Constant Head BC Ditch & Fluctuating GWT

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MAri
Posts: 6
Joined: Tue Mar 24, 2020 8:07 pm
Location: Netherlands

Constant Head BC Ditch & Fluctuating GWT

Hello,

I am currently modelling a (woodland) peat fen in the Netherlands, I am however having some struggles determining the right constant head boundary conditions for the drainage ditches on either side of the modelled transect and the lower boundary condition. I hope someone can give me advice on this. I hope I don;t give too much information, but i tried to be as clear as possible.

The System:
I am modelling an transect in the peat area that is 210m wide and 5m in depth. With several different material types, overall a thin layer of sphagnum peat can be found at the top, followed by Carex peat (with difference gradations of humification). In the middle a layer of 'slurry' with very high conductivity is located. After the slurry layer a thin Carex peat layer is present before a sandy layer starts at around ~2.5-3m. On both sides of the transect a shallow ditch is located, on the left side this ditch is 0.4m in depth and on the right side 0.3m.

I do not have a lot of data on the pressure heads in the system, but what I have is:
- at depth is 4.35m in the model the hydraulic head is 1.1m --> so the pressure head is3.9m.
- at depth is 0.20m in the model the water table occurs --> so the pressure head should be 0m.
- Based on these two data points i created a linear graph giving a pressure head of 4.5m at the maximum depth of the model (5m).
- The surface level of both ditches is located at -0.13m --> pressure head should be 0m.

From these data I have created the following B.C.'s:
- At the bottom of the transect a 'constant head = 4.5 m'
- At the left ditch I have put a 'constant head = 0.27m' with 'equilibrium from lowest nodal point' from the bottom of the ditch up to -0.13m (after which a seepage face follows) to obtain pressure head = 0 at the water level in the ditch
- In the right ditch i have applied the same technique only now with 'constant head = 0.17' (as this ditch is 0.10m shallower).

This gives the following view at the ditch:
BoundaryCond.png (187.05 KiB) Viewed 665 times

I was however wondering if this approach is correct, as there is now a large pressure difference between the bottom of the ditch and the lower boundary, a difference of 3,67m.
While the difference between the hydraulic heads is much smaller. In the ditch the hydraulic head is -0.73 compared to NAP (NAP is a national determined zero level for height and water levels in the Netherlands) while at the bottom the hydraulic head is -1.1m compared to NAP --> giving a difference of 0.37m.

I have tried solving this large difference by applying a constant head boundary to the whole left and right sides of the system. By giving the left and right boundary a constant head of 4.87m with equilibrium from lowest nodal point. However then at the bottom left and right node there is a simultaneaous pressure head of 4.5m and 4.87m, which seems odd to me. This method also does not necessarily influence my results.

What I am mainly questioning is wheter my approach to the constant head boundary in the side ditches is correct? And if the large pressure head difference is problematic?

Greetings,
Mary
Last edited by MAri on Fri Apr 24, 2020 11:37 am, edited 1 time in total.

MAri
Posts: 6
Joined: Tue Mar 24, 2020 8:07 pm
Location: Netherlands

Dear all,

After perusing the forum I've found how to view not only the pressure head but also the total pressure head in the view. From this I was able to determine that my pressure head BC settings indeed create the 'correct' hydraulic head at the lower boundary (-1.1) and at the ditch (-0.73). As such I think the BCS should be ok.

Although currently the whole domain (expect from the ditches) has a H=-1.1, which is not necessarily correct since the area i am modelling is an area with downward seepage. So H=-1.1m occurs at the bottom of the domain, but at z=-0.60m the hydraulic head is -0.8m. Is there a way to take this into account?

However, currently I am struggeling with the modelled outcome. I would like to model changes in the water table due to rainfall. At the moment there is almost no change in water table with time, probably due to the constant head at the bottom. I read on the forum that for fluctuating groundwater table it is needed to use a 'no flux' or 'deep drainage' BC. However for both these BC's the model will not converge. Is there a different approach I perhaps could use for a fluctuating GWT?

Kind regards,
Mary

Jirka
Posts: 4922
Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA

Re: Constant Head BC Ditch & Fluctuating GWT

If you have a constant head BC at the bottom of the domain, you cannot expect that the water table will be moving, as GWT will simply reflect this BC. GWT can move up and down only when you allow the pressure head at the bottom BC to change in time, which can be accomplished by a no flow BC, by a deep drainage BC (with some reasonable coefficient for the governing function, or time variable head BC. You have to make sure that all BCs and initial conditions make physical sense, i.e., they are not in conflict with each other, otherwise HYDRUS will not converge. HYDRUS will not find a solution for a physically unrealistic conditions. Jirka

MAri
Posts: 6
Joined: Tue Mar 24, 2020 8:07 pm
Location: Netherlands

Re: Constant Head BC Ditch & Fluctuating GWT

Dear Jirka,

Thank you for your quick response and your time. I have decided to input a time variable head BC. However, throughout the modelling period the pattern of the 'Total Pressure Head' seems odd to me. (It makes sense as it is H=h+z and thus mathematically correct.)

However, as there is infiltration in this study area the Total Pressure Head should decrease with depth in the middle of the transect. Not just beside the two ditches. I have two piezometer measurements:
At 1.25m depth, H= -0.8m (so h=0.45m) and at 5.00m depth H=-1.1 (so h= 3.9)

Is there a way to approach such a condition in the model? Where the total head is not constant with depth throughout the domain?
Attachments
Total_Pressure_Head.png (981.33 KiB) Viewed 618 times

Jirka
Posts: 4922
Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA

Re: Constant Head BC Ditch & Fluctuating GWT

I have to admit that I have trouble understanding your description of the problem and thus can only answer generally. For the pressure head BCs on one boundary segment, you can only have either constant pressure head or constant total head (hydrostatic conditions). However, for initial conditions, you can have anything you want. You can assign either constant pressure head, constant total head, or a linear change in the pressure head to any part of the domain. J.

MAri
Posts: 6
Joined: Tue Mar 24, 2020 8:07 pm
Location: Netherlands

Re: Constant Head BC Ditch & Fluctuating GWT

In such a case I am very sorry for my unclear explanation! I do think however you answered my problem.

From what I understand I now created hydrostatic conditions due to the fact that I applied a constant pressure head to only the bottom boundary. I however do not have hydrostatic conditions in the field.

Is it then the case that for non-hydrostatic conditions, i.e. infiltration/downward seepage such as here, I would need to apply a different BC?
Would this be done by applying a constant head BC to both the bottom and the sides? Or could another method be used?

I sadly have not enough information to base a constant flux BC on (this seems like the BC needed to remove the hydrostatic conditions).

Again thank you for your quick response and time. I really appreciate it.

Jirka
Posts: 4922
Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA

Re: Constant Head BC Ditch & Fluctuating GWT

If you apply the head BC at the boundary, you will not necessarily have hydrostatic conditions during the simulations; you will likely have some inflow or outflow through that boundary in response to the other factors. The reason that the time-variable head BC automatically assume hydrostatic equilibrium is due to the fact that these BCs are usually used to represent external water bodies (water in a well, furrow, river), and then hydrostatic equilibrium is a necessity on such a boundary. J.

MAri
Posts: 6
Joined: Tue Mar 24, 2020 8:07 pm
Location: Netherlands

Re: Constant Head BC Ditch & Fluctuating GWT

Dear Jirka,

Thank you for your response. I was just wondering for some clarification, as i think i do not fully grasp it yet.

"you will not necessarily have hydrostatic conditions during the simulations;" - Does this mean that where the results show -1.1 for total head across for every time step this is not indicative of hydrostatic conditions occuring in the whole during the modelling?
Because currently the total head does not change in time across the domain, making it seem like there is no flow. This while the particles flowing do have a clear downward pattern (indicating infiltration). This contrast seems strange to me.

I am not using the time-variable head BC for an external water body, but rather a certain groundwater level at that boundary, is that problematic?

Additionally, if the(& constant head BC) automatically assume hydrostatic equilibrium is there a possibility to turn that off?

I am sorry for the continued questions. I am kind of struggling with this as it determines wether my model correctly represents the downwards infiltration in my transect.

Thank you again for your time and effort.

Kind Regards,
Mary

MAri
Posts: 6
Joined: Tue Mar 24, 2020 8:07 pm
Location: Netherlands

Re: Constant Head BC Ditch & Fluctuating GWT

Dear Jirka,

Sorry for yet another question on this subject. It seems however that after some weeks I am still no further in resolving my problems. I've several things I found on the forum (f.e. adapting time and spatial discretization, adapting hCritA, and more) but can't seem to get any further.

I have tried applying several different boundary conditions in the transect in order to obtain the hydraulic head pattern that should occur. As the area i am modelling has vertical downward flow i would expect the total head to reduce downward horizontally. I tried sketching this out in the following figure (the lines represent total head isolines) (the first attachement) :

Results
Using a constant head boundary conditon at the bottom of the transect I keep finding the same results as in "total_pressure_head.png". Which, although not completely hydrostatic also does not show the expected gradient of total head.

Using either a no flux or a constant flux boundary I find that the total head reduces in value across the vertical (see attachement 2). Although for a constant flux of -0.05m/d the values for total head do seem to fit with my data the pattern does not fit with my expectation. Additionally, I have large uncertainties wether this flux is correct but it is the only flux for wich the Hydraulic head assumes "correct" values.

I was wondering if there is an 'option', setting or button I missed that could be the cause for the vertical pattern? Or if there is a suitable approach to make sure the total head decreases horizontally?
Attachments
totalheadsketch.png (794.5 KiB) Viewed 255 times
Total_Head_CF-0.05.png (408.75 KiB) Viewed 255 times

Jirka
Posts: 4922
Joined: Sat Mar 16, 2002 3:47 pm
Location: USA
Location: Riverside, CA

Re: Constant Head BC Ditch & Fluctuating GWT

I have no more comments. To me, it seems that if you control pressure heads at the bottom of the transport domain and in the two ditches on the side, it should be pretty straightforward to control the pressure head gradients throughout the domain. I wonder if you somehow misinterpret how HYDRUS works. All initial and boundary conditions are entered in terms of the pressure heads (h) (not in total heads, H=h+z). In your posts, you always refer to total heads, which HYDRUS does not use, except as an alternative display of results. J.