On the Influence of the Soil and Groundwater to the Subsidence of Houses in Van Quan, Hanoi

VNU Journal of Science: Earth and Environmental Sciences, Vol. 36, No. 4 (2020) 42-51 
42 
Original Article 
On the Influence of the Soil and Groundwater to the 
Subsidence of Houses in Van Quan, Hanoi 
Dinh Xuan Vinh 
Hanoi University of Natural Resources and Environment, 41 Phu Dien, Tu Liem, Hanoi, Vietnam 
Received 11 January 2020 
Revised 14 April 2020; Accepted 22 August 2020 
Abstract: The area of Van Quan, Hanoi before 2004 was the rice field. Nearby, Ha Dinh water plant 
has well-drilled underground water for residential activities. Van Quan's new urban area after being 
formed has detected many subsidences. The objective of this study is to assess the main causes of 
the subsidence of the houses, based on groundwater and soil. This paper applied the regression 
method to study the effect of soil and groundwater on the residential constructions in Van Quan 
urban area, Hanoi. Subsidence monitoring was carried out for 4 consecutive years, from 2005 to 
2009, including over 500 subsidence monitoring points with high-precision Ni007 and INVAR 
gauges. A groundwater observation well is 30 meters deep at the site of the settlement. The results 
show a small effect of groundwater on subsidence. The characteristics of the young sediment area 
and the soil consolidation process are the main causes leading to serious subsidence in residential 
constructions in Van Quan urban area. This paper provides a different perspective on the impact of 
groundwater on the subsidence of residential structures within approximately 100 ha. 
Keywords: monitoring, subsidence, residential houses, groundwater, soil. 
1. Introduction 
The situation of land subsidence in the 
region due to various subjective and objective 
causes that many scientists as Tuong The Toan, 
Tu Van Tran, Ty Van Tran [1-3] agreed as 
follows: Characteristics of sedimentary basins 
during consolidation, denudation or accretion of 
topographic surfaces, groundwater extraction 
________ 
 Corresponding author. 
 E-mail address: dxvinh@hunre.edu.vn 
 https://doi.org/10.25073/2588-1094/vnuees.4539 
activities, and construction process. urban floor. 
In this paper, we want to explore the impact of 
groundwater on the upper floor and the 
consolidation process of soil on shallow 
foundation constructions, in particular, houses 
under 5 floors in Van Quan urban area, Hanoi. 
We have built a groundwater monitoring well 
with a depth of 30 meters in the survey area. 
Observation data of groundwater and subsidence 
D.X. Vinh / VNU Journal of Science: Earth and Environmental Sciences, Vol. 36, No. 4 (2020) 42-51 43 
of residential houses of Van Quan urban area 
were conducted regression analysis. Thereby we 
assess the influence of each cause to the 
settlement of the houses on the young 
sedimentary basin. 
Some studies use the method of Terzaghi as 
Ty Van Tran, Hiep Van Huynh [3], or the Finite 
Element method as Tu Van Tran et al [2], based 
on groundwater monitoring data to forecast 
ground subsidence. In this study, we use the 
groundwater monitoring data in the subsidence 
area (about 100 hectares) and the subsidence 
monitoring data of the houses according to 
national Class II leveling Regulation. 
Conducting the regression analysis for each 
cause of subsidence. The first is groundwater. 
The second is the during consolidation 
subsidence of the soil because Van Quan urban 
area is located on a young sedimentary basin [2]. 
2. Research Methods and Data 
The raw monitoring data including 
appropriate measurements is a very important 
part of the building safety data. Based on the 
monitoring data, one can recheck the design plan 
as well as the construction process and the 
operation of the building. The raw data provide 
valuable information that sheds light on the 
stability of the building. However, the raw data 
cannot reveal the shifting field or the 
deformation trend of the building. A 
comprehensive analysis is therefore needed to 
accurately and comprehensively identify various 
deformations from a large volume of raw data. 
Two types of dynamic models are formulated to 
analyze deformation monitoring test data, non-
parametric models based on mathematical-
statistical theory, and principles-based parametric 
models major of continuous mechanics. 
Non-parametric model based on 
mathematical - statistical prediction algorithms. 
The first model is based on a functional 
relationship between the independent variables 
(the environment variables) and the dependent 
variables (are the deformations). Models of this 
type can be interpreted as internal causes and 
results within the system. This format includes 
multiple regression (MR) model, stepwise 
regression (SR), principal component regression 
(PCR), partial least square regression (PLSR) 
and artificial neural network (ANN). The second 
model is based on the statistical rule of 
dependent variables ie using linear statistical 
models themselves, not by other environment 
variables. They do not establish a model between 
cause and effect. This type includes Time series 
(TS series), Gray system (GS). The deformation 
prediction model is based on information drawn 
from the deformation monitoring data series, 
these processes are performed in different ways. 
Parameter model based on the analysis of 
monitoring data by continuous mechanical rules. 
First, determine the relationship between the 
dependent variables and the independent 
variables built on mechanical rules. Next, linear 
statistics are applied to correct the assumed 
calculation values or parameters throughout the 
calculation. This model type has a Kalman filter 
[4]. 
Regression analysis is a statistical method 
where the expected value of one or more random 
variables is predicted based on the condition of 
other (calculated) random variables. Regression 
analysis is not just about curve match ... 
(𝑛 −𝑚 − 1)
< 𝑇
𝑛−𝑚−1,
𝛼
2
 (6) 
qβ̂jβ̂j
 is the jth element on the main diagonal of 
the matrix 𝑄�̂��̂�, where 𝑞�̂�𝑗�̂�𝑗 is the variance of 
the regression coefficient estimates (𝑆𝛽𝑗
2 ); Q is 
the residual sum of square. Look at the 
distribution table of T, get significance level of 
5%, dominance of deformation influence 
coefficient �̂�𝑗 is 95% respectively. If 𝑇 <
𝑇𝑛−𝑚−1,𝛼
2
, then the corresponding deformation-
cause factor 𝑥𝑗 has a very small effect on 
deformation, which can be removed from the 
regression equation. 
In the regression model, we must put the 
deformation-cause factors into the regression 
equation. In the process of testing their 
dominance, if any factors do not pass the test, 
they will be removed, and other factors must be 
included in the evaluation model. Assume a 
following multivariate linear regression equation 
�̂� = �̂�0 + �̂�1𝑥1 +⋯+ �̂�𝑚𝑥𝑚 
The residual sum of squares and the 
explained sum of squares is Qm + 1, Um + 1, now we 
have 
{
∆𝑄 = 𝑄𝑚 −𝑄𝑚+1
∆𝑈 = 𝑈𝑚 − 𝑈𝑚+1
∆𝑄 = ∆𝑈
Thus, the residual sum of squares increases 
by the reduction of the explained sum of squares 
after increasing the deformation-cause factor xm 
+ 1, through which the regression equation also 
reflects the contribution of the additional 
increase factor with the regression effect. The 
predominance test for the added deformation-
cause factor is as follows 
𝐻0: 𝐸(�̂�′𝑚+1) = 0 
𝐻𝐴: 𝐸(�̂�′𝑚+1) = �̂�′𝑚+1 ≠ 0 
Forming the F statistical distribution 
 𝐹 =
∆𝑄
𝑄𝑚+1
(𝑛 − 𝑚 − 2)⁄
=
∆𝑄
(𝑛 −𝑚 − 2)⁄
𝑄𝑚+1
~𝐹1,𝑛−𝑚−2 (7) 
Taking the significance level of 5%, when 
𝐹> 𝐹1, 𝑛 − 𝑚 − 2, 𝛼, the original hypothesis is 
accepted, that is, the increased deformation-
cause factor has a significant effect on the 
house's deformation, in contrast. it should not be 
added. In the regression equation, the influence 
factors of deformation often correlate with each 
other, that is, there is some relation to each other. 
The close correlation between the variables in 
the regression model created a multicollinearity 
phenomenon, making the variance of the 
regression coefficient estimates big valuable. 
The multicollinearity phenomenon also reverses 
the regression coefficient, instead of positive 
coefficients, that is, the high water level causes 
the deformation of the dam to be large, resulting 
in negative results, the high water level makes 
the dam less deformed. 
Based on the above test steps, it is possible 
to induce the following step regression: 
a) Prequalification of independent variables 
affecting the deformation 
b) Determine the first univariate linear 
regression equation. Assuming that m 
D.X. Vinh / VNU Journal of Science: Earth and Environmental Sciences, Vol. 36, No. 4 (2020) 42-51 48 
independent variables affect deformation, each 
of these independent variables creates a 
univariate linear regression equation, for a total 
of m equations. Calculate the residual sum of 
squares Q of each equation. If the regression 
equation with 𝑄𝑘 = 𝑚𝑖𝑛{𝑄𝑖}, 𝑖 = 1,𝑚̅̅ ̅̅ ̅̅ , then 
the regression equation with Qk is collected after 
testing its according to equations (6) and (7). 
c) Determine the best two-variable regression 
equation based on the univariate linear regression 
equation, in turn increasing the independent 
variables affect deformation, and have (m-1) two 
linear regression equations. Calculate (m-1) the 
residual sum of squares ΔQ, consider the 
difference ∆Qj = max{∆Qi}, i = 1,m̅̅ ̅̅ ̅. 
The jth incremental independent variable is 
the “waiting” independent variable, conducting 
its test, if adopted, it will be included in the 
equation. It is the best two-variable linear 
regression equation. If not, then stop at the 
univariate regression equation. 
d) If two independent variables affecting 
deformation are dominant for dependent variable 
Y (amount of deformation), then according to the 
above method, continue to select independent 
variables to affect the third and fourth 
deformation,... So on until it is impossible to 
increase the new independent variable and can 
not remove any independent variables selected, 
then stop. As a result, we have the best 
regression model. 
The independent variable affecting 
deformation is groundwater and time. The 
observation time characterizes the deformation 
of the test point over time, so its first-order 
differential is the subsidence rate, its second-
degree differential is the subsidence 
acceleration. Simultaneous time represents the 
level of consolidation of the soil under the 
construction. It can be said that: the consolidation 
subsidence time lasts correspondingly the soil 
belongs to young sediments. 
Develop a regression equation for 
groundwater variable γ and for time variable θ. 
We have a linear regression equation for 
groundwater 
�̂� = 𝛽0 + 𝛽1𝑥𝛾 
The linear regression equation for time 
�̂� = 𝛽0 + 𝛽2𝑥𝜃 + 𝛽3𝑥2𝜃 
Based on the observed data series we have 
the following regression equation 
- For the effect of groundwater on the 
subsidence of houses 
�̂� = 9876.1124 + 309.3856 𝑥𝛾 + 56.5974 
The correlation coefficient 𝑅2 = 0.0628 = 
6.28%, that is, the water table affects only 6.28% 
to the subsidence of the structure. The posterior 
error of regression is 56.5974 mm. The posterior 
error of the estimated coefficient 𝛽1 is 𝑆𝛽1 = 
158.29. The test value according to (6) for 𝛽1 is 
T = - 1.9545, corresponding to the significance 
level of 5.55%. The correlation coefficient is too 
low and the post-estimation error 𝑆𝛽1 is too high, 
so we remove the groundwater element from the 
regression model. 
- For the effect of soil consolidation time on 
the subsidence of the houses 
�̂� = 6694.9641-1.4108 𝑥𝜃+0.0024 𝑥2𝜃+ 6.7862 
The correlation coefficient 𝑅2 = 0.9809 = 
98.09%, ie the time of soil consolidation affects 
98% of the settlement of the building. The slope 
coefficient 𝛽2 indicates the settlement rate and 
𝛽3 indicates the settlement acceleration is 0.0024 
mm2 /week. The posterior error of the regression 
is 6.7862 mm. The posterior error of the 
estimated coefficient 𝛽2 is 𝑆𝛽2 = 0.0422, the 
coefficient 𝛽3 is 𝑆𝛽3 = 0.0002. The test value 
according to (6) for 𝛽2 is T = - 33,4372, 
corresponding to the significance level of 6.6.10-
74%, and 𝛽3 is T = 9.8588, corresponding to the 
significance level of 2.3.10-16%, the value This 
is very small by our standards (5%). 
4. Results and Discussion 
Based on the results of regression analysis of 
the causes of subsidence of residential houses, 
the groundwater level and the time of consolidation 
of the soil from 2005 to 2009, we can draw a 
regression line of subsidence according to the 
consolidation time of the soil background.
D.X. Vinh / VNU Journal of Science: Earth and Environmental Sciences, Vol. 36, No. 4 (2020) 42-51 49 
Figure 5. Soil consolidation plays a major role in subsidence of the Van Quan houses. 
Although some scientific studies suggest that 
the groundwater level strongly affects the 
background subsidence. But to consider specific 
residential constructions, when the soil 
background is loaded with the houses under 5 
floors with the foundation structure without 
reinforced concrete piles. This case has shown 
that the cohesive subsidence factor of the soil is 
the main cause of the subsidence of the houses. 
The underground water observation well in 
Van Quan urban area is made of Tien Phong 
plastic pipe with a diameter of 90 mm, a depth of 
30 m from the protective steel pipe mouth on the 
ground, the bottom of the tube is in direct contact 
with the soil and is not prevented way. Due to 
insufficient funds, we could not build a deeper 
groundwater monitoring well, or have a higher 
standard. This aquifer is at the top of the 
aquifers, not surface water or affected by surface 
water. Monitoring data of groundwater level 
directly at the well did not notice much change 
in the period 2005-2009. The fluctuations are 
mainly recorded during the rainy and dry 
seasons. Because of the relatively stable 
groundwater level in Van Quan, it cannot cause 
the subsidence of residential houses. 
For the young sedimentary areas, the 
consolidation element subsided over time, 
constructions from three floors should have 
reinforced concrete foundation piles, constructed 
by the method of pressing piles. The depth of 
reinforced concrete piles should exceed the fill 
and soft soil layers, for Van Quan area is about 
15 m depth, based on the geological survey 
drilling boreholes (Figure 6). 
In fact, after 2008, most of the residential 
houses in VanQuan's new urban area have to 
reinforce their foundations with piles, increasing 
construction costs, but ensuring stable and safe 
houses for a long time. This is also an experience 
for civil engineering designers in delta areas with 
weak soil.
6400
6450
6500
6550
6600
6650
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6750
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 (
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Actual Regression
D.X. Vinh / VNU Journal of Science: Earth and Environmental Sciences, Vol. 36, No. 4 (2020) 42-51 50 
Figure 6. Cylindrical of Borehole No. 3 at the Van Quan residential houses. 
Sheet number: 1/2
BOREHOLE No.3
Construction Residential houses Coordination: 
Position Van Quan - Ha Noi - Y:
Start day 25/01/2006 End day: 26/01/2006 The height of borehole,m:0,000
Groundwater level, m : The depth of borehole,m:53,90
Soil layer Samples SPT
Desc r ipt io n
`
From To 15 15 15 N
1
1
2
3
3,70 -3,70 3,70
4 U1 3,8 4,00
4,0 4,45 1 1 1 2
5
U2 5,80 6,00
6 6,00 6,45 1 1 2 3
7
U3 7,80 8,00
8 8,00 8,45 1 2 2 4
9
U4 9,80 10,00
10 10,00 10,45 1 1 2 3
11 2
U5 11,80 12,00
12 12,00 12,45 1 2 2 4
13
U6 13,80 14,00
14 14,00 14,45 1 1 2 3
15
U7 15,80 16,00
16 16,00 16,45 1 2 2 4
17
U8 17,80 18,00
18 18,00 -18,00 14,30 18,00 18,45 3 4 3 7
19
20 D2 20,00 20,45 5 7 7 14
21
22 D3 22,00 22,45 5 9 11 20
23
24 3 D4 24,00 24,45 7 11 12 23
25
26 D5 26,0 26,45 7 10 12 22
27
Note: - M : Original form
 - D : Disturbance form
Fine grained sand ash 
gray, gray, sometimes 
mixed with organic, 
medium compacted 
state
H
ei
gh
t, 
m
T
hi
ck
ne
ss
,m
N
um
be
r
Depth, m
Clay, clay mixed with 
dark gray color, mixed 
with plant organic 
matter, plasticity 
flowing
Land fi l l : Sand, clay 
mixed with 
construction waste
CYLINDRICAL BOREHOLE
D
ep
th
, m
L
ay
er
N
um
be
r
D
ep
th
, m
X
Number of 
hammers
2
3
4
3
4
3
4
7
14
20
23
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
0 20 40 60 80 100
Ex per i men t al ch a r t
Number, N
D
ep
th
, m
D.X. Vinh / VNU Journal of Science: Earth and Environmental Sciences, Vol. 36, No. 4 (2020) 42-51 51 
5. Conclusions 
Regression model is a traditional analytical 
method to evaluate the impact of independent 
causes on measured values. Groundwater level 
and soil consolidation process over time are 
factors to consider when designing a building. 
The study showed that the groundwater level in 
the upper floor fluctuated very small and 98% of 
subsidence of residential houses in VanQuan's 
new urban area was due to the weak soil. 
This study case is only for residential 
buildings from 3 to 5 floors with non-reinforced 
concrete foundation and only consider the top 
aquifer. For buildings under 3 floors are not 
covered by this study. Buildings above 5 floors 
often have foundations made of reinforced 
concrete piles up to a depth of 20 to 60 meters, 
so they may be affected by deeper aquifers. More 
comprehensive studies are needed on this issue 
to be clear about the impact of groundwater on 
the subsidence of buildings. 
Acknowledgments 
The author thanks the support for monitoring 
data of Van Quan of HUDCIC Consulting 
Investment and Construction Joint Stock 
Company. The author also thanks the comments 
of reviewers who helped improve the content of 
this article. 
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