal three-point algo-
rithm proposed by Wang etal. (2020a) is used to estab-
lish a new coordinate system for the feature points. In
this new coordinate system, the x-axis corresponds to
the direction between the two endpoints of the contour
line, while the y-axis is perpendicular to the x-axis and
passes through another point. Since all the points lie on
the same plane, their z-coordinate can be considered
as 0. Consequently, the 3D mathematical problem is
reduced to a 2D plane, which facilitates data processing
and graph creation. The following outlines the specific
procedure for coordinate system transformation:
(11)
JRC
n≈JRC0
[
Ln
L
0]−0.03JRC0

Bulletin of Engineering Geology and the Environment (2024) 83:142 Page 11 of 21 142
(1) Assuming three points P1(x1, y1, z1), P2(x2, y2, z2), and
P3(x3, y3, z3) are not coplanar, the coordinate system
P1 − X″Y″Z is obtained by translation (O → P1) and
counterclockwise rotation around the z-axis:
where 1/λ is the scaling.
When ΔX21 = 0
(12)





X��
i
Y��
i
Zi





=
1
𝜆






Xi−X1

⋅cos 𝜀Z+

Yi−Y1

⋅sin 𝜀Z
−Xi−X1⋅sin 𝜀Z+Yi−Y1⋅cos 𝜀Z
Zi−Z1





when ΔX21 ≠ 0
(2) Rotating the coordinate system P1 − X″Y″Z around Y″
axis clockwise to get coordinate system P1 − X′Y″Z″
(13)
𝜀
Z=
{
𝜋∕2, ΔY21 >0
3𝜋∕2, ΔY
21
<
0
(14)
𝜀
Z=





arctan

ΔY21∕ΔX21

,ΔX21 >0, ΔY21 >0
2𝜋+arctan

ΔY21∕ΔX21

,ΔX21 >0, ΔY21 <
0
𝜋+arctan

ΔY21∕ΔX21

,ΔX21 <0
(15)




X
�
i
Y��
i
Z��
i




=
1
𝜆





Xi−X1

⋅cos 𝜀Zcos 𝜀Y+

Yi−Y1

⋅sin 𝜀Zcos 𝜀Y+

Zi−Z1

⋅sin 𝜀Y
−

Xi−X1

⋅sin 𝜀Z+

Yi−Y1

⋅cos 𝜀Z
−

X
i
−X
1
⋅cos 𝜀
Z
sin 𝜀
Y
−

Y
i
−Y
1
⋅sin 𝜀
Z
sin 𝜀
Y
+

Z
i
−Z
1
⋅cos 𝜀
Y




where
(3) Rotating coordinate system P1 − X′Y″Z″ around X′ axis
counterclockwise to get coordinate system P1 − X′Y′Z′
(16)
𝜀
Y=





arctan

Z2−Z1
(X2−X1)⋅cos 𝜀Z+(Y2−Y1)⋅sin 𝜀Z

,ΔZ21 >0
2𝜋+arctan Z2−Z1
(X2−X1)⋅cos 𝜀Z+(Y2−Y1)⋅sin 𝜀Z,ΔZ21 <
0
(17)
⎛
⎜
⎜
⎝
X�
i
Y�
i
Z�
i
⎞
⎟
⎟
⎠
=1
𝜆
⎛
⎜
⎜
⎝
10 0
0 cos 𝜀Xsin 𝜀X
0−sin 𝜀Xcos 𝜀X
⎞
⎟
⎟
⎠
⎛
⎜
⎜
⎝
cos 𝜀Y0 sin 𝜀Y
0 10
−sin 𝜀Y0 cos 𝜀Y
⎞
⎟
⎟
⎠
⎛
⎜
⎜
⎝
cos 𝜀Zsin 𝜀Z0
−sin 𝜀Zcos 𝜀Z0
0 01
⎞
⎟
⎟
⎠
⎛
⎜
⎜
⎝
Xi−X1
Yi−Y1
Zi−Z1
⎞
⎟
⎟
⎠
Fig. 7 The principle diagram
for JRC interpretation. a Meas-
urement of the fluctuation fea-
ture points for planar outcrop. b
Measurement of the fluctuation
feature points for linear outcrop.
c The calculation principle of
the fluctuation parameter of the
fracture

Bulletin of Engineering Geology and the Environment (2024) 83:142 142 Page 12 of 21
when
Δ
Y
��
31
=
0
:
when
ΔY��
31 ≠0
:
where
ΔZ��
31 =P�
3P��
3
,
ΔY��
31 =P1P��
3
.
After the coordinate transformation, the feature points can be
used to draw the undulating curve of the discontinuity. Accord-
ing to the undulation curve, the maximum undulation parameter
and sampling length can be obtained (Fig.7c). Then, the JRC
can be solved based on the above results. This method is suited
for the JRC survey of rock discontinuity with any angle, direc-
tion, and sample length because it can quickly generate a large
number of discontinuity contours for batch computation.
Aperture interpretation
The essence of aperture measurement is to determine the
distance between two walls of discontinuity. However, the
(18)
𝜀
X=
{
𝜋∕2, ΔZ
��
31 >0
3𝜋∕2, ΔZ��
31
<
0
(19)
𝜀
X=
{
arctan
(
ΔZ��
31∕ΔY��
31
)
,ΔY��
31 and ΔZ��
31 have the same sign
2𝜋+arctan
(
ΔZ��
31
∕ΔY��
31)
,ΔY��
31
and ΔZ��
31
have the different
sign
aperture of the discontinuity is often uneven, and applying
the “two-point method” to calculate the aperture will be
influenced by the surveyor’s subjective factors. Therefore,
this study proposes an adaptive shape aperture algorithm to
automatically solve the maximum, minimum, and average of
the aperture to characterize the aperture of the discontinuity
comprehensively. In this algorithm, the opening of the dis-
continuity is regarded as an irregular polygon, and the aper-
ture is obtained by setting the measuring line perpendicular
to the central axis of the irregular polygon through the exten-
sion direction of the opening of the adaptive discontinuity.
Therefore, this method is applicable to linear outcrops, the
linear part of mixed outcrops, and stepped outcrops, but not
to planar outcrops. The specific process is as follows:
(1) All vertices of an irregular polygon are measured along
the fracture section on a slope 3D model (Fig.8a). To
ensure the real shape of a fracture, the edge inflection
points should be measured as much as possible.
(2) All feature points are used to fit the fracture section
(Eqs. (6)–(8)), and all points are projected to the plane.
Assuming that the coordinate of a feature point is
P(x0, y0, z0) and the vertical line of the crossing point P
to the fracture section is taken to obtain the projection
point Pt(xt0, yt0, zt0) of this point on the fracture section
where
The coordinate system is transformed by using the uni-
versal model of generating a new coordinate system. In the
new coordinate system, the direction of the link between the
two endpoints of the fracture is the x-axis, and the direction
perpendicular to the link between the two endpoints of the
fracture is the y-axis.
(3) All feature points in the new coordinate system are linked
sequentially to construct a closed irregular polygon. The
irregular polygon is split into two parts by using the frac-
ture’s starting and ending points as the limit. Each part is
represented as a piecewise function. Given the measure-
ment interval k, the line L1 is oriented vertically along the
x-axis. On average, intervals equal to approximately 1%
of the total measuring length are sufficient to give a good
overall impression of the aperture. The aperture of the
position is the length of the intersection of the line L1 with
the upper and lower parts of the polygon (Fig.8b). How-
(20)
⎧
⎪
⎨
⎪
⎩
xt0=x0−A×
u
yt0=y0−B×
u
zt0=z0+u
(21)
u
=
Ax
0
+By
0
−z
0
+C
A
2
+B
2
+1
Fig. 8 The principle diagram for aperture interpretation. a Measure-
ment of the fluctuation feature points for linear outcrop. b The con-
ventional vertical line method. c The adaptive direction method

Bulletin of Engineering Geology and the Environment (2024) 83:142 Page 13 of 21 142
ever, if the fracture profile fluctuates greatly, the method
will have a large error (a purple circle in Fig.8b). To solve
this issue, the adaptive direction method is used to re-lay
the survey line.
(4) Obtain the midpoints of each measuring line acquired
in step (3), and link the midpoints of all measuring lines
to obtain the central axial line of the fracture. Assuming
the total number of measuring lines set in step (3) is n,
the number of segments on the fracture’s central axis is
n + 1. Obtain the midpoint coordinates of each segment
of the central axis, and then, draw the measuring line L2
perpendicular to the central axis across the midpoint.
The final aperture of the position is the length of the
intersection of the line L2 with the upper and lower
sections of the polygon (Fig.8c).
Assume that the coordinates of the midpoint of the cen-
tral axis are M(xi, yi), (i = 1, 2, 3, ⋯, n + 1), the endpoint
coordinates of each segment of the central axis are J(xi, yi),
(i = 1, 2, 3, ⋯, n + 2), and the starting and ending coordinates of
the fracture are Ps(xs, ys) and Pe(xe, ye). The coordinates of the
intersection point of the measuring line L2 and the edge line
of the upper part of the fracture Pu(xui, yui) can be calculated
according to the following equation:
when J(yi + 1) − J(yi) = 0:
when J(xi + 1) − J(xi) = 0:
when J(xi + 1) − J(xi) ≠ 0 and J(yi + 1) − J(yi) ≠ 0:
where
k
=−
J
(
xi+1
)
−J
(
xi
)
J
(
y
i+1)
−J
(
y
i)
, Δx = xe − xs, Δy = ye − ys.
In the same way, the coordinates of the intersection point
of the measuring line L2 and the edge line of the lower part of
the fracture Pl(xli, yli) can be calculated. Then, the aperture di,
(i = 1, 2, 3, ⋯, n + 1) at the current position can be expressed as
Then, the maximum aperture dimax, minimum aperture
dimin, and average aperture diavg of the fracture can be cal-
culated. This study takes the average aperture as the final
result.
(22)
{
xui =M
(
xi
)
yui =
(
M
(
yi
)
−xs
)
Δy
Δx
+y
s
(23)
{
xui =
(
M
(
yi
)
−ys
)
Δx
Δy+x
s
yui =M
(
yi
)
(24)





xui =

kM

xi

−M

yi

−xs
Δy
Δx+ys

∕

k−Δy
Δx

yui =

M

yi

−kM

xi

−kys
Δx
Δy+kxs

∕

1−kΔx
Δy

(25)
di
=
√(
x
ui
−x
li)
2
+
(
y
ui
−y
li)
2
Engineering application forstudy area
Study area image acquisition andoptimization
Three types of UAVs are used in the study, namely, FeiMa
D200, DJI Phantom 4 RTK, and DJI Matrice 300 RTK.
All 3 UAVs are equipped with GPS and inertial navigation
systems, which can record 3D spatial coordinates and the
orientation of every shot of the camera. In addition, these
UAVs are equipped with an RTK measurement module, and
the highest positioning accuracy can reach the centimeter
level (Liu etal. 2019; Kersten etal. 2022). The specific UAV
hardware parameters, flight parameters, and obtained image
data are shown in Table1.
The undulating topography of the slope results in a slight
deviation between the actual photography distance of the UAV
and its intended value, leading to differences between the actual
GSD of the UAV images and their theoretical values (Table1).
Upon inspecting the images, it is evident that the overall resolu-
tion and visual quality are good, but there are localized issues
with lighting and color effects, which can hinder the identifi-
cation of small-scale structural features (Fig.9a). Therefore, it
is necessary to enhance the image quality to fully exploit the
potential of multi-angle close-range images. For batch process-
ing of multiple images, the UAV Manager software developed
by FeiMa Corporation can be used. For individual images,
manual adjustments can be made using Photoshop software.
After applying the enhancement techniques, the visibility and
discernibility of the images are significantly improved (Fig.9b),
which facilitates the identification and interpretation of finer
parameters such as aperture and JRC.
Study area’s 3D reconstruction andmodel accuracy
verification
The 3D real-scene models of the study area (Fig.10) are
established using the DJI Terra software (https:// enter prise.
dji. com/ cn/ dji- terra, last access: October 2, 2023). To check
whether the scale of the 3D model is correct and whether the
point coordinates are accurate, it needs to be verified with
the existing data.
Due to the steep terrain, it is difficult to obtain verifica-
tion points on-site by conventional measurement methods.
Therefore, in this study, 16 verification points are selected
on the 3D model of the right bank slope in the study area
(Fig.10d), and the accuracy of the 3D model is verified by
comparing it with the existing topographic map. Through
the coordinate verification, it can be seen that the coordi-
nate errors of the 3D model established in this study are
all less than 1 m in the x, y, and z directions. Therefore, the
scale of the 3D model established in this study is correct,
and the point coordinates are reliable.

Bulletin of Engineering Geology and the Environment (2024) 83:142 142 Page 14 of 21
Verifying accuracy of3D model–based discontinuity
parameter interpretation
As verification data, the orientation of 54 discontinuities,
the trace lengths and apertures of 25 fractures, and the JRC
of 20 discontinuities are measured manually in the field. The
verified discontinuities are identified on the 3D model using
the principles introduced in the “Identifying and interpreting
discontinuities in a 3D model of high-steep rock slope” sec-
tion, and their orientation, trace length, aperture, and JRC are
interpreted.
When the results of the two methods are compared
(Tables2, 3, and 4), it is clear that the largest difference
in dip direction is 9° and the average difference is 2°. The
largest dip difference is 5°, with an average difference of
2°. The maximum trace length difference is 2.6 cm, and
Fig. 9 Optimized comparison of UAV image effects. a Image before optimization. b The optimized image
Fig. 10 3D models of study
area. a A 3D model of right
bank based on UAV terrain-
following oblique photogram-
metry. b A 3D model of right
bank based on multi-angle
nap-of-the-object image. c A
3D model of left bank based on
multi-angle nap-of-the-object
image. d The location distri-
bution of 3D model accuracy
verification points

Bulletin of Engineering Geology and the Environment (2024) 83:142 Page 15 of 21 142
the average difference is 1.3 cm. The maximum aperture
difference is 1.7 cm, with an average difference of 0.9 cm.
The maximum JRC difference is 3.67, and the minimum
JRC difference is 0.04, with an average difference of 1.89.
This level of accuracy meets the engineering requirements.
Interpretation andanalysis ofdiscontinuities
forthestudy slope
A total of 1728 discontinuities are interpreted on the study
slope based on the methods described in the “Identifying and
interpreting discontinuities in a 3D model of high-steep rock
slope” section. The discontinuity sets of the right bank study
slope are grouped using the QPSO-optimized C-means algo-
rithm (Song etal. 2017), and set pole diagrams representing the
discontinuity orientations are generated for each set (Fig.11a).
The results (Table5) show that the discontinuities on the right
bank are divided into four sets, consistent with the field inves-
tigation findings. As depicted in Fig.11a, the dip directions of
the discontinuities are distributed mainly in the range of 140 to
260°, with a concentration of dips between 60 and 85°. The sec-
ond set exhibits a dip direction parallel to the slope and a nearly
vertical dip angle, indicating a potential for toppling deforma-
tion that poses a significant threat to slope stability.
Based on Table6, it is evident that the average trace length
of the third set of discontinuities is relatively larger at approxi-
mately 14.48 m. In contrast, the average trace lengths of the
remaining three sets are approximately 9 m, exhibiting simi-
lar values. Additionally, the chi-square test and K-S test are
conducted to examine the probability distribution of the trace
lengths. The results indicate that the trace lengths of the four
sets follow a lognormal distribution at a significance level of
0.05 (Fig.11b). The spacing of each discontinuity set is inter-
preted using the measurement method described in the “Spac-
ing interpretation” section. The first set has a spacing of 3.10
m, the second set has a spacing of 2.51 m, the third set has a
spacing of 0.64 m, and the fourth set has a spacing of 1.79 m.
Table 2 A comparison of the
orientation obtained by the two
methods
No. 3D model–based measurement Field survey Difference
Dip direction
(°)
Dip (°) Dip direction
(°)
Dip (°) △ Dip direction
(°)
△ Dip (°)
1 166 89 166 89 0 0
2 279 68 281 67 − 2 1
3 35 68 35 69 0 − 1
4 266 69 270 69 − 4 0
5 104 70 105 70 − 1 0
… … … … … … …
54 236 63 238 64 − 2 − 1
Table 3 A comparison of
the trace length and aperture
obtained by the two methods
No. Trace length Aperture
3D model–based
measurement (m)
Field survey (m) Difference (m) 3D model–based
measurement
(cm)
Field
survey
(cm)
Difference (cm)
1 6.62 6.64 − 0.02 1.9 0.8 1.1
2 8.42 8.43 − 0.01 0.7 1.7 − 1.0
3 28.32 28.33 − 0.01 2.2 2.2 0.0
4 12.26 12.27 − 0.01 0.6 0.4 0.2
5 4.56 4.58 − 0.02 0.7 1.5 − 0.8
… … … … … … …
25 12.46 12.46 0.00 0.6 0.3 0.3
Table 4 A comparison of the JRC obtained by the two methods
No. Type Sampling
length (cm)
JRC based
on 3D
model
JRC based on
field survey
Difference
1 Linear 31.00 11.63 11.47 0.16
2 Linear 37.88 8.49 6.36 2.13
3 Linear 31.99 9.13 7.50 1.63
4 Linear 76.08 0.20 3.46 − 3.26
5 Linear 34.38 3.76 6.88 − 3.12
… … … … … …
20 Planar 32.20 6.15 7.37 − 1.22

Bulletin of Engineering Geology and the Environment (2024) 83:142 142 Page 16 of 21
Discussion
Different photography methods’ 3D reconstruction
effect onhigh‑steep rock slopes
From Fig.12a, c, it can be observed that in the 3D model
established based on oblique photogrammetry, there are
issues such as texture distortion and shadow occlusion that
affect the recognition and interpretation of rock mass struc-
tures. However, in the 3D model established based on UAV
multi-angle close-range photogrammetry, these issues have
been effectively addressed (Fig.12b, d), and the model reso-
lution has been significantly improved (Fig.12e, f). This
indicates that the multi-angle nap-of-the-object photogram-
metry can adapt to the complex terrain of high-steep rock
slopes, providing a higher-quality reconstruction of the mor-
phology and texture of the high-steep slope rock mass.
In the high-altitude environment, the effective operational
time for a single sortie of the DJI Phantom 4RTK UAV is
approximately 20 min, whereas the DJI Matrice 300 RTK
UAV exceeds twice that duration. Additionally, the DJI Matrice
300 RTK UAV is equipped with a higher-resolution camera,
enhanced controllability, and superior safety features, making it
the preferred choice for executing UAV multi-angle nap-of-the-
object photogrammetry missions in the current scenario.
UAV image GSD andinterpretable discontinuity
scale
The resolution of the 3D model plays a crucial role in deter-
mining the scale of interpretable discontinuities. To explore
the relationship between the GSD of UAV images and the
interpretable scale of discontinuities, a comparative analy-
sis is conducted by acquiring images using two different
photography techniques for the same region (Fig.13). The
images are processed using a computer program, revealing
that the terrain-following oblique photogrammetry-based
images consisted of 667 × 592 pixels, while the multi-angle
nap-of-the-object images consisted of 1852 × 1698 pixels.
Evidently, the latter exhibited a higher pixel density per unit
area, indicating its superior performance. The GSD of the
UAV images is further verified using a length calculation
method.
The GSD is determined by dividing the field length
(L) of the aerial image by the number of pixels (C) in that
direction:
Table7 shows that the GSD of the compared area images
obtained through terrain-following oblique photogramme-
try and multi-angle nap-of-the-object image acquisition
technology is 1.5 cm and 0.5 cm, respectively. By referring
to Fig.13, it can be observed that the minimum scale of
interpretable discontinuities for the UAV terrain-following
oblique photogrammetry image is approximately 2.9 cm,
which is approximately twice the GSD of the image. Con-
versely, the minimum interpretable scale for the image
acquired through multi-angle nap-of-the-object image acqui-
sition technology is approximately 7 mm, about 1.4 times
the GSD. This indicates that the effective pixel spacing of
the 3D model is approximately 1–2 times the GSD of the
(26)
GSD =L∕C
Fig. 11 Schmidt upper hemisphere equal-area projection of the orientation data (a) and the lognormal distribution probability density function
curve of trace length (b)

Bulletin of Engineering Geology and the Environment (2024) 83:142 Page 17 of 21 142
UAV image, and the precision falls within an acceptable
range. Moreover, enhancing sensor performance and reduc-
ing the shooting distance can further improve the GSD of the
captured images, consequently reducing the scale of inter-
pretable discontinuities.
Applicability andlimitations ofthis method
The UAV multi-angle nap-of-the-object photogrammetry
technology, along with the proposed method for fine identi-
fication and interpretation of discontinuity parameters based
on a 3D model, aims to offer a more effective and accurate
approach for investigating complex rock mass engineering
involving high-steep rock slopes. This method proves appli-
cable not only to high-steep rock slopes terrain but also to
conventional rock mass engineering, including small and
medium-sized rock and soil mass slopes. Moreover, certain
considerations must be taken into account when interpreting
the discontinuity parameters in practical operations:
(1) Orientation interpretation:
The selection of feature points follows the principles
outlined in the “Orientation interpretation” section. It is
noted that when using the “three-point method,” the inner
angle of the triangle formed by feature points should be nei-
ther greater than 150° nor less than 30°. This is because,
in surveying, angles smaller than 30° or larger than 150°
result in increased mean error during point computation.
The mean error is minimized when the intersection angle
ranges from 90 to 120°. However, determining the interior
angle of the triangle during the interpretation process can
be challenging. Therefore, it is generally recommended to
select as many inflection points as possible on the edge of
the discontinuity as feature points. The least-squares method
is used for plane fitting to determine the average orientation
of the discontinuity.
(2) JRC and aperture interpretation:
The interpretation of discontinuity JRC requires careful
consideration of maximum fluctuation, which is typically
at the centimeter or millimeter scale. Based on the discus-
sion in the “UAV image GSD and interpretable disconti-
nuity scale” section, the minimum scale of interpretable
discontinuity parameters on 3D models is approximately
1–2 times the GSD of UAV images. In other words, when
the GSD of the UAV image is 1 cm and the fluctuation
or aperture of the discontinuity exceeds 1–2 cm, the JRC
and aperture interpretation results are more accurate.
According to the findings of this study, the optimal GSD
of the images captured by the DJI Matrice 300 UAV for
the left bank is approximately 5 mm (Table1), indicating
Table 5 Interpretation results of discontinuity parameters
No. Endpoint coordinates of the trace line Trace length (m) Dip direc-
tion (°)
Dip (°) Aperture (cm) JRC
x1 (m) y1 (m) z1 (m) x2 (m) y2 (m) z2 (m)
1 2,648,922.385 2,129,073.535 3995.256 2,648,930.871 2,129,080.758 3996.23 11.19 124 31 0.9 6
2 2,648,942.57 2,129,083.597 3960.366 2,648,935.21 2,129,082.575 3985.493 26.20 358 74 1.1 8
3 2,648,945.587 2,129,091.728 3964.854 2,648,934.197 2,129,117.476 3993.421 40.11 345 80 0.7 17
4 2,648,926.48 2,129,062.821 3977.544 2,648,921.93 2,129,074.779 3996.076 22.52 339 83 2.4 13
5 2,648,950.536 2,128,964.32 3922.724 2,648,949.154 2,128,967.812 3937.553 15.30 351 90 1.1 9
6 2,648,971.495 2,128,896.754 3846.827 2,648,967.262 2,128,953.909 3886.497 69.70 303 53 2.6 17
7 2,648,963.09 2,128,986.005 3909.72 2,648,991.649 2,128,946.443 3859.283 70.18 200 75 1.4 19
8 2,648,688.874 2,129,461.529 3099.528 2,648,755.436 2,129,425.694 3082.764 77.43 215 74 0.8 14
9 2,648,717.294 2,129,456.154 3089.696 2,648,718.477 2,129,434.079 3150.015 64.24 341 88 3.7 15
10 2,648,959.997 2,129,140.006 3970.069 2,648,966.593 2,129,161.176 3983.323 25.83 150 62 1.3 9
··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ··· ···
1728 2,648,948.109 2,129,148.058 3991.022 2,648,952.745 2,129,087.947 3954.124 70.68 192 47 1.7 16

Bulletin of Engineering Geology and the Environment (2024) 83:142 142 Page 18 of 21
a minimum interpretable aperture of about 0.5–1 cm. Fur-
ther reduction in the photography distance would increase
the GSD and enhance the interpretation accuracy of the
aperture and JRC.
Conclusion
This study explores high-quality image acquisition tech-
niques for high-steep rock slopes in complex terrain envi-
ronments and proposes a method for interpreting key param-
eters of discontinuities based on the 3D real-scene model of
high-steep rock slopes. Through the practical application at
a railway construction site in Southeast Tibet, the reliability
and accuracy of the method were validated, leading to the
following conclusions:
(1) The UAV multi-angle nap-of-the-object photogram-
metry technique is developed to support the establish-
ment of high-quality 3D real-scene models of high-
steep rock slopes. During the photography process, the
terrain development characteristics of high-steep rock
slopes and the orientation characteristics of dominant
discontinuity sets are comprehensively considered.
This significantly reduced blind spots in photography,
lessened texture distortion in 3D models, and effec-
tively improved the resolution of the 3D model and the
interpretability of discontinuities. This provides strong
support for the fine identification and interpretation of
rock mass structures on high-steep rock slopes.
(2) A non-contact interpretation method based on the 3D
real-scene model of high-steep rock slopes is pro-
posed for orientation, trace length, spacing, aperture,
Table 6 Grouping results of
discontinuities on the right bank
of the study area
Set Number of dis-
continuities
Average dip
direction (°)
Average
dip (°)
Trace line
Min (m) Max (m) Mean (m) Distribution
1 346 76 81 0.66 209.09 9.80 Lognormal
2 443 325 88 0.51 355.39 14.48 Lognormal
3 310 20 78 0.65 93.50 9.56 Lognormal
4 629 225 45 0.65 161.15 9.63 Lognormal
Fig. 12 Quality comparison of 3D models based on terrain-following
oblique photogrammetry (a, c, e) and multi-angle nap-of-the-object
image acquisition technology (b, d, f). a There are shadow areas. b
The brightness is normal. c The texture is distorted. d The texture is
clear. e Low resolution and blurry. f High resolution clearer

Bulletin of Engineering Geology and the Environment (2024) 83:142 Page 19 of 21 142
and roughness of discontinuities. An RPA software is
developed to automate the batch calculation of these
parameters. Comparisons with on-site manual measure-
ments show differences of 2° for both dip direction and
dip; differences of 1.3 cm and 9 mm for trace length
and aperture, respectively; and differences of 1.89
for JRC. This confirms the reliability of the proposed
method for interpreting discontinuity parameters.
(3) The study indicates that the effective resolution of
the 3D real-scene model of high-steep rock slopes is
approximately 1 to 2 times the theoretical resolution of
a UAV image. This finding is of significant guidance
for acquiring a high-resolution UAV image of high-
steep rock slopes. It holds important engineering appli-
cation value for acquiring discontinuity parameters and
analyzing the stability of rock masses on high-steep
rock slopes.
Acknowledgements This work was financially supported by the
National Nature Science Foundation of China (grant number:
42177139, 41941017, 42077242), the Natural Science Foundation
Project of Jilin Province (grant number: 20230101088JC), and the Sci-
entific Research Project of the Education Department of Jilin Province
(grant number: JJKH20231182KJ).
Author contribution Shengyuan Song: writing (original draft), visuali-
zation, funding acquisition, and supervision. Mingyu Zhao: software,
visualization, investigation, and writing (review and editing). Wen
Zhang: conceptualization, methodology, and supervision. Fengyan
Wang: project administration, investigation, and data curation. Chen
Cao: software, validation, and writing (review and editing). Jianping
Chen: formal analysis and writing (review and editing). Yongchao Li:
investigation and data curation.
Data availability Most of the data generated during this study are
included in this article, and other datasets generated during the cur-
rent study are available from the corresponding author on reasonable
request.
Declarations
Competing interests The authors declare no competing interests.
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